Vol. 16, No. 2, 2021

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Shear vertical waves in laminated coupled electro-mechanic materials with imperfect contact conditions at the interfaces

J. H. Cabanas, J. A. Otero, G. Monsivais, R. Rodríguez-Ramos and C. Stern

Vol. 16 (2021), No. 2, 123–137
Abstract

A dynamic model to study shear vertical waves in laminated coupled electro-mechanical materials is proposed. The mechanical imperfections at the interface between two materials or phases that constitute an heterogeneous medium are considered. The behavior of vertical transverse waves is analyzed by considering two types of imperfect contact. On the one hand, imperfect contact is taken into account through the motion of layers in the perpendicular direction to the interface. On the other hand, imperfect contact is considered through the motion of layers in a tangential direction to the interface. The layers are coupled through a spring obeying Hooke’s law. The degree of imperfection is incorporated through the magnitude of the spring’s elastic constant in both scenarios. The stress is proportional to the jump of the displacement vector at the layer interface and to the magnitude of the spring’s elastic constant. Dispersion relations for different volumetric fractions of the piezoelectric phase and different degrees of imperfection are obtained. Crossover regions are observed in the dispersion curves. Changes in the oscillation modes could be identified through the material displacements in these regions. Displacements within the composite material, used to describe the nature of the oscillations, are illustrated in some cases. Additionally, the perfect contact case is reproduced by solving the proposed model for large values of the spring’s elastic constant, showing a good agreement when compared with the solutions to models proposed by other authors. A comparison between theory and experimental results for the electromechanical coupling factor is presented. Finally, the experimental data for the coupling factor can be better explained by including the degree of imperfection through the model proposed in this work.

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Keywords
shear vertical waves, laminated piezocomposite, imperfect contact, dispersion curve, vibration modes
Milestones
Received: 26 June 2020
Revised: 16 October 2020
Accepted: 25 November 2020
Published: 6 June 2021
Authors
J. H. Cabanas
Escuela de Ingeniería y Ciencias, Departamento de Ciencias
Campus Ciudad de México
Tecnológico de Monterrey
Ciudad de México
Mexico
J. A. Otero
Escuela de Ingeniería y Ciencias, Departamento de Ciencias
Campus Estado de México
Tecnológico de Monterrey
Ciudad de México
Mexico
G. Monsivais
Instituto de Física, Departamento de Estado Sólido
Universidad Nacional Autonoma de Mexico
Ciudad de México
Mexico
R. Rodríguez-Ramos
Facultad de Matematica y Computación, Departamento de Matemática
Universidad de la Habana
Habana
Cuba
C. Stern
Departamento de Fìsica
Universidad Nacional Autonoma de Mexico
Facultad de Ciencias UNAM
Ciudad Universitaria
Ciudad de México
Mexico