Quasi-Green’s Function Method for Free Vibration of Simply-Supported Trapezoidal Shallow Spherical Shell

The idea of quasi Green's function method was clarified in detail by considering a free vibration problem of smiply-supported trapezoidal shallow spherical shell. A quasi-Green's function was established by using the fundamental solution and boundary equation of the problem. This function satis fies the homogeneous boundary condition of the problem. The mode shape differential equation of the free vibration problem of simply-supported trapezoidal shallow spherical shell is reduced to two smiultaneous Fredholm in tegral equations of the second kind by Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of in tegral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a non trivial solution in the numerically discrete algebraic equations derived from the in tegral equations. Numerical results show highaccuracy of the quasi-Green's function method.