Vibration characteristics analysis of various types of plates is of great significance in engineering applications. In this paper, an effective analytical method is developed to investigate the vibration properties of irregular plates with a lumped mass. The assumed mode method is extended to establish the equations of motion of irregular plates with a lumped mass, and vibration properties of the structural system are studied. The accuracy of this method is verified by the finite element method (FEM) and the vibration experiments. The natural frequencies and mode shapes of a typical irregular plate, i.e. cantilever trapezoidal plate, with a lumped mass obtained by the present method are in good agreement with the FEM and the vibration experiments. The influences of some parameters such as the additional lumped mass and the position of the additional mass on the vibration characteristics of cantilever trapezoidal plates are analyzed. The results could provide a reference for the vibration characteristics analysis of various irregular plates.

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