Vibration of arbitrarily shaped membranes with elastical supports at points
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This paper presents a new method for solving the vibration of arbitrarily shaped membranes with elastical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.
KeywordsMathematical Modeling Exact Solution Linear Relationship External Force Industrial Mathematic
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