<p>This paper develops a forced-vibration analysis due to a time-harmonic oblique force acting on a perfectly bonded bi-layered piezoelectric plate resting on a rigid half-plane. Within the framework of the three-dimensional linearized theory of elasticity for solids under initial stress (TLTESIS), each layer is independently subjected to normal biaxial initial forces along horizontal directions. In this scope, the governing equations of motion and their boundary-contact conditions are derived via the piece-wise homogeneous body model. Based on the principles of virtual work and the calculus of variation, the three-dimensional finite element model (3D-FEM) is derived to investigate the dynamic behavior of the plate. Numerical comparisons with the available literature and a relative error analysis prove that the analysis model and the obtained algorithm agree well with the previous ones. Next, the influences of aspect ratio, thickness ratio, initial stress parameter, etc., on the frequency response of the plate are investigated. The results prove that while the angle between the force and the free surface directly affects the resonant mode of the plate, the one between the force projection and the horizontal axis has an indirect relation to that mode. Initial tensile stress and a larger aspect ratio enhance stability by delaying resonance, while compressive stress and increased thickness reduce the stability. The results provide key guidance for designing materials in a pre-stressed piezoelectric medium.</p>

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Dynamic analysis of the forced response of a bi-layered piezoelectric plate in an initial stress state under an inclined harmonic force

  • Ahmet Daşdemir

摘要

This paper develops a forced-vibration analysis due to a time-harmonic oblique force acting on a perfectly bonded bi-layered piezoelectric plate resting on a rigid half-plane. Within the framework of the three-dimensional linearized theory of elasticity for solids under initial stress (TLTESIS), each layer is independently subjected to normal biaxial initial forces along horizontal directions. In this scope, the governing equations of motion and their boundary-contact conditions are derived via the piece-wise homogeneous body model. Based on the principles of virtual work and the calculus of variation, the three-dimensional finite element model (3D-FEM) is derived to investigate the dynamic behavior of the plate. Numerical comparisons with the available literature and a relative error analysis prove that the analysis model and the obtained algorithm agree well with the previous ones. Next, the influences of aspect ratio, thickness ratio, initial stress parameter, etc., on the frequency response of the plate are investigated. The results prove that while the angle between the force and the free surface directly affects the resonant mode of the plate, the one between the force projection and the horizontal axis has an indirect relation to that mode. Initial tensile stress and a larger aspect ratio enhance stability by delaying resonance, while compressive stress and increased thickness reduce the stability. The results provide key guidance for designing materials in a pre-stressed piezoelectric medium.