Eigenfrequencies of a 3D piezoelectric cylinder

Gunnar Johansson; Anders Bostrom

doi:10.1117/12.388805

19 June 2000 Eigenfrequencies of a 3D piezoelectric cylinder

Gunnar Johansson, Anders Bostrom

Proceedings Volume 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures; (2000) https://doi.org/10.1117/12.388805
Event: SPIE's 7th Annual International Symposium on Smart Structures and Materials, 2000, Newport Beach, CA, United States

Abstract

The free vibrations of a solid 3D piezoelectric cylinder of class 6 mm are investigated. First the equations of motion are reformulated with the help of three scalar potentials. This decouples the SH waves and is done in a way which is coordinate-free in the transverse coordinates. Next the modes in an infinite plate are derived in cylindrical coordinates, and this involves Bessel functions in the radial direction. A superposition of these modes is then used to form the eigenmodes of the cylinder with a finite radius. The remaining lateral boundary conditions give a determinantal condition for the eigenfrequencies. Numerical results are given and are compared with previous published results.

Citation Download Citation

Gunnar Johansson and Anders Bostrom "Eigenfrequencies of a 3D piezoelectric cylinder", Proc. SPIE 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures, (19 June 2000); https://doi.org/10.1117/12.388805

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