Vibration of a Free Rectangular Parallelepiped

Abstract

A series solution of the general equations of linear elasticity is used to determine accurate natural frequencies for the vibrations of a rectangular parallelepiped with traction-free surfaces. The series solution is found to converge to accurate frequencies with the use of very few terms. Resulting frequences are tabulated for comparison with previous experimental results and are shown graphically for comparison with elementary rod, beam, and plate solutions. The comparisons with elementary solutions show good agreement, and comparisons with the experiment results shows excellent agreement.