Spectral element modeling and experimental investigations on vibration behaviors of imperfect plate considering irregular hole and curved crack

A weak-form spectral element modeling and the corresponding experimental studies in this work are concerned to clarify free vibration mechanism for the plate of arbitrary shape having built-in complex hole and crack. To effectively address the discontinuity problem at irregular hole as well as crack of varying curvature, some quadrilateral plate elements with variable curvature edges are rigidly coupled together to form the investigated structural system. A flexible coordinate mapping strategy is here employed for satisfying the adaptability requirements of the introduced displacement functions to the sophisticated solution domain. Accordingly, the complete vibration equation of the physical model is solved based on the well-known first-order scheme of plate in conjunction with 2D spectral element functions, where the boundary constraints and compatibility relations in the form of energy quantification are imposed through the penalty function method. After that, modal experiments considering six unconstrained imperfect plates with pre-configured crack and hole, are incorporated with a series of acceptable solutions, provided by the available literature and some associated models of FEM, for disclosing the excellent predictive capability of the spectral element methodology in vibration performance. The reported eigenfrequencies and eigenmodes respecting arbitrarily shaped plate introducing intricate hole and curved crack are the first presented vibration solutions, and meaningful benchmarks for evaluating correctness of other numerical or analytical approaches.