Nonlinear Vibration Analysis of Hyperelastic Structures
Summary
Nonlinear vibration analysis of hyperelastic structures investigates the dynamic response of materials and components that undergo large elastic deformations. Such structures, found in soft robotics, biomedical devices and flexible electronics, require specialised constitutive laws to describe a highly nonlinear relationship between stress and strain. Analyses draw on continuum mechanics, energy methods and perturbation techniques to capture geometric nonlinearity, material nonlinearity and coupling between modes. Central challenges include accurate representation of strain energy density functions, handling of shear deformation in thick or layered media, and prediction of resonance phenomena under varying boundary conditions. Advances in analytical, semi-analytical and numerical approaches have enabled insight into amplitude-dependent frequency shifts, internal resonances and stability thresholds, guiding the design of resilient, tunable and efficient hyperelastic systems with global applicability.
Research from Nature Portfolio
No recent Nature Portfolio content available.
Nonlinear Vibration Analysis of Hyperelastic Structures publication trend
The graph below shows the total number of articles in nonlinear vibration analysis of hyperelastic structures across all publications each year (not limited to Nature Index journals).
Technical terms
Hyperelastic material: A material model in which stress–strain behaviour derives from a strain energy density function, enabling description of large elastic deformations.
Strain energy density function: A scalar potential function defining stored elastic energy per unit volume as a function of strain measures in hyperelastic models.
Nonlinear vibration analysis: The study of oscillatory responses when restoring forces or kinematic relations include nonlinear terms due to large deformations or material behaviour.
Geometrical nonlinearity (von Kármán): An approximation retaining quadratic terms in the strain–displacement relations to capture moderate rotations and large deflections.
Internal resonance: A dynamic condition in which energy is exchanged between vibration modes whose natural frequencies satisfy specific integer ratios.
Shear deformable beam theory: Beam formulations that account for transverse shear strains—such as Timoshenko or higher-order models—enhancing accuracy in thick or layered structures.
References
- A review on the nonlinear dynamics of hyperelastic structures. Nonlinear Dynamics (2022).
- Nonlinear continuum mechanics of thick hyperelastic sandwich beams using various shear deformable beam theories. Continuum Mechanics and Thermodynamics (2022).
- Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect. Nanomaterials (2021).
About these summaries
This Nature Research Intelligence Topic summary is created with the cited references and a large language model. We take care to ground generated text with facts, and have systems in place to gain human feedback on the overall quality of the process in line with our AI principles. We strive to create accurate and useful summaries for people unfamiliar with the research topic and that supports this goal. These pages are a beta release and will be updated as we learn how best to help people gain value from a research topic summary.
Turn complex research questions into confident strategic decisions
When you're under pressure to set direction, justify investment, or understand your competitive position, you need more than raw data — you need trusted insights you can act on.
Benchmark your performance against global peers using robust, methodologically sound analysis.
Combine quantitative metrics with qualitative expert insight to uncover strengths, gaps and emerging opportunities.
Gain tailored, decision-ready recommendations aligned to your strategic priorities.
Talk to us to learn more about our data dashboards and bespoke strategy reports.
Grow research skills, confidence and careers with training built for every stage of the research lifecycle.
Developed with Nature Portfolio journal Editors and internationally renowned experts. Discover three ways to learn:
Self-paced, online courses in convenient bite-sized units, covering key skills across scientific writing, publishing, grant writing, data analysis, and more.
Expert trainer-led workshops with hands-on exercises and real-time feedback across core research skills, delivered via interactive group sessions.
Editor-led workshops combining core principles in writing and publishing, personalised 1:1 feedback from Nature Portfolio Editors and hands-on exercises.
Explore course catalogues and workshop agendas, enquire about the options or request institutional pricing.