Nonlinear Vibration Control in Structural Dynamics

Nonlinear vibration control in structural dynamics addresses the suppression or mitigation of complex oscillatory behaviour in engineering systems where linear assumptions break down. Such nonlinearity may stem from large deformations, geometric effects, material characteristics or coupled modes of vibration. The field encompasses passive, active and semi-active strategies, underpinned by analytical methods (for example multiple-timescale perturbation), numerical schemes (finite-element discretisation) and experimental validation. Key objectives include avoiding resonance-induced damage in civil, aerospace and offshore structures, extending service life and enhancing safety. Practical applications range from vibration isolation of tall buildings and bridges, to precision control in aerospace components and energy harvesting devices. A unifying challenge is to devise robust controllers that remain effective amid parameter uncertainty and environmental variability.

Research from Nature Portfolio

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Research from all publishers

Recent studies have applied time-delayed displacement feedback control to piezoelectric beams, demonstrating effective suppression of superharmonic and subharmonic resonances. Extended beam models based on Euler–Bernoulli theory were discretised via Galerkin’s method and analysed through multiple-timescale techniques to derive stability criteria and quantify the influence of delay parameters and control gain on vibration amplitudes. Similarly, the nonlinear dynamics of rotating slender beams have been controlled via boundary actuation using classical proportional, nonlinear cubic and mixed control laws with embedded time delay. Analytical solutions of the coupled partial differential equations revealed hardening and softening phenomena across first and second mode resonances, and showed substantial vibration reduction over a range of rotational speeds. In the context of offshore wind turbine towers, a nonlinear proportional–derivative controller has been employed to attenuate tower vibrations under aerodynamic excitation. Using averaging methods and Poincaré maps, researchers have characterised stability boundaries and energy transfer pathways, demonstrating significant amplitude suppression and improved operational safety under worst-case resonance conditions.

Nonlinear Vibration Control in Structural Dynamics publication trend

The graph below shows the total number of articles in nonlinear vibration control in structural dynamics across all publications each year (not limited to Nature Index journals).

Technical terms

Geometric nonlinearity: Non-proportional relationship between displacement and applied load arising from large rotations or strains.

Time-delayed feedback control: Active strategy in which the control force is a function of past system states to stabilise resonant oscillations.

Proportional–derivative (PD) controller: Control algorithm combining proportional and derivative terms to regulate vibration based on error and rate of change.

Internal resonance: Condition in which two or more natural frequencies satisfy an integer ratio, enabling energy exchange between modes.

Hardening/softening behaviour: Nonlinear frequency-response phenomenon where resonant peaks shift to higher (hardening) or lower (softening) frequencies with amplitude.

References

1. Time-Delayed Feedback Control of Piezoelectric Elastic Beams under Superharmonic and Subharmonic Excitations. Applied Sciences (2019).
2. Nonlinear vibrations and time delay control of an extensible slowly rotating beam. Nonlinear Dynamics (2020).
3. Nonlinear Structural Control Analysis of an Offshore Wind Turbine Tower System. Processes (2019).