Recent development in modeling and analysis of functionally graded materials and structures

The present paper addresses developing the Dynamic Stiffness Method (DSM) for natural frequency analysis of functionally graded beam with piezoelectric patch based on the Timoshenko beam theory and power law of material grading. Governing equations and general solution of free vibration are conducted for the beam element with piezoelectric layer that is modelled as a homogeneous Timoshenko beam. The obtained solution allows establishing dynamic stiffness matrix for modal analysis of FGM beam with bonded piezoelectric distributed sensors/actuators. Effect of thickness and position of the smart sensors/actuators and material parameters on natural frequencies is studied with the aim for dynamic testing and health monitoring of FGM structures. The theoretical developments are validated and illustrated by numerical examples.

Section: Introductionmentioning

confidence: 99%

Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Khiem

Hai

Huong

2020

“…In recent few decades, FGM materials receives significant research interest due to decreased jumps in inplane stresses unlike the laminated composites and better thermal response. Studies related to synthesis, modelling and analysis of FGM structures can be seen in state of the art reviews (Birman andByrd 2007, Gupta andTalha 2015). We present review studies related to modelling and analysis of smart FGM structures related to active shape and vibration control.…”

Section: Introductionmentioning

confidence: 99%

Finite element model based on an efficient layerwise theory for dynamics and active vibration control of smart functionally graded beams

Yasin

Prakash

Khan

2020

In this work, we present a two-noded efficient finite element (FE) model incorporating the layer-wise mechanics for the dynamics and active vibration control of smart functionally graded (FG) beams. The material properties in the FG beam are assumed to vary smoothly in the thickness direction according to power law variation. The effective properties are computed using Mori-Tanaka homogenization scheme. Electric potential profile in the electroded piezoelectric layers/patches is assumed quadratic across its thickness. The equations of motion are derived using extended Hamilton's principle. Due to the complex algebraic expressions involved in the effective properties of FG system, the inertia and stiffness parameters are computed numerically using six point Gauss integration method. To fulfill the convergence requirements for weak integration of various energy terms in the variational formulation, the transverse displacement is interpolated with Hermite interpolation function possessing C 1 -continuity while the inplane displacement, shear rotation and quadratic component of the electric potential are interpolated with linear Lagrangian functions of C 0 -continuity. The equipotential condition of the electroded piezoelectric sensors and actuators is conveniently modelled using electric node concept. The control system is designed for constant gain velocity feedback (CGVF), and optimal LQR and LQG control strategies for a reduced order model using state space approach. The control performance is studied for single-input-single-output (SISO) and multi-input-multi-output (MIMO) configurations under various excitations. The effect of material inhomogeneity on stability/instability of the closed-loop response in the CGVF control has been discussed.

“…Last few years, functionally graded materials (FGMs) have been explored because of their capacity to modify their mechanical behaviors by designing the material parameters with certain functional forms. And this material has been applied in many designing fields [4][5][6]. In this manner, with such appealing and viable points of interest, combing FGMs with piezoelectric materials creates functionally graded piezoelectric materials (FGPMs) with more thorough applications.…”

Section: Introductionmentioning

confidence: 99%

Revisiting the electroelastic solution for an FGPM thick-walled cylinder subjected to mechanical and electric loadings

Wang

Dui

Xin

2020

Theoretical analysis for an empty thick-walled FGPM cylinder exposed to electric and mechanical loadings are investigated. The cylinder is a composite material composed of PZT4 and PVDF and the volume fraction of PZT4 is given by the power law with three controllable parameters which can cover more complex circumstances. The hypergeometric equation of the radial displacement is acquired by utilizing the Voigt method, and the solutions of the stresses and the electric potential are obtained after solving the radial displacement. The method in this paper is appropriate for real functionally graded piezoelectric materials and can avoid assumptions about unknown overall material parameters appeared in previous references. Finally, the impacts of the parameter n in volume fraction of FGPM cylinder on mechanical and electric behaviors are examined. Furthermore, the distinction between the hoop stress and radial stress is discussed to decrease the pressure concentration in FGPM cylinder. Nomenclature a, b inner and outer radii r radial coordinate c(r) volume fraction of material A c 0 , k, n material parameters in the volume fraction c(r) p a , p b internal and external pressures j a , j b internal and external electric potentials C ijkl i (i=1, 2) elastic modulus of the component e mij i (i=1, 2) piezoelectric tensor modulus of the component k mk i (i=1, 2) dielectric modulus of the component u radial displacement j electric potential e , r i ( ) e q i ( ) radial and hoop strains of the component e , r e q average radial and hoop strains of the cylinder s , r i ( ) s q , i ( ) s z i ( ) radial, hoop, and axial stresses of the component s , r s q , s z average radial, hoop, and axial stresses of the cylinder E , r i ( ) D r i ( ) radial electric field and electric displacement of the component E , r D r average radial electric field and electric displacement of the cylinder a(r), b(r), d(r), g(r), f (r), h(r), k(r) functions related to the volume fraction c(r)