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

Abstract

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.

Bending and vibration study of carbon nanotubes reinforced functionally graded smart composite beams

“…Rafiee et al [12] examined thermal bifurcation buckling of CNT reinforced piezoelectric composite beams and concluded that frequency increases with higher CNT volume fraction. Yasin et al [13] performed dynamic study of smart FG beams by FE method using an efficient layer wise theory. They observed splitting of the piezoelectric material surface and the natural frequency is marginally increased for open circuit condition which is not affected in close circuit condition.…”

On the Vibration Analysis of Rotating Piezoelectric Functionally Graded Beams Resting on Elastic Foundation with a Higher-Order Theory

“…Larkin and colleagues [9] used the modified couple stress theory to investigate the impact of small-scale phenomena on the natural frequencies and power density of macro-to nanoscale functionally graded energy harvesters with beam lengths ranging from 62.5 mm to 6.25 m. They found that the natural frequencies and power density of the harvesters were affected by small-scale phenomena. A two-node efficient finite element model combining layerwise mechanics was used by Yasin and colleagues [10] to assess the active vibration stabilization of piezoelectric functionally graded beams. A functionally graded porous piezoelectric sandwich nanobeam reinforced by graphene platelets was investigated by Chen et al [11] using the Euler-Bernoulli beam theory and a differential quadrature technique in order to capture the effect of flexoelectricity on the vibration responses of the nanobeam.…”

Finite Element Analysis of Carbon Nanotubes Reinforced Smart Functionally Graded Beam

“…Vodenitcharova and Zhang [11] performed buckling and bending analysis of nanocomposite beam made of single wall CNT. Yasin et al [12] performed dynamic analysis of smart FG beam by FEM using an efficient layer wise theory. They observed that splitting of the piezoelectric material surface increases the natural frequency for open circuit condition but not effective in close circuit condition.…”