Effect of fibre orientation on non-linear vibration of partially cracked thin rectangular orthotropic micro plate: An analytical approach

Abstract

A nonlinear analytical model for vibration analysis of partially cracked thin orthotropic plate as affected by the fibre orientation and arbitrary position of a partial crack is presented. The approach is based on the classical plate theory and the effect of microstructure is incorporated using the modified couple stress theory. A single partial crack located at an arbitrary position along the line of symmetry is parallel to one of the edges of the plate. The crack considered is in the form of a continuous line and its effect is incorporated in the form of moment and in-plane forces based on a simplified line spring model. Non-linearity in the model is introduced by Berger׳s formulation for the in-plane forces while the Galerkin׳s method with modal functions is used to obtaining the solution of the governing differential equation. A nonlinear frequency response relation and peak amplitude is obtained by the application of the method of multiple scales. Extensive results for the fundamental frequencies and peak amplitude as affected by the fibre orientation, plate aspect ratio, crack length, crack position and internal material length scale parameter are presented for two boundary conditions. It is found that the fibre orientation and the microstructure of the plate affect the fundamental frequencies of the partially cracked orthotropic plates. The linear and nonlinear frequency response curves based on the classical plate theory and the modified couple stress theory are plotted which shows the effect of internal material length scale parameter and crack position on the bending hardening or softening phenomenon.