Abstract
The recently-developed scaled boundary finite element method combines advantages of the finite element method and the boundary element method. Its governing differential equations in the radial coordinate can be readily solved analytically for elastostatics. For elastodynamics, however, an analytical solution to the non-homogeneous differential equations in frequency domain has so far only been obtained by a rather tedious series-expansion procedure. This paper develops a much simpler procedure to obtain such an analytical solution using the Frobenius method. The steady-state frequency response of a square plate subjected to harmonic excitation is calculated using both the new procedure and the finite element method to validate the procedure. It is shown that the new procedure leads to comparable results to the finite element method, but requires only a fraction of the degrees of freedom.