Free vibration analysis of shear deformable rectangular plates with a line hinge

Abstract

A discrete method is proposed for analysing the natural vibration problem of shear deformable rectangular plates with a line hinge. The fundamental differential equations and the solutions of these equations are derived for two parts of the plate, which are obtained by dividing the plate along the line hinge. By transforming these equations into integral equations, and using numerical integration and the continuous conditions along the line hinge, the solutions of the whole plate can be expressed by the unknown quantities on the boundary and the quantities of the rotation along the hinge. Green function which is the solution of deflection of the bending problem of plate is used to obtain the characteristic equation of the free vibration. The effects of the position of the line hinge, the aspect ratio, the thickness-to-length ratio and the boundary condition on the natural frequency parameters are considered. By comparing the numerical results obtained by the present method with those previously published, the efficiency and accuracy of the present method are investigated.