Vibration and buckling analysis of partially cracked thin orthotropic rectangular plates in thermal environment

An analytical model is presented for vibration of a thin orthotropic plate containing two perpendicular continuous line surface cracks located at the centre of the plate in the presence of thermal environment. 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 based on Classical Plate Theory is used to derive the equations of motion for cracked plate, wherein the crack terms are formulated using the line spring model. The moments due to thermal environment are neglected in the results and only uniform heating of the cracked plate is considered. The solution for natural frequencies of cracked plate is obtained by Galerkin's method. A relation for thermal buckling phenomenon for the cracked plate is also formulated. The influence of the lengths of the two cracks and their location along the thickness of the plate on critical buckling temperature and first mode natural frequency is demonstrated. The geometrically linear frequency response relation for cracked plate is formulated using the method of multiple scales. It is thus concluded that the presence of the two cracks affect the critical buckling temperature and natural frequencies.