Abstract
The purpose of this paper is to present a general theory for analysis of the effect of initial geometrical imperfections on vibration frequencies of undamped, conservatively loaded, linear elastic beam and shell structures. The theory will be restricted to single mode vibrations with imperfections in the same shape as the vibration modes. The mathematical tool is a perturbational procedure developed with the aid of the principle of virtual work. The approach is illustrated by applications to beams, plates and axisymmetric shell structures. The examples show that the vibration frequency of these structures may be significantly raised or lowered due to imperfections.
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