1. Forced vibration analysis of composite beams with piezoelectric layers based on the variable separation method
- Author
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Laurent Gallimard, María Infantes, Olivier Polit, Philippe Vidal, Rafael Castro-Triguero, Universidad de Granada = University of Granada (UGR), Laboratoire Energétique Mécanique Electromagnétisme (LEME), Université Paris Nanterre (UPN), and Universidad de Córdoba = University of Córdoba [Córdoba]
- Subjects
PGD ,Frequency response ,Iterative method ,Mathematical analysis ,[SPI.MECA.VIBR]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph] ,02 engineering and technology ,Finite Element ,021001 nanoscience & nanotechnology ,Variable separation ,Smart structures ,Finite element method ,Vibration ,Forced vibration ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Dynamic problem ,Frequency domain ,Ceramics and Composites ,Harmonic ,Boundary value problem ,Piezoelectric beam ,0210 nano-technology ,Civil and Structural Engineering ,Mathematics - Abstract
International audience; This paper proposes a new strategy based on the proper generalized decomposition method to solve the forced vibration problem for bi-dimensional piezoelectric composite beams. The approach considers a classical harmonic space-frequency description of the dynamic problem and redefines it by approximating the displacement and electric potential fields as a sum of separated functions of x (beam axis coordinate), z (thickness coordinate) and (load frequency). The methodology consists in an iterative algorithm that solves three one-dimensional linear problems at each iteration. The result is a 2D solution in frequency domain with 1D computational complexity. Several numerical tests with wide range of slenderness ratios are considered in order to assess the validity of the method. Moreover, a study of different combinations of boundary conditions is carried out. The results in terms of modal parameters and frequency response functions are analysed and compared with exact elasticity solution and finite element simulations.
- Published
- 2021
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