Mathematical Study for the Rayleigh Wave Propagation in a Composite Structure with Piezoelectric Material

Subject Areas : Mechanics of Solids

Brijendra Paswan ¹ , P Singh ² , Sanjeev A Sahu ³

1 - Department of Mathematics,Guru Ghasidas Vishwavidyalaya Bilaspur, Chhattisgarh-495009, India
2 - Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines) Dhanbad-826004, India---- Department of Mathematics,Buddha Post Graduate College, Kushinagar (Affiliated-DDU Gorakhpur University, Gorakhpur), Uttar Pradesh-274403, India
3 - Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines) Dhanbad-826004, India

Received: 2023-02-12 Accepted : 2023-04-03 Published : 2023-06-01

Keywords: Frequency equation, Corrugation, Generalized Rayleigh-type wave, Piezoelectricity, Initial stress,

Abstract :

The undulated characteristics of the irregular boundaries in the layered structure with piezoelectric materials generate some prominent effects on wave propagation. On the other hand, initial stress in the layered structure also play an important role in velocity characterization of the surface seismic waves. In light of the above, this paper studies the Rayleigh-type wave propagation in a composite structure with piezoelectric materials. Mathematical expressions for the mechanical displacement and electric potential function are obtained for both the piezoelectric layer and elastic substrate with the aid of coupled electromechanical field equations. Frequency equations for the waves are derived for both electrically open and short cases. The effects of the corrugation parameters, initial stress, piezoelectric constant, dielectric constant and thickness of the piezoelectric layer on the phase velocity of Rayleigh-type wave are discussed graphically for both the electrically open and short cases. Numerical examples and discussions are made to exhibit the findings graphically. The validation of the problem is made with the classical result.

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