Natural vibration study on rectangular plates with a line hinge and various boundary conditions

A discrete method is proposed for analyzing the natural vibration problem of 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. The Green function of the deflection problem 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 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.