EFFECT OF THERMAL ENVIRONMENT ON VIBRATION ANALYSIS OF ISOTROPIC MICRO PLATE WITH INCLINED CRACK BASED ON MODIFIED COUPLE STRESS THEORY

摘要

An analytical model for vibration analysis of partially cracked thin rectangular isotropic micro plate as affected by crack orientation under thermal environment is presented. The analytical model is derived based on the Kirchhoff's classical plate theory and the modified couple stress theory. The arbitrarily oriented crack is in the form of continuous line and is located at the center of the rectangular plate. Line spring model is used to incorporate the effect of crack in the form of moments and in-plane forces. Also, the moment's and in-plane forces arising due to temperature is introduced in the analytical model. A single internal material length scale parameter is used to capture the size effect. The solution for fundamental frequencies of the cracked plate is obtained by Galerkin's method by neglecting the geometric non linearity. Results for the fundamental frequencies as affected by the temperature, internal material length scale parameter and crack orientations are presented for simply supported boundary condition.