Finite Element Model of Smart Beams with Distributed Piezoelectric Actuators

The convergence characteristic of the conventional two-noded Euler-Bernoulli piezoelectric beam finite element depends on the configuration of the beam cross-section. The element shows slower convergence for the asymmetric material distribution in the beam cross-section due to 'material-locking' caused by extension-bending coupling. Hence, the use of conventional Euler-Bernoulli beam finite element to analyze piezoelectric beams which are generally made of the host layer with asymmetrically surface bonded piezoelectric layers/patches, leads to increased computational effort to yield converged results. Here, an efficient coupled polynomial interpolation scheme is proposed to improve the convergence of the Euler-Bernoulli piezoelectric beam finite elements, by eliminating ill-effects of material-locking. The equilibrium equations, derived using a variational formulation, are used to establish relationships between field variables. These relations are used to find a coupled quadratic polynomial for axial displacement, having contributions from an assumed cubic polynomial for transverse displacement and assumed linear polynomials for layerwise electric potentials. A set of coupled shape functions derived using these polynomials efficiently handles extension-bending and electromechanical couplings at the field interpolation level itself in a variationally consistent manner, without increasing the number of nodal degrees of freedom. The comparison of results obtained from numerical simulation of test problems shows that the convergence characteristic of the proposed element is insensitive to the material configuration of the beam cross-section.

“…The Euler-Bernoulli theory is used for which the field expressions are given as (Bendary et al, 2010):…”

Section: Mechanical Displacements and Strainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element

Sulbhewar

Raveendranath

2015

“…On the other hand, the distributed actuator element produces control forces/moments and restrains the undesirable structural vibrations through the converse piezoelectric phenomenon (Cady, (1946), Baileyand Hubbard (1985, Crawley (1987)). Recent literature reviews show that significant achievements have been obtained on distributed structural modelling, identification, and active vibration or shape control of smart beam, plate and shell structures integrated with spatially continuous piezoelectric sensor and actuator layers (Chee et al (2000), Sunar and Rao (1999), Saravanos and Heyliger (1995), Kapuria and Yasin(2010), Bendary et al (2010), Kerur and Ghosh(2011)). In the following paragraph, a brief overview regarding key contributions on active vibration control of smart composite beams, integrated (surface-bonded or embedded) with distributed piezoelectric sensor/actuator layers, is presented.…”

Section: Introductionmentioning

confidence: 99%

“…The discretization was carried out using finite elements, and the simulations were performed in the MATLAB environment demonstrating that the robust H2 and H∞-controllers can achieve effective suppression of low-frequency disturbed vibrations of the composite beam while they preserve the efficiency in case of signal excessiveness due to high-frequency modes. Bendary et al (2010) used the classical laminate (Euler-Bernoulli) beam theory to present a finite element model for the static and dynamic analysis of an intelligent advanced beam structure integrated with a distributed piezoelectric actuator layer and subjected to axial/transverse mechanical loads in addition to electrical load. The beam was composed of an isotropic and/or anisotropic substrate, completely or partially covered with the piezoelectric actuator layer.…”

Section: Introductionmentioning

confidence: 99%

Active vibration control of an arbitrary thick piezolaminated beam with imperfectly integrated sensor and actuator layers

Hasheminejad

Vahedi

Hoshangi

2014

A spatial state-space formulation based on the linear twodimensional piezoelasticity theory and involving local/global transfer matrices is applied to investigate the active vibration suppression of a simply supported, arbitrarily thick, orthotropic elastic beam, imperfectly integrated with spatially distributed piezoelectric actuator and sensor layers on its top and bottom surfaces, respectively. A linear spring-layer model is adopted to simulate the bonding imperfections between the host structure and the piezoelectric layers. To assist control system design, system identification is conducted by applying a frequency domain subspace approximation method with N4SID algorithm based on the first five structural modes of the system. The state space model is constructed from system identification and used for state estimation and development of control algorithm. A linear quadratic Gaussian (LQG) optimal controller is subsequently designed and simulated based on the identified model in order to actively control the response of the smart structure in both frequency and time domains.

“…Closed form solutions for axial strain, curvature and natural frequencies based on Euler-Bernoulli beam theory have been provided by Abramovich and Pletner (1997). Plate and beam elements based on classical laminate theory, given by Hwang and Park (1993) and Bendary et al (2010) can be used for static and dynamic analyses of thin smart beams. However, all these models based on classical theory neglect transverse shear and hence are inadequate for shorter and thick beams (Benjeddou et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

An accurate novel coupled field Timoshenko piezoelectric beam finite element with induced potential effects

Sulbhewar

Raveendranath

2014

An accurate coupled field piezoelectric beam finite element formulation is presented. The formulation is based on First-order Shear Deformation Theory (FSDT) with layerwise electric potential. An appropriate through-thickness electric potential distribution is derived using electrostatic equilibrium equations, unlike conventional FSDT based formulations which use assumed independent layerwise linear potential distribution. The derived quadratic potential consists of a coupled term which takes care of induced potential and the associated change in stiffness, without bringing in any additional electrical degrees of freedom. It is shown that the effects of induced potential are significant when piezoelectric material dominates the structure configuration. The accurate results as predicted by a refined 2D simulation are achieved with only single layer modeling of piezolayer by present formulation. It is shown that the conventional formulations require sublayers in modeling, to reproduce the results of similar accuracy. Sublayers add additional degrees of freedom in the conventional formulations and hence increase computational cost. The accuracy of the present formulation has been verified by comparing results obtained from numerical simulation of test problems with those obtained by conventional formulations with sublayers and ANSYS 2D simulations.