Free vibration analysis of rectangular plate with a hole by means of independent coordinate coupling method

This paper is concerned with the vibration analysis of a rectangular plate with a rectangular hole or a circular hole. In the previous researches, the effect of the hole is taken into account by subtracting the energies of the hole domain from the total energies of the whole plate. In doing so, the integrals of the functions consisting of the admissible functions based on the plate domain over hole domain lead to complex numerical computations. In this paper, a new methodology called Independent Coordinate Coupling Method (ICCM) was developed, in which the energies corresponding to the rectangular plate domain and the hole domain were derived independently and the two independent coordinates were coupled by imposing kinematic relations. By matching the deflection condition imposed on the expressions, the relationship between the global axes and the local axes can be easily derived and then used to construct the mass and stiffness matrices. The numerical results show the efficacy of the proposed method.