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Interaction of acoustic waves and piezoelectric structures
Author(s) -
Chkadua George,
Natroshvili David
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3210
Subject(s) - helmholtz equation , mathematics , sobolev space , partial differential equation , mathematical analysis , bounded function , domain (mathematical analysis) , hyperbolic partial differential equation , wave equation , elliptic partial differential equation , boundary value problem , uniqueness
In the paper, we investigate the basic transmission problems arising in the model of fluid‐solid acoustic interaction when a piezo‐ceramic elastic body ( Ω + ) is embedded in an unbounded fluid domain ( Ω − ). The corresponding physical process is described by boundary‐transmission problems for second order partial differential equations. In particular, in the bounded domain Ω + , we have 4 × 4 dimensional matrix strongly elliptic second order partial differential equation, while in the unbounded complement domain Ω − , we have a scalar Helmholtz equation describing acoustic wave propagation. The physical kinematic and dynamic relations mathematically are described by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations, the uniqueness and existence theorems are proved in Sobolev–Slobodetskii spaces. Copyright © 2014 John Wiley & Sons, Ltd.