A free vibration analysis of piezo-electric beams via hierarchical one-dimensional finite elements

Abstract

In this article, several one-dimensional finite elements for the free vibration analysis of composite beams with piezo-electric layers or patches are presented. The displacement components and the electric potential are approximated above the cross section through Lagrange’s polynomials in a layer-wise sense. Thanks to a Unified Formulation, elements’ stiffness and mass matrices are derived in a general, nuclear form that does not depend upon the approximation order of the displacements and the electric potential over the cross section as well as the number of element nodes along the axial direction. Higher-order, layer-wise theories accounting for non-classical effects can be, therefore, straightforwardly formulated. Beam with full piezo-electric layers or piezo-patches are investigated. Results are given in terms of natural frequencies and electro-mechanical coupling coefficients of the bending and torsional modes. Several mechanical and electrical boundary conditions as well as stacking sequences are investigated. Comparison with three-dimensional finite element models is provided showing that the proposed class of finite elements is able to yield accurate results.

Optimization of rectifier circuits for a vibration energy harvesting system using a macro-fiber composite piezoelectric element

“…In most of the researches, the piezoelectric elements generate electricity using the movement of various things such as the human body [10][11][12][13] or wind [14,15]; however, these systems are not yet practical to use. In addition, the fundamental analysis [16][17][18] and design [5,[19][20][21] of vibration energy harvesting has also been studied intensively, as well as the circuit modeling of vibration energy generation based on the piezoelectric elements [22][23][24][25]. These two main factors are directly related to the efficiency of the electricity generated from the piezoelectric elements.…”

Finite element modelling to assess the effect of surface mounted piezoelectric patch size on vibration response of a hybrid beam

“…They used various higher-order and classical theories for the analysis and approximated the through the thickness displacement field in the form of a polynomial expansion. Koutsawa et al [13] presented 1D finite elements to attain the free vibration response of composite smart beams. They approximated displacements and electric potential using Lagrange's polynomials.…”

A smart composite-piezoelectric one-dimensional finite element model for vibration damping analysis

“…For this reason, two-dimensional laminate theories for shell-like structures, two-dimensional theories for piezoelectric plane stress analysis, and one-dimensional models for beam structures play an important role in the design and optimization step, because they allow to reduce the computational effort preserving a suitable level of accuracy (Alaimo et al, 2011; Carrera et al, 2011; Gopinathan et al, 2000; Kapuria et al, 2010). Alternatives are represented by one-dimensional beam theories that take advantage of Lagrange’s polynomials to approximate the distribution of displacements and electrical potential above the beam cross-section (Giunta et al, 2013; Koutsawa et al, 2013, 2014).…”