Wave propagation in rods with an exponentially varying cross-section — modelling and experiments

13th International Conference on Motion and Vibration Control; 12th International Conference on Recent Advances in Structural Dynamics

Kalkowski, Michal K.^1 ; Muggleton, Jen M.^1 ; Rustighi, Emiliano^1

University of Southampton, Highfield, Southampton

SO17 1BJ, United Kingdom^1

关键词: Analytical description;    Classical solutions;    Finite element simulations;    Infinite solids;    Longitudinal wave propagation;    Longitudinal waves;    Modelling and experiments;    Varying cross section;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/744/1/012036/pdf
DOI  :  10.1088/1742-6596/744/1/012036

来源: IOP

【 摘 要 】

In this paper we analyse longitudinal wave propagation in exponentially tapered rods from both a theoretical and an experimental perspective. The tapering introduces significant changes to the behaviour of the rod. The longitudinal wave does not propagate from zero frequency, its cut-off frequency depending on the coefficient in the exponent. The analytical description of this phenomenon is well established, however little experimental work has been published to date. After a brief review of the classical solution of the exponential rod equation, we derive a methodology allowing the wavenumbers to be estimated from a set of equally spaced dynamic responses. Our approach is verified numerically against a finite element simulation and validated experimentally, both showing very good agreement. To further explain the results and provide an outlook for future work, we present a finite element model of the tapered rod embedded in an infinite solid medium. We conclude with a discussion on the effects of the surrounding medium on the behaviour of the structure and resulting characteristic features of the wavenumber.