Natural Frequencies and Mode Shapes of a Square Plate with Discontinuous Boundary Conditions.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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The natural frequencies and mode shapes are theoretically determined for a simply supported square plate with discontinuous boundary conditions created by clamping segments of the boundary. Two different clamping configurations are investigated 1 partial clamping at the end of one edge, and 2 partial clamping on opposite edges. Satisfying the conditions of clamping leads to a Fredholm integral equation of the first kind for the first clamping configuration and a system of integral equations for the second configuration. The frequencies are found by approximating the integral equations with a finite set of homogeneous algebraic equations and insisting that this set have a nontrival solution. Author