Open AccessParametric vibrations of piezoelectric viscoelastic cylindrical panels taking into account transverse shear deformations
Author(s) -
В. І. Козлов,
Liubov Zinchuk
Publication year - 2021
Publication title -
progresivna tehnìka, tehnologìâ ta ìnženerna osvìta
Language(s) - English
Resource type - Journals
ISSN - 2409-7160
DOI - 10.20535/2409-7160.2021.xxii.239022
Subject(s) - linearization , parametric statistics , mathematical analysis , vibration , viscoelasticity , piezoelectricity , dissipation , mechanics , mathematics , classical mechanics , physics , nonlinear system , acoustics , statistics , quantum mechanics , thermodynamics
The paper presents a numerical-analytical approach to solving problems of parametric vibrations of layered hinged piezoelectric viscoelastic cylindrical panels under electromechanical harmonic loading. The mathematical model is constructed using mechanical hypotheses about layer-by-layer approximation of shear deformations by quadratic functions on the thickness of panel, which are supplemented by adequate hypotheses on the distribution of electric field quantities when the components of the electric field strength vector and the normal component of the electric induction vector are different from zero. The dissipative properties of materials are taken into account on the basis of the theory of linear viscoelectric elasticity. To solve the problems, a technique based on the use of the variation principle and the representation of the required quantities in the form of decomposition into double trigonometric series has been developed. This makes it possible to reduce the considered problems to Mathieu-Hill-type equations taking into account energy dissipation, which are solved by the method of harmonic linearization, which allows to determine the boundaries of the regions of dynamic instability.