Analytical study and numerical experiments of true and spurious eigensolutions of free vibration of circular plates using real-part BIEM

Abstract

Following the success of the CHEEF method [Chen IL, Chen JT, Kuo SR, Liang MT. A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method. J Acoust Soc Am 2001; 109(3):982–98] and the real-part BEM [Kuo SR, Chen JT, Huang CX. Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real-part dual BEM. Int J Numer Methods Eng 2000; 48:1401–22] for solving the membrane eigenproblem, we extend to the plate problem in this paper. The boundary integral equation method (BIEM) using only the real-part kernel instead of the complex-valued kernel is employed to solve the plate eigenproblem for saving half effort in computation. The spurious eigenvalue that resulted due to insufficient constraint is examined. To deal with this problem, a combined Helmholtz exterior integral equation formulation method (CHEEF) is employed to provide sufficient constraints to filter out spurious eigenvalues. The constraint equations of the transverse displacement, normal derivative and tangent derivative for the exterior collocating points are derived. If these constraint equations are properly chosen, one collocating point was sufficient to filter out all the spurious eigenvalues easily and efficiently, even for the repeated spurious eigenvalues. Finally, numerical experiments are performed to verify the analytical results.