Nonlinear Vibration Analysis of Viscoelastic Plates

Nonlinear vibration analysis of viscoelastic plates investigates how thin structural elements, whose material behaviour exhibits both elastic and time-dependent viscous characteristics, respond under large deformations or dynamic loading. Beyond the classical linear theory, geometric nonlinearity (arising from moderate to large deflections) combines with the intrinsic viscoelastic constitutive relations to produce amplitude-dependent stiffness, damping and even internal resonances. Modern analytical and numerical frameworks—ranging from von Kármán plate theory to fractional-derivative models—capture the coupling between bending, stretching and time-dependent energy dissipation. Such coupled models are vital in assessing the dynamic stability, resonance frequencies and transient responses of plates used in aerospace panels, automotive components, civil infrastructure and micro-electromechanical systems. Advances in computational algorithms, including Galerkin projections, harmonic balance and polynomial approximation methods, have enabled efficient evaluation of response curves, bifurcations and chaotic regimes. Material formulations often employ relaxation kernels or fractional-order operators to characterise memory effects over a broad frequency spectrum. As a result, designers and analysts now possess predictive tools to optimise plate geometry, lay-up and boundary conditions, ensuring both durability and vibrational performance in critical engineering applications.

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Nonlinear Vibration Analysis of Viscoelastic Plates publication trend

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Technical terms

Viscoelasticity: Material behaviour combining elastic (instantaneous) and viscous (time-dependent) deformation under load.

Geometric nonlinearity: Deviation from linear strain–displacement relations when deflections are moderate or large, often modelled by von Kármán theory.

Relaxation kernel: Mathematical function describing the time-dependent stress decay in a viscoelastic material following an applied strain.

Fractional derivative model: Constitutive framework employing non-integer order derivatives to capture memory effects over multiple time scales.

References

1. Dynamic Stability of Orthotropic Viscoelastic Rectangular Plate of an Arbitrarily Varying Thickness. Applied Sciences (2021).
2. A Numerical Method for Simulating Viscoelastic Plates Based on Fractional Order Model. Fractal and Fractional (2022).
3. A New Approach for Studying Nonlinear Dynamic Response of a Thin Plate with Internal Resonance in a Fractional Viscoelastic Medium. Shock and Vibration (2015).