Nonlinear thermally induced vibration of matrix-cracked variable stiffness composite laminated beams

Abstract

The laminated composites are highly suitable for fabricating spacecraft components due to their exceptional performance-to-weight ratio. However, during orbital operations, these structures undergo severe thermal cycling, triggering thermally induced vibrations that necessitate rigorous investigation of their nonlinear dynamic responses under thermal shock. To the best of the authors’ knowledge, this study presents the first comprehensive analysis of nonlinear thermally induced vibrations in variable stiffness composite laminated (VSCL) beams. The theoretical framework employs classical lamination theory integrated with the Poisson effect and von Kármán geometric nonlinearity. An exact temporal temperature profile through the thickness is derived using the one-dimensional transient heat conduction equation with Dirichlet boundary conditions. Coupled thermomechanical governing equations are formulated through the Lagrangian method and the Ritz method, while a self-consistent model addresses matrix crack evolution. Nonlinear dynamic responses are resolved via the Newmark-β method combined with Newton–Raphson iteration. Parametric studies reveal that lay-up configuration, boundary constraints, and crack density critically influence vibration characteristics. The results indicate that reasonable laminate and angle designs can effectively reduce the response amplitude of thermally induced vibrations. Comparative case studies show that the maximum difference in thermally induced vibration responses between different laminate designs can reach 17.04%. By optimizing the angles, the thermally induced vibration response of variable stiffness composite beams is reduced by 8.74% compared to constant stiffness composite beams.