Time-harmonic wave propagation in a pre-stressed compressible elastic bi-material laminate |
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Authors: | Priza Kayestha Anil C Wijeyewickrema Kikuo Kishimoto |
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Institution: | 1. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China;2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China;3. Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, China;4. Mechanical Engineering Department, Northwestern University, Evanston 60208, USA |
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Abstract: | The dispersive behaviour of time-harmonic waves propagating along a principal direction in a perfectly bonded pre-stressed compressible elastic bi-material laminate is considered. The dispersion relation which relates wave speed and wavenumber is obtained by formulating the incremental boundary value problem and the use of the propagator matrix technique. At the low wavenumber limit, depending on the pre-stress, both the fundamental mode and the next lowest mode may have finite phase speeds. For the higher modes which have infinite phase speeds in the low wavenumber region, an expression to determine the cut-off frequencies is obtained. At the high wavenumber limit, the phase speeds of the fundamental mode and higher modes tend to phase speeds of the surface wave, the interfacial wave or the limiting phase speed of the composite. For numerical examples, either a two-parameter compressible neo-Hookean material or a two-parameter compressible Varga material is assumed. |
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