Invariance of Eigenfrequencies and Eigenmodes Under Geometric Transformation in Elongated Elastic Structures

Abstract

The problem of transformation optics for longitudinal and flexural waves in monodimensional elastic systems is analyzed. System of finite dimensions are considered and it is shown that, under appropriate interface conditions, eigenfrequencies in finite systems remain unchanged while eigenmodes can be tuned depending on the applied geometric transformation. Eigenfrequency analysis can be used in cloaking problem in order to demonstrate the quality of the cloak.