Free in-plane vibration of isotropic non-rectangular plates

A numerical study for the free in-plane vibration of non-rectangular plate is presented in this paper. The plate is defined by four curved boundaries using eight points and natural co-ordinates to map the geometry. The displacement nodes are introduced at the boundary of the plate as well as inside the perimeter. Each displacement node has two degrees of freedom and much higher order polynomials than the ones used for the geometric representation are used to represent the displacement fields. Using the energy functional, the matrix equation is obtained and solved for natural frequencies and associated mode shapes. Numerical results are calculated first for rectangular plates with three sets of boundary conditions and then compared with the data published in the literature by other researchers. Additional results are also presented and discussed in this paper for the in-plane vibration of rhombic and circular–annular–sector plates.