Abstract

An analytical model is proposed for vibration analysis of a thin orthotropic rectangular plate containing two perpendicular continuous line surface cracks located at the centre of the plate. Also new configuration of two perpendicular cracks as internal cracks, located along the thickness of the plate is studied by considering appropriate crack compliance coefficients based on line-spring model. Equilibrium principle is used to derive the equation of motion of the specially orthotropic cracked plate. Using Berger’s formulation for the in-plane forces and Galerkin's method, the equation is converted into a nonlinear system. The nonlinear frequency amplitude relation for the cracked plate subjected to transverse harmonic excitation is derived using the method of multiple scales thereby the bending hardening or softening phenomenon is presented. The influence of varying crack length ratio, the three boundary conditions and various locations of the two cracks along the thickness of the plate on the natural frequencies of square and rectangular plate is demonstrated.

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