Free Vibration of Elastic Solids: Effect of Boundary Perturbation on Fundamental Frequencies
The objective of the paper is to study the effect of imperfections (such as cracks, cavities or inclusions) on dynamic characteristics of elastic solids. As an illustrative example, we consider in-plane vibrations of a two-dimensional elastic domain with a small cavity. We present results that indicate the effect of the geometry and location of the cavity on fundamental frequencies, and show that the change in frequency is specified by an integral characteristic that may have the same value for a certain class of defects. The latter implies that the solution of the inverse problem is not unique; one can find a certain class of cavities which produce the same change in frequency.
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- Movchan, A.B., and Movchan, N.V. (1995) Mathematical Modelling of Solids with Nonregular Boundaries. CRC Press.Google Scholar