1998 Volume 64 Issue 617 Pages 45-51
This paper deals with a method for analysis of the in-plane vibrations of plates. The in plane vibration is described as a plane stress problem with inertia forces. The governing equation can be reduced into two Helmholtz's equations which express the P- and S-waves respectively. The general solutions in the polar coordinates of the reduced equations can be obtained easily in terms of the Bessel functions. Boundary conditions are satisfied approximately at some discrete points on the edges of the plates. A frequency equation is derived in a determinant form. Natural frequencies of a square, a rectangular and a trapezoidal plate, with free edges, calculated by this method agree well with measured ones. Furthermore, boundary conditions of clamped edges and sliding edges are studied.
Transactions of the Society of Mechanical Engineers
Transactions of the Japan Society of Mechanical Engineers
Transactions of the Japan Society of Mechanical Engineers Series A
Transactions of the Japan Society of Mechanical Engineers Series B
TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C
TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B
TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A
