Abstract
An analytical method of predicting the mode shapes and natural frequencies of vibration for continuous structures with elastic edge constraints is presented. The method consists of formulating dynamic edge receptances for the structure using classical solution techniques and matching the receptance of the structure with the receptance of the constraining boundary. The technique is illustrated by the solution of a beam and a circular plate with elastic boundaries and with boundary damping. A discussion is presented giving the influence of the boundary conditions on the vibration of the structure. These examples show numerically the effect of elasticity of the support on the resonant frequencies and mode shapes of the structure. Parameters are obtained which indicate when one may assume simply supported or clamped boundaries for the actual case of elastic boundaries without introducing large errors in the natural frequency or mode shape.
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