Vibrations of Thin Plates--A New Approach.
MASSACHUSETTS UNIV AMHERST DEPT OF CIVIL ENGINEERING
Pagination or Media Count:
The investigation extends the method of Edge-Functions, previously employed only for elastostatic and electrostatic considerations, to the determination of natural frequencies and associated mode shapes of free vibration of thin elastic plates with a variety of boundary conditions. The Edge-Function technique essentially associates an independent coordinate system with every edge of the plate, and for every edge employs functions satisfying the governing plate vibration equations that rapidly decay with increasing distance from the plate boundary. Appropriate superposition of solutions stemming from all edges of the plate leads to an approximate representation of the time-dependent deflection surface. Results obtained by the elastodynamic Edge-Function investigation are shown to be in excellent agreement with existing results for natural frequencies and mode shapes of a rectangular plates subject to a wide variety of boundary conditions, including the case of a rectangular cantilever plate, and b parallelogram shaped plates with simply supported edges. Modified author abstract