Nonlinear Dynamics of Composite Laminated Plates
Summary
Composite laminated plates are characterised by multiple bonded layers of anisotropic material designed to achieve high stiffness-to-weight ratios and tailored mechanical properties. Under transverse and in-plane dynamic loading, these structures exhibit pronounced nonlinear behaviour due to geometric large deflections, interlaminar shear and material anisotropy. Analytical models based on von Kármán large-deformation theory and higher-order shear deformation plate theories capture the coupling between bending and stretching, while numerical schemes such as Galerkin projection and finite-element discretisation resolve complex mode interactions. When natural frequencies satisfy simple rational ratios, internal resonance may occur, giving rise to energy exchange between modes, jump phenomena and bifurcation cascades. In certain parameter regimes, multipulse homoclinic orbits and chaotic responses emerge, challenging conventional design assumptions. Control strategies employing piezoelectric actuation or tuned damping layers have been proposed to stabilise undesirable motions. Understanding these nonlinear dynamics is essential for aerospace panels, precision sensors, vibration energy harvesters and civil infrastructure, where accurate prediction of stability thresholds and resonance behaviour under multi-frequency excitations ensures structural integrity and performance.
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Nonlinear Dynamics of Composite Laminated Plates publication trend
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Technical terms
Composite laminated plate: A structural panel composed of multiple bonded layers (plies) of anisotropic materials, offering enhanced stiffness and tailored mechanical properties.
Von Kármán nonlinearity: Geometric nonlinear formulation accounting for large transverse deflections that couple in-plane stretching and out-of-plane bending.
Internal resonance: A condition where two or more vibration modes have commensurate natural frequencies, enabling strong energy exchange and coupled dynamics.
Singularity analysis: A mathematical technique that classifies equilibrium behaviour near critical parameter values where qualitative changes and bifurcations occur.
Homoclinic orbit: A trajectory in phase space that departs from and returns to the same saddle equilibrium, often signalling the onset of complex bifurcations and chaos.
References
- Singularity Analysis of Composite Laminated Piezoelectric Rectangular Plate Structure with 1 : 2 Internal Resonance. Mathematical Problems in Engineering (2021).
- Multipulse Homoclinic Orbits and Chaotic Dynamics of a Reinforced Composite Plate with Carbon Nanotubes. Mathematical Problems in Engineering (2020).
- Analysis of Nonlinear Vibrations and Dynamic Responses in a Trapezoidal Cantilever Plate Using the Rayleigh‐Ritz Approach Combined with the Affine Transformation. Mathematical Problems in Engineering (2019).
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