Wave propagation in compact, thin-walled, layered, and heterogeneous structures using variable kinematics finite elements

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ABSTRACTThe article investigates wave propagation characteristics for a class of structures using higher-order one-dimensional (1D) models. 1D models are based on the Carrera Unified Formulation (CUF), a hierarchical formulation which provides a framework to obtain refined structural theories via a variable kinematics description. Theories are formulated by employing arbitrary expansions of the primary unknowns over the beam cross-section. Two classes of beam models are employed in the current work, namely Taylor Expansion (TE) and Lagrange Expansion (LE) models. Using the principle of virtual work and finite element method, the governing equations are formulated. The direct time integration of equation of motion is carried through an implicit scheme based on the Newmark method and a dissipative explicit method based on the Tchamwa–Wielgosz scheme. The framework is validated by comparing the response for the stress wave propagation in an isotropic beam to an analytical solution available in the literature. The capabilities of the proposed model are demonstrated by presenting results for wave propagation analysis of a sandwich beam and a layered annular cylinder structure. The ability of CUF models to detect 3D-like behavior with a reduced computational overhead is highlighted.