Anti-plane time-harmonic Green's functions for a circular inhomogeneity in piezoelectric medium with a spring- or membrane-type interface |
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| Affiliation: | 1. Institute of Applied Mechanics, Tongji University, Shanghai 200092, China;2. Department of Bridge Engineering, State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, China;1. University of Porto, Faculty of Engineering, Department of Mechanical Engineering, Portugal;2. University of Aveiro, Department of Mechanical Engineering, Portugal;1. Engineering Department, Federal University of Lavras - UFLA, 37200-000 Lavras, MG, Brazil;2. Department of Computational Mechanics, Faculty of Mechanical Engineering, University of Campinas - UNICAMP, 13083-970 Campinas, SP, Brazil |
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| Abstract: | The present work focuses on the two-dimensional anti-plane time-harmonic dynamic Green's functions for a circular inhomogeneity immersed in an infinite matrix with an imperfect interface, where both the inhomogeneity and matrix are assumed to be piezoelectric and transversely isotropic. Two types of imperfect interface, the spring-type interface with electromechanical coupling and the membrane-type interface, are considered. The former type is often used to model the electromechanical damage along the interface while the latter is largely employed to simulate surface/interface effect of nano-sized inhomogeneity. By using the Bessel function expansions, explicit solutions for the electromechanical fields induced by a time-harmonic anti-plane line force and line charge located in an unbounded matrix as well as the circular inhomogeneity are respectively derived. The present solutions can recover the anti-plane Green's functions for some special cases, such as the dynamic or quasi-static Green's functions of piezoelectricity with perfect interface as well as the dynamic or quasi-static Green's functions of pure elasticity with imperfect interface. For detailed discussions, selected analytical results are presented. Dependence of the electromechanical fields on circular frequency as well as interface properties is examined. The size effect related to interfacial imperfection is also discussed. |
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| Keywords: | Dynamic Greens’ functions Piezoelectric composites Spring-type interface Membrane-type interface Size effect |
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