Green quasifunction method for free vibration of clamped thin plates

The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates. A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula. Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation. Two examples demonstrate the validity of the present method. Comparison with both the series solution and ANSYS finite-element solution shows fine agreement. The present method is a novel and effective mathematical one.