Introduction

Distributed Acoustic Sensing (DAS) is an emerging fiber-optic technology that offers significant advantages, including high spatial resolution, real-time data acquisition, and immunity to electromagnetic interference. By leveraging Rayleigh backscattering along standard optical fibers, DAS systems enable long-range, distributed detection of acoustic disturbances1,2. This unique capability makes DAS invaluable across diverse fields such as subsurface infrastructure monitoring3,4,5, seismic early warning6,7,8,9,10,11, and pipeline integrity assessment12,13,14. Across these domains, the ability to detect faint acoustic signals with high sensitivity is often critical. However, the sensitivity of conventional DAS configurations is often insufficient for the reliable detection of weak acoustic signals, particularly in complex underground environments or conditions of low acoustic pressure15,16. Consequently, enhancing the sensitivity of DAS sensors is a critical research priority to unlock the technology’s full potential and improve performance in both established and new applications.

In recent years, considerable efforts have been devoted to enhancing the sensitivity of DAS systems, primarily through advancements in fiber material selection, sensor configuration, and signal processing methodologies17,18,19. Notably, studies have explored the use of low-loss fibers, cladding-softened fibers, and fibers embedded with elastic enhancement layers to improve strain responsiveness and signal fidelity20,21,22,23,24,25,26,27. However, the improvement in DAS signal sensitivity achieved through these approaches still lacks systematic quantitative characterization. Beyond material optimization, structural design has emerged as a key factor influencing DAS performance. Helically wound cable configurations have been shown to improve spatial resolution28,29, while the integration of specialized geometric structures with optical fibers has demonstrated improved sensing capabilities in complex environments30,31. Among these structural innovations, the thin-walled cylindrical form has attracted increasing attention due to its favorable mechanical characteristics and potential for sensitivity enhancement32. Existing studies indicate that parameters such as elastic modulus, wall thickness, and diameter directly affect DAS response33,34. However, the quantitative relationship between these physical parameters and DAS testing sensitivity has not yet been systematically studied, and previous work has not evaluated their combined effects on thin-walled cylindrical DAS sensors in a controlled, comparative framework. Moreover, the fundamental mechanisms by which such structures enhance sensitivity have yet to be fully elucidated.

To address this knowledge gap, this study develops and evaluates a thin-walled cylindrical DAS sensor, in which an optical fiber is helically wound around the cylinder’s outer surface to enhance sensitivity. We conducted a series of controlled experiments in combination with theoretical analysis to systematically analyze the influence of the cylinder’s elastic modulus, wall thickness, and diameter on DAS testing sensitivity, revealing the underlying physical mechanisms driving the performance improvements. This work provides valuable guidance for the optimized structural design of DAS sensors and supports their broader implementation in practical engineering applications.

The remainder of the paper is organized as follows. Section "Methodology" develops the theoretical model and methods; Section "Experimental design" details the experimental design; Section "Results" presents the results; Section "Discussion" discusses mechanisms and implications; and Section "Conclusions" concludes.

Methodology

Principle of DAS

DAS technology is an optical fiber sensing technique that enables continuous, distributed acoustic monitoring along the entire length of the fiber. As shown in Fig. 1, the DAS technology used in this experiment is based on the principle of Phase-Sensitive Optical Time Domain Reflectometry (Φ-OTDR)3.

Fig. 1
figure 1

The operating principle of the DAS system based on Φ-OTDR.

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The DAS system emits ultra-narrow coherent laser pulses (pulse width: 40 ns), generating Rayleigh backscatter (RBS) light when encountering nanoscale impurities in the fiber. When external vibrations or acoustic waves affect the fiber, they cause localized disturbances, leading to phase difference changes in the RBS signals at both ends of the disturbed section35. The performance of the Φ-OTDR system strongly depends on the laser coherence length: to ensure proper interference of the backscattered light, the coherence length must exceed the pulse length of the emitted laser. In this study, the laser coherence length is sufficiently long to maintain high-quality DAS testing sensitivity.

The single-pass optical phase of the fiber over the gauge length is:

$$\varphi = \frac{2\pi }{\lambda }n \cdot S$$
(1)

where λ denotes the wavelength of the light (λ =1550nm), n represents the effective refractive index of the optical fiber (n = 1.468), and S denotes the optical path length.

The Φ-OTDR measures the backscattered phase. Since light undergoes two-way propagation along the measurement section, the backscattered phase increment for a small strain ε over the gauge length G can be expressed as:

$$\Delta \varphi = \frac{4\pi n \cdot G}{\lambda } \cdot \left( {1 - p_{e} } \right) \cdot \varepsilon$$
(2)

where pe denotes the effective photoelastic constant of the optical fiber (pe =0.22), G represents the gauge length, and ε denotes the strain of the optical fiber.

Under the thin-wall approximation and the assumption of linear elasticity, the local strain induced in the thin-walled cylinder by an external acoustic pressure P can be approximated as:

$$\varepsilon = \mu \cdot P$$
(3)

where μ denotes the strain coefficient, which depends on the cylinder’s geometry and material properties (see Section "Analytical model and derivation of DAS testing sensitivity" for a detailed derivation). Combining this with the phase expression yields the approximate linear phase–pressure relation:

$$\Delta \varphi = Q \cdot P$$
(4)
$$Q = \frac{4\pi nG}{\lambda } \cdot \left( {1 - p_{e} } \right) \cdot \mu$$
(5)

Therefore, under typical conditions, the magnitude of the phase difference variation is approximately linearly related to the strain induced by acoustic pressure, allowing DAS to detect vibrations by measuring the phase of the RBS light along the fiber. However, this relationship can be influenced by factors such as fiber path length, phase unwrapping errors, and the spatial resolution of the system36.

Principle of acoustic sensitization of thin-walled cylinders

The structural advantages of the thin-walled cylinder

In DAS systems, the mechanical response characteristics of the sensing structure are crucial to its sensitivity. Compared to traditional sensitivity enhancement methods, using a thin-walled cylinder with the fiber helically wound around its surface can significantly improve strain transfer efficiency within the “acoustic pressure-structure-fiber” system. Combined with the thick-walled cylinder theory37, as shown in Fig. 2, under the same acoustic pressure, the thin-walled cylindrical structure (KThin = 0.00897 Pa⁻1) achieves approximately 6.1 times greater strain amplification than the thick-walled cylindrical structure (KThick = 0.00147 Pa⁻1)38,39.

Fig. 2
figure 2

Comparison of strain response between thin-walled and thick-walled cylinders under identical acoustic pressure.

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Analytical model and derivation of DAS testing sensitivity

Radial deformation of the thin-walled cylinder under external acoustic pressure is the key physical process for sensitivity enhancement. When acoustic pressure is applied to the surface of the thin-walled cylinder, the cylinder wall undergoes radial stretching or contraction due to its mechanical properties. This deformation induces axial strain in the fiber wound helically around the surface of the thin-walled cylinder40.

The physical model of the thin-walled cylinder under external acoustic pressure is shown in Fig. 3, where R and H represent the radius and wall thickness of the thin-walled cylinder, respectively.

Fig. 3
figure 3

Mechanical model of a thin-walled cylinder under external acoustic pressure (p), indicating the cylinder radius (R) and wall thickness (H).

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Assuming the thin-walled cylinder is homogeneous, continuous, and isotropic in both mechanical and optical properties, with small strains induced by acoustic pressure such that higher-order nonlinear terms can be neglected, and the optical fiber perfectly bonded to the cylinder surface for full strain transmission, its stress-strain relationship can be expressed using Hooke’s Law41:

$$\left\{ \begin{gathered} \sigma_{x} = 0 \hfill \\ \sigma_{y} = P \cdot \frac{{R^{2} + \left( {R - H} \right)^{2} }}{{R^{2} - \left( {R - H} \right)^{2} }} \hfill \\ \sigma_{z} = P \hfill \\ \end{gathered} \right.$$
(6)

The constitutive equation for the stress-strain relationship is given by:

$$\left\{ \begin{gathered} \varepsilon_{y} = \frac{1}{E}\left( {\sigma_{y} - \nu \sigma_{z} } \right) \hfill \\ \varepsilon_{z} = \frac{1}{E}\left( {\sigma_{z} - \nu \sigma_{y} } \right) \hfill \\ \end{gathered} \right.$$
(7)

where p represents the incident acoustic pressure, E and ν denote the elastic modulus and Poisson’s ratio of the thin-walled cylinder, and \({\varepsilon }_{y}\) and \({\varepsilon }_{z}\) represent the circumferential and radial strains, respectively.

As shown in Fig. 4, where α represents the winding angle of the fiber, the axial strain in the fiber wound around the surface of the thin-walled cylinder is:

$$\varepsilon_{fiber} = \varepsilon_{y} \cdot \cos^{2} \alpha$$
(8)
Fig. 4
figure 4

Optical fiber helical winding geometric model. (a) Helical winding trajectory of a single optical fiber. (b) Development of the helical winding plane.

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When the winding angle is 0 degrees, the axial strain in the fiber is equivalent to the circumferential strain of the thin-walled cylinder:

$$\varepsilon_{fiber} = \varepsilon_{y}$$
(9)

The total phase change Δφ induced in the thin-walled cylinder under acoustic pressure arises from the superposition of the mechanical strain effect ∆φ1 and the photoelastic effect ∆φ2.

The circumferential strain of the thin-walled cylinder induces a phase change ∆φ1 in the fiber corresponding to the mechanical strain effect:

$$\Delta \varphi_{1} = \frac{{2\pi nL\varepsilon_{y} }}{\lambda }$$
(10)

The phase change ∆φ2 in the fiber due to the variation in the refractive index of the fiber core, corresponding to the photoelastic effect:

$$\Delta \varphi_{2} = - \frac{{\pi Ln^{3} \varepsilon_{y} }}{\lambda }\left[ {\left( {1 - \nu_{f} } \right)p_{12} - \nu_{f} p_{11} } \right]$$
(11)

where L denotes the fiber length, λ is the wavelength of the light (λ =1550nm), n is the effective refractive index of the core (n = 1.468), \({\nu }_{f}\) is the Poisson’s ratio of the core (\({\nu }_{f}\) = 0.17), and the photoelastic coefficients are P₁₁ = 0.121 and P₁₂ = 0.270.

In summary, the total phase change \(\Delta \varphi\) in the fiber due to the acoustic pressure applied to the thin-walled cylinder is:

$$\Delta \varphi = \frac{{2\pi nL\varepsilon_{y} }}{\lambda } - \frac{{\pi Ln^{3} \varepsilon_{y} }}{\lambda }\left[ {\left( {1 - \nu_{f} } \right)p_{12} - \nu_{f} p_{11} } \right]$$
(12)

The DAS testing sensitivity Mp based on Φ-OTDR technology is defined as the ratio of phase change to acoustic pressure42,43:

$$M_{p} = \frac{\Delta \varphi }{P}$$
(13)

where the unit of DAS testing sensitivity Mp is rad/Pa.

In engineering applications, it is commonly represented by the sensitivity level M, defined as the logarithmic ratio of fiber acoustic pressure sensitivity to the reference value Mr:

$$M = 20\log \left( {\frac{{M_{p} }}{{M_{r} }}} \right)$$
(14)

where the acoustic pressure sensitivity level M is expressed in dB, with a reference value of Mr = 1rad/Pa.

In summary, we present the relationship between strain and acoustic pressure, while the theoretical model predicts the phase change in the DAS system. The link between the two lies in the circumferential strain of the thin-walled cylinder. Therefore, the experimental strain–pressure curve and the theoretical phase–pressure prediction describe the same underlying physical process. With a known conversion factor, quantitative comparison is also possible.

Experimental design

Parameter design of thin-walled cylinders

Based on the principle of acoustic sensitivity enhancement in thin-walled cylinders, the elastic modulus (E), wall thickness (H), diameter (D), and Poisson’s ratio (ν) are the four core parameters that govern the DAS testing sensitivity. Since the Poisson’s ratio of common engineering materials varies only slightly (0.25-0.35), this study focuses on the elastic modulus, wall thickness, and diameter of thin-walled cylinders. To this end, thin‑walled cylindrical fiber‑optic sensors with varying elastic moduli, wall thicknesses, and diameters were designed.

Considering material machinability and acoustic impedance matching, five materials were selected – ABS (2.3 GPa), epoxy glass fiber (25 GPa), aluminum alloy (70 GPa), brass (110 GPa), and stainless steel (193 GPa) – to establish an elastic modulus gradient. To investigate the effects of wall thickness and diameter, thin-walled cylinders made of ABS (2.3 GPa) were used to establish gradients of wall thickness and diameter, respectively. The specific test parameters are shown in Table 1.

Table 1 Parameters of thin-walled cylinders.
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Experimental procedures

As shown in Fig. 5, all thin-walled cylinders used in the experiments had a length of 25 cm. To enhance pre-tension and ensure a tight fit, a distributed strain‑sensing optical cable with a diameter of 0.9 mm was helically wound onto the thin‑walled cylinder surface using a fiber‑winding device.

Fig. 5
figure 5

The sensor fabrication process. (a) Thin-walled cylinder. (b) Distributed strain‑sensing optical cable. (c) Helical winding of the strain-sensing optical fiber onto a thin-walled cylinder. (d) The fiber is wound at a 0° angle (zero-spacing tight winding) and then bonded with epoxy resin to ensure a secure fit and efficient strain coupling.

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As the winding angle increases, the helical optical fiber exhibits enhanced sensitivity to signals along the winding axis and reduced sensitivity to signals perpendicular to the winding axis34. Therefore, a winding angle of 0° (zero-spacing tight winding) was employed to maintain angular consistency while ensuring maximum achievable sensitivity.

After winding, the optical fiber was bonded to the cylinder surface with epoxy resin. This bonding process both secured the fiber in place and ensured efficient coupling between the optical fiber and the thin-walled cylinder.

As shown in Fig. 6, all thin-walled cylindrical fiber-optic sensors are connected in series to form a sensor array, which is integrated into the DAS monitoring system.

Fig. 6
figure 6

Experimental setup for DAS sensitivity testing. (a) The thin-walled cylindrical fiber-optic sensors are connected in series and arranged in a circular array around the acoustic source. The speaker is placed on cushioning material to prevent resonance. (b) The DAS interrogator used for data acquisition. (c) The audio generator that provides the signal to the speaker.

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The DAS system sampling frequency was set to 10 kHz. Thin-walled cylindrical fiber-optic sensors were evenly arranged in a circular array, and the two ends of the sensor were unconstrained and in a free state, consistent with the theoretical model. A speaker connected to an audio generator was positioned at the center of the array (Fig. 6c) and emitted a linear sine-sweep signal from 10 to 5 kHz. The sound frequency was incremented in 10 Hz steps to enable precise excitation across the frequency spectrum. Sound waves radiate outward as acoustic pressure waves, propagating radially and acting on the cylinder’s outer surface, inducing radial stretching or compression. The optical fiber wound around the thin-walled cylinder surface converts radial deformation into axial strain, detected by the DAS system through minute phase changes in the fiber, enabling the quantitative capture of acoustic signals. As shown in Fig. 6(a), the speaker is placed on a cushioning material (to prevent resonance), 100 mm from each sensor. Data is recorded each time the audio is played. Each frequency is tested three times, and the average of the three tests is used for data analysis, which minimizes the potential effects of mode coupling and signal distortions.

To ensure the comparability of DAS signals from thin-walled cylindrical sensors with different diameters, the incident sound pressure levels (SPL) at each sensor position were measured, as shown in Table 2.

Table 2 Measured sound pressure levels (SPL) for sensors of different diameters.
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The results indicate that the SPL differences among sensors of different diameters are minor, with the slight variations falling within the typical measurement error range for acoustics (standard deviation of merely ±0.3 dB). Therefore, it can be considered that during the experiments, all cylinders were essentially exposed to the same sound pressure level, and the observed differences in DAS sensitivity are primarily attributed to the structural characteristics of the cylinders rather than the influence of the sound source.

Results

Comparison of single-sensor baseline and series configuration

To evaluate whether neighbouring thin-walled cylindrical sensors exhibit acoustic coupling via airborne sound or structural vibration transmission, we selected a sensor with an elastic modulus of 2.3 GPa, wall thickness of 1 mm, and diameter of 50 mm, and measured its responses under identical experimental conditions (including excitation and sampling parameters) in both an isolated configuration and the serial (arrayed) configuration used in the main experiments. Fig. 7 presents representative comparisons of the frequency-domain and time-domain responses for the two conditions.

Fig. 7
figure 7

Comparison of sensor responses in isolated and serial configurations. (a) Frequency-dependent signal strength. (b) Phase response comparison. (c) Per-frequency difference.

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As shown, the mean difference in the frequency domain between the single-sensor and arrayed configurations is 0.281 dB, with a mean absolute deviation of 1.26 dB and a standard deviation of 1.6 dB. Across the measured frequency points from 10 to 5000 Hz, 93.4% of the points exhibit absolute differences of no more than 3 dB (Fig. 7c), and the maximum single-point deviation is approximately 3.98 dB. In the time domain, the root-mean-square (RMS) values of the two signals are 0.3082 and 0.2769, respectively.

Overall, the spectral shapes for the two arrangements are highly consistent across the operating band, indicating that acoustic coupling between neighbouring cylinders does not introduce a systematic bias to the relative sensitivity conclusions reported in this paper.

Frequency response of thin-walled cylindrical fiber-optic sensors

Resonance frequency analysis

To investigate the potential influence of resonance frequencies, experimental modal tests were conducted on thin-walled cylindrical fiber-optic sensors made of different materials. Each cylinder was excited by impact, and the corresponding response frequencies and mode shapes were measured. The results are presented in Fig. 8.

Fig. 8
figure 8

Measured resonance frequencies of thin-walled cylinders. (a) ABS. (b) Epoxy glass fiber. (c) Aluminum alloy. (d) Brass. (e) Stainless steel.

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Therefore, under external impact excitation the thin-walled cylinders exhibit pronounced amplitude peaks in their frequency responses; the frequency of each peak corresponds to the first (fundamental) resonance frequency. This observation indicates that the cylindrical sensors are most responsive at these frequencies and exposes material-dependent differences in their dynamic behavior. The resonance frequencies measured for sensors of different materials are summarized in Table 3. These modal measurements therefore provide an empirical basis for the subsequent analysis.

Table 3 Resonance frequencies of thin-walled cylinders.
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The frequency response analysis

The material and geometric parameters of the thin-walled cylinders significantly influence the DAS signal response under external acoustic pressure across the full 10 Hz to 5 kHz frequency range. Fig. 9 illustrates the signal strength for sensors with varying structural parameters, revealing clear performance trends.

Fig. 9
figure 9

Frequency-dependent signal strength of the thin-walled cylindrical fiber-optic sensors. (a) Response comparison for sensors with different elastic moduli. (b) Response comparison for sensors with different wall thicknesses. (c) Response comparison for sensors with different diameters.

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The signal strength response curves for all sensors show peaks and troughs at identical frequencies. Notably, at the identified resonance frequencies, we did not observe pronounced fluctuations; the signals exhibited good uniformity across the tested cylinders. This uniformity indicates that the fluctuations in signal strength are not caused by the inherent resonant modes of individual cylinders but rather by the combined frequency response characteristics of the experimental setup, including the sound source, the acoustic environment, and the DAS system itself. The speaker’s output and the laboratory’s acoustic field create amplification or attenuation in specific frequency bands, while the DAS system’s own sensitivity varies across its detectable range.

The results show three clear trends. As the elastic modulus of the cylinder increases from 2.3 to 193 GPa, the overall DAS signal strength decreases (Fig. 9a). The sensor with the lowest elastic modulus consistently produces the strongest signal. As the wall thickness increases from 1 to 5 mm, the DAS signal response shows a similar downward trend (Fig. 9b). As the diameter increases from 10 to 50 mm, the DAS signal strength shows a clear upward trend, with the 50 mm diameter sensor maintaining the highest amplitude (Fig. 9c).

These results demonstrate that thin-walled cylindrical sensors designed with a low elastic modulus, thin walls, and a large diameter are most effective at enhancing DAS testing sensitivity. To analyze these effects in greater detail, 2 kHz was selected as the representative excitation frequency. This frequency falls within a typical acoustic band, effectively simulates common environmental vibrations, and allows the cylinder’s deformation to clearly reflect how structural parameters impact DAS sensitivity.

Impact of elastic modulus on DAS sensitivity

The elastic modulus of the thin-walled cylinder is a critical parameter that governs the strain-transfer efficiency in the “acoustic pressure-structure-fiber” system. To isolate its effect, a single-variable experiment was conducted using five sensors with identical dimensions (D = 50 mm, H = 1 mm) but made from materials with elastic moduli ranging from a flexible 2.3 GPa (ABS) to a rigid 193 GPa (stainless steel).

The results, shown in Fig. 10, demonstrate that a lower elastic modulus directly enhances sensor performance. In the time domain (Fig. 10a), the sensor with the lowest elastic modulus (2.3 GPa) exhibits the strongest amplitude response to the acoustic signal applied at 2.1 s. As the material’s elastic modulus increases, the response amplitude systematically weakens. This trend is mirrored in the phase response (Fig. 10d), where the phase amplitude is greatest for the most flexible material and diminishes as stiffness increases.

Fig. 10
figure 10

Impact of elastic modulus on DAS testing sensitivity at 2 kHz. (a) Time-domain signal waterfall plot. (b) Frequency-domain signal characteristics and SNR comparison. (c) Relationship between sensitivity, circumferential strain, and elastic modulus. (d) Phase response comparison.

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In the frequency domain (Fig. 10b), all sensors show a distinct peak at the 2 kHz excitation frequency, but the peak’s amplitude is inversely proportional to the elastic modulus. The 2.3 GPa sensor achieves the highest peak and the best signal-to-noise ratio (SNR), which is defined as the ratio of the peak amplitude at the target frequency to the average noise amplitude in the adjacent band. In contrast, sensors with higher moduli show attenuated peaks and elevated baseline noise. This confirms that lower-modulus materials enable more efficient coupling of acoustic energy, leading to a stronger, clearer signal.

This relationship is quantified in Fig. 10(c), which shows that DAS testing sensitivity decays exponentially as the elastic modulus increases. Specifically, as the modulus rises from 2.3 to 193 GPa, sensitivity plummets from 0.98 to 0.06 rad/Pa—a 16-fold decrease. According to Eqs. (6) and (7), this trend can be explained using thin-walled cylinder elasticity theory.

$$\varepsilon_{y} \propto \frac{P \cdot R}{{H \cdot E}}$$
(15)

Since the DAS phase change Δφ is directly proportional to the circumferential strain of the thin-walled cylinder, the following relationship can be obtained:

$$\Delta \varphi \propto \varepsilon_{y} \propto \frac{P \cdot R}{{H \cdot E}}$$
(16)

This confirms the theoretical mechanism: a lower elastic modulus enhances the cylinder’s flexibility, allowing it to undergo greater circumferential strain under a given acoustic pressure. This larger strain is efficiently transferred to the fiber, producing a larger phase shift and ultimately leading to a significant enhancement in DAS sensitivity.

In existing studies on the impact of elastic modulus on DAS signal sensitivity, researchers typically select only a single comparative material. For instance, a novel acoustic sensor based on polypropylene/polyethylene terephthalate (PP/PET) film demonstrates a sensitivity exceeding 0.4 rad/Pa within the 90–4000 Hz frequency range and achieves a signal-to-noise ratio of approximately 42 dB at 600 Hz44; a graphene oxide-based optical fiber sensor exhibits a minimum detectable sound pressure of 10.2 μPa/Hz1/225. In contrast, this study introduces multiple materials to construct a gradient of elastic modulus, systematically quantifying the influence of elastic modulus on DAS signal sensitivity, thereby providing a valuable complement to existing research.

Impact of wall thickness on DAS sensitivity

Wall thickness is a key geometric parameter that determines not only the stiffness of the cylindrical structure but also its damping behavior. In theory, a thicker wall introduces greater structural damping, which dissipates vibrational energy and suppresses the response to external forces. This can be modeled by defining a damping ratio (ζ) that that is inversely proportional to the square root of the wall thickness (H)45,46:

$$\varsigma = \frac{c}{{2\sqrt {km} }} \propto \frac{H}{{2\sqrt {H^{3} m} }} = \frac{1}{2\sqrt m }H^{ - 0.5}$$
(17)

where c denotes the structural damping coefficient; k denotes the structural equivalent stiffness; and m denotes the equivalent mass. This model predicts that as the wall becomes thicker, the damping effect will more significantly reduce the strain transferred to the optical fiber.

The experimental results at 2 kHz, shown in Fig. 11, confirm this damping mechanism. The time-domain waterfall plot (Fig. 11a) and the phase response (Fig. 11d) both show that the sensor with the thinnest wall (1 mm) produces the largest response amplitude, with a phase fluctuation of approximately ±0.95 rad. As wall thickness increases to 5 mm, the phase amplitude is significantly attenuated to just ±0.25 rad, which demonstrates the suppression of the energy response due to the increased damping from the thicker material.

Fig. 11
figure 11

Impact of wall thickness on DAS testing sensitivity at 2 kHz frequency. (a) Time-domain signal waterfall plot. (b) Frequency-domain signal characteristics and SNR comparison. (c) Relationship between sensitivity, damping ratio, and wall thickness. (d) Phase response comparison.

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In the frequency domain (Fig. 11b), the 1 mm sensor exhibits the highest peak amplitude at 2 kHz, indicating strong resonance and efficient energy accumulation. As the wall thickens, the peak amplitude progressively decreases while the baseline noise increases, resulting in a lower SNR. This shows that by minimizing damping, thinner walls enhance the sensor’s ability to resonate at the target frequency.

This strong influence on performance is quantified in Fig. 11(c), which shows that DAS testing sensitivity decays exponentially as wall thickness increases. As the wall thickens from 1 mm to 5 mm, sensitivity drops sharply from 0.98 to 0.27 rad/Pa, with the most significant decrease (over 60%) occurring between 1 and 2 mm. This trend is directly correlated with the modeled increase in the structural damping ratio. Therefore, reducing wall thickness is critical for minimizing damping losses, preserving the strain response, and ultimately enhancing DAS testing sensitivity.

Impact of diameter on DAS sensitivity

When an external acoustic pressure P acts on the surface of the thin-walled cylinder, the total applied force F can be expressed as:

$$F = P \cdot A$$
(18)
$$A = 2\pi R \cdot Z$$
(19)

where A denotes the surface area of the thin-walled cylinder, and Z represents its length. As the cylinder radius increases, the effective force-bearing area grows linearly with the radius. Therefore, we have:

$$F \propto R$$
(20)

According to Eqs. (6) and (7), the radial displacement u of the thin-walled cylinder is:

$$u = \varepsilon_{y} \cdot R \Rightarrow u \propto \frac{P \cdot R}{{H \cdot E}} \cdot R$$
(21)

For a linearly elastic structure47, the equivalent stiffness k of the thin-walled cylinder is given by:

$$k \propto \frac{F}{u} = \frac{P \cdot 2\pi R \cdot Z}{u} \Rightarrow k \propto \frac{1}{R}$$
(22)

Therefore, the diameter of the thin-walled cylinder enhances sensitivity through two key mechanical principles. First, a larger diameter increases the effective surface area exposed to external acoustic pressure, which linearly increases the total applied force on the structure. Second, a larger diameter reduces the cylinder’s equivalent stiffness, making it more susceptible to deformation. Together, these effects lead to greater radial displacement and circumferential strain for a given acoustic pressure, which in turn should produce a larger phase shift in the fiber and higher DAS sensitivity.

The experimental results at 2 kHz, shown in Fig. 12, provide strong validation for this model. The time-domain plots (Fig. 12a) and phase responses (Fig. 12d) clearly demonstrate that signal amplitude scales with diameter. The sensor with the largest diameter (50 mm) exhibits the strongest signal and the largest phase amplitude (close to ±1 rad), which is approximately four times greater than the response from the 10 mm diameter sensor (±0.25 rad). This directly shows that a larger diameter induces greater structural strain.

Fig. 12
figure 12

Impact of diameter on DAS testing sensitivity at 2 kHz. (a) Time-domain signal waterfall plot. (b) Frequency-domain signal characteristics and SNR comparison. (c) Relationship between sensitivity, acoustic pressure effect, and diameter. (d) Phase response comparison.

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In the frequency domain (Fig. 12b), the peak amplitude at 2 kHz increases significantly as the cylinder’s diameter grows. The 50 mm diameter sensor achieves the highest peak and the best SNR, indicating superior signal stability and clarity at the target frequency.

This relationship is quantified in Fig. 12(c), which reveals a strong linear correlation between DAS testing sensitivity and the cylinder’s diameter. As the diameter increases from 10 mm to 50 mm, the sensitivity rises from 0.244 to 0.9767 rad/Pa—a nearly four-fold increase. This corresponds to an average sensitivity gain of 0.02 rad/Pa for every millimeter increase in diameter, confirming that a larger diameter effectively enhances the sensor’s ability to capture sound wave energy by amplifying the total applied force and increasing structural deformation.

It should be noted that this linear gain is concluded based on an experimental diameter range of 10–50 mm. Considering the applicability of sensor specifications, diameters beyond this range were not investigated in this study. Therefore, for larger diameters, factors such as structural instability of the thin-walled cylinder or acoustic diffraction may influence the continuity of the linear gain. Future research should further explore the upper limit of diameter-dependent sensitivity.

Discussion

This study systematically demonstrates how the mechanical and geometric properties of a thin-walled cylinder can be engineered to optimize DAS sensitivity. The experimental results align strongly with established theoretical models of structural mechanics, providing a validated framework for sensor design. As illustrated in Fig. 13, the interplay between elastic modulus, wall thickness, and diameter creates a multi-parameter optimization challenge, where each property influences the final performance through distinct physical mechanisms.

Fig. 13
figure 13

Combined influence of structural parameters on DAS testing sensitivity. (a) Sensitivity as a function of elastic modulus and wall thickness. (b) Sensitivity as a function of elastic modulus and diameter. (c) Sensitivity as a function of wall thickness and diameter.

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The exponential sensitivity gains achieved by using a low-modulus material are directly moderated by the cylinder’s wall thickness. As shown in Fig. 13(a), a low-modulus, thin-walled structure provides the highest sensitivity because the material’s inherent flexibility is complemented by low structural damping. Conversely, a sensor made from a low-modulus material will perform poorly if its walls are too thick; the increased damping dissipates the vibrational energy and negates the material advantage. This finding, which shows a spectral peak drop of approximately 15 dB as thickness increases, is consistent with established models in material science and damping theory, where thicker structures exhibit greater energy loss48,49.

In contrast to the exponential effects of material and thickness, the cylinder’s diameter acts as a linear amplifier for sensitivity. As shown in Fig. 13 (b) and Fig. 13 (c), increasing the diameter provides a consistent and predictable sensitivity boost across all combinations of elastic modulus and wall thickness. This is because a larger diameter simultaneously increases the force-receiving area and reduces curvature stiffness, leading to greater overall strain. This makes diameter a reliable parameter for tuning sensor performance and maximizing the gains achieved from material selection and wall thickness reduction.

Ultimately, sensor performance is dictated by the coupling efficiency between the “acoustic pressure-structural strain-fiber phase”. To maximize this efficiency, this study proposes three key structural optimization principles based on the validated relationships:

  1. (1)

    Material Selection: Prioritize materials with low elastic moduli (e.g., 2.3–25 GPa) to achieve an exponential increase in the fundamental strain transfer efficiency.

  2. (2)

    Damping Control: Design for minimal wall thickness (e.g., 1–2 mm), balanced against the need for mechanical durability, to suppress damping losses and enhance the resonant energy response.

  3. (3)

    Force Amplification: Employ the largest feasible diameter (e.g., 30–50 mm), within spatial and installation constraints, to linearly amplify the applied force and circumferential strain.

By implementing these principles, the strain and energy accumulation capabilities of the thin-walled cylinder are maximized, providing a practical and scalable pathway to developing highly sensitive DAS sensors for demanding applications.

However, for practical deployment in harsh environments such as underground or marine settings, several critical trade-offs must be considered. The choice of a low-modulus, thin-walled structure, while optimal for sensitivity, may present challenges in mechanical durability, potentially requiring protective housing or reinforcement to withstand high external pressures and mechanical impacts. Furthermore, environmental tolerance necessitates careful material selection to ensure long-term resistance to corrosion, biofouling, and chemical degradation, which could increase material costs and design complexity. Consequently, the pursuit of ultimate sensitivity must be balanced against factors of robustness, longevity, and overall system cost to arrive at a viable solution for real-world deployment.

Conclusions

This study successfully demonstrated that the sensitivity of DAS systems can be significantly enhanced through the strategic structural design of a thin-walled cylindrical sensor. Systematic experimental evaluation, supported by theoretical analysis of acoustic-strain coupling, yielded several key conclusions for optimizing sensor performance:

  1. (1)

    The cylinder’s elastic modulus is a primary driver of sensitivity. A lower modulus exponentially increases sensitivity—from approximately 0.06 to 0.98 rad/Pa as the modulus was reduced from 193 to 2.3 GPa. This is achieved by enhancing the structure’s flexibility, which promotes greater circumferential deformation and maximizes strain transfer to the optical fiber.

  2. (2)

    Structural damping, governed by wall thickness, is critical to signal integrity. Decreasing the wall thickness from 5 to 1 mm produced a corresponding exponential rise in DAS sensitivity from 0.2732 to 0.9767 rad/Pa. Thinner walls minimize energy dissipation and vibration suppression, thereby preserving the strain response under acoustic excitation.

  3. (3)

    The cylinder’s diameter provides a linear and predictable method for sensitivity enhancement. Increasing the diameter from 10 to 50 mm boosted sensitivity from 0.244 to 0.9767 rad/Pa, with an average gain of 0.02 rad/Pa per millimeter. A larger diameter improves performance by increasing the effective area for acoustic pressure reception and lowering curvature stiffness.

  4. (4)

    These findings converge on a clear optimization strategy. Optimal DAS sensitivity is achieved by combining low-modulus materials (2.3–25 GPa), thin walls (1–2 mm), and large diameters (30–50 mm) to maximize strain transfer, minimize damping, and amplify the applied force area.

Together, these conclusions clarify the structural-mechanical mechanisms underlying DAS sensitivity enhancement and provide a robust theoretical and experimental basis for engineering high-performance sensors for complex acoustic environments.