Free vibration analysis of variable stiffness composite laminated beams and plates by novel hierarchical differential quadrature finite elements

The present work deals with the free vibration behavior of the variable stiffness composite laminates (VSCLs)featured by spatially varyingfibre orientation angles via novel quasi‐three‐dimensional solutions. The CarreraUnified Formulation (CUF) is employed to construct such novel models, where cross‐section kinematics aredescribed with the improved hierarchical Legendre expansion (IHLE) of primary mechanical variables. Theproposed expansions not only maintain the hierarchical properties of the HLE model but also become less sen-sitive to the numbering sequence of expansion terms. As a result of these enhanced kinematics, EquivalentSingle Layer (ESL) and Layer‐Wise (LW) models can be formulated more robustly. The weak form differentialquadraturefinite element method (DQFEM) is employed to solve the governing equations derived by the prin-ciple of virtual displacements. Based on CUF‐based DQFEM, even a single beam element is sufficient to tacklemany complex issues with high accuracy. Compact VSCL beams and plates with variousfibre paths, boundaryconditions, lamination schemes, and thickness‐to‐width ratios have been studied in several numerical exam-ples. The proposed method’s accuracy and effectiveness are validated by comparing results to published data