In-Plane Dynamic Analysis of Complex-Shaped Laminated Cracked Plates with Irregular Holes

This paper reports the unified in-plane vibration solutions of irregular laminated cracked plates having complex holes under various boundary restrictions. According to the geometric features of the studied structure, an irregular plate with/without the dropoff ply is decomposed into a variety of intact triangular and quadrilateral laminated elements. These elements are then mapped to two-dimensional regular square plates for deriving the unified formulations of the element energy integral. Simultaneously, the boundary restrictions at the external edge of the plate and fully rigid connections between the substructures are emulated through in-plane translational springs. The in-plane variables of intact plate elements are characterized by Chebyshev element expansions. Thus, the in-plane modal and harmonic response solutions are extracted by performing the general Rayleigh-Ritz procedures. Some in-plane vibration tests and finite element simulations concerning cracked plates with built-in holes are further executed. The applicability and accuracy of the proposed dynamic model are validated by comparison with the experimental data and those computed by finite element models (FEM). Also, some parametric cases are presented to investigate the influence of structural parameters, laminated configurations, and the dropoff ply effect on the in-plane dynamic characteristics of complex-shaped plates, which may provide useful benchmarks for structural design and damage detection of engineering structures.