Free Vibration Analysis of Thermally Prestressed Constant and Variable Stiffness Laminated Beams using Strong Unified Formulation

Abstract

Free vibration analysis is an essential requirement to capture the behaviour of composite structures subject to dynamic loading environment. To enhance the vibratory behaviour of composite structures, variable stiffness (VS) concept offers increased design flexibilities to tailor the structural response to meet a wide range of applications. Mechanically, the increased design space created by VS techniques leads to complexities of non-classical stiffness couplings which necessitate robust computational frameworks with enriched kinematics to predict the dynamic response accurately and efficiently. In this regard, this study proposes an enhanced differential quadrature based Strong Unified Formulation (SUF) to investigate the free vibration behaviour of thermally prestressed constant and variable stiffness composite beams. The proposed SUF model exploits the flexible kinematical description of the Theory of Unified Formulation to combine a hierarchical serendipity Lagrange-based 2D finite element (FE) with 1D differential quadrature method beam element for efficient free vibration characterisation of composite beams induced with prestress at different temperatures. The proposed SUF free vibration solutions of constant stiffness and VS beams demonstrate satisfactory accuracy and achieved improved efficiency with up to 99.9% computational savings when benchmarked against ABAQUS 3D FE solutions. Finally, a numerical study reveals that the effects of thermal prestress significantly contribute to the free vibration response of constant stiffness and VS laminated beams underscoring the importance of the study.

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