Natural Frequencies of Membranes and Plates with Slightly Noncircular Boundaries.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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A theoretical study was made to determine whether or not the first natural frequencies of noncircular membranes and plates could be obtained using regular perturbation theory. The boundary equation of the noncircular membrane or plate is given by a chosen circular radius plus a term which represents the deviation of the noncircular boundary from a circle. The mode shape of free vibration for the noncircular membrane or plate is assumed to be represented by an asymptotic series which contains the mode shape for a circular membrane or plate plus additional terms of decreasing magnitude. Boundary conditions are imposed on the resulting expressions and through Taylor series expansions about the circular radius, a characteristic equation for frequency is obtained for the noncircular membrane or plate. The correspondence between the term of the boundary expression giving the noncircularity of the membrane or plate and any general shape varying from circular was established. Specific values of the term are given for an ellipse and a square. Author