Piezoelectric Beam Element Research Articles

Laminated piezoelectric beam element for dynamic analysis of piezolaminated smart beams and GA-based LQR active vibration control

This paper presents an accurate two-noded laminated piezoelectric beam element for the dynamic analysis and active vibration control of laminated composite beams with piezoelectric layers. A refined third-order shear deformation plate theory is used to model the kinematics, and a piecewise linear interpolation is used to characterize the electrical potential. The equations of motion are derived from Hamilton’s principle. The quasi-conforming element technique is adopted to evaluate the explicit element stiffness matrix. The resulting two-noded piezolaminated beam element is free from shear locking and the numerical integration. Linear Quadratic Regulator (LQR) control scheme is used for the active vibration control and Genetic Algorism (QA) is employed to determine the optimal weighting matrix used in the control performance index. The laminated piezoelectric beam element is validated by numerical examples. The numerical results show that present laminated piezoelectric beam element is very accurate in dynamic analysis of laminated piezoelectric beams and it is an effective strategy to use QA to merely evaluate the optimal weighting matrix for the vibration control performance by fixing the weighting matrix for the control input cost as an identity matrix in the LQR-based active vibration control.

Electromechanical properties of Boron Nitride Nanotube: Atomistic bond potential and equivalent mechanical energy approach

We present a molecular mechanics-based approach to model the isolated zigzag BNNTs bonds by an (energy-)equivalent piezoelectric beam element. The harmonic DREIDING force field is employed for bonded and nonbonded interatomic interactions. To investigate the effectiveness of the proposed method we predict the elastic modulus and piezoelectric coefficients of BNNTs and demonstrate good accuracy compared to quantum mechanics predictions. Subsequently, we study the influence of some input parameters such as the tube diameter, aspect ratio and chirality. Finally, our approach is validated by comparison to data from the literature.

A locking-free coupled polynomial Timoshenko piezoelectric beam finite element

Purpose – Piezoelectric extension mode smart beams are vital part of modern control technology and their numerical analysis is an important step in the design process. Finite elements based on First-order Shear Deformation Theory (FSDT) are widely used for their structural analysis. The performance of the conventional FSDT-based two-noded piezoelectric beam formulations with assumed independent linear field interpolations is not impressive due to shear and material locking phenomena. The purpose of this paper is to develop an efficient locking-free FSDT piezoelectric beam element, while maintaining the same number of nodal degrees of freedom. Design/methodology/approach – The governing equations are derived using a variational formulation to establish coupled polynomial field representation for the field variables. Shape functions based on these coupled polynomials are employed here. The proposed formulation eliminates all locking effects by accommodating strain and material couplings into the field interpolation, in a variationally consistent manner. Findings – The present formulation shows improved convergence characteristics over the conventional formulations and proves to be the most efficient way to model extension mode piezoelectric smart beams, as demonstrated by the results obtained for numerical test problems. Originality/value – To the best of the authors’ knowledge, no such FSDT-based finite element with coupled polynomial shape function exists in the literature, which incorporates electromechanical coupling along with bending-extension and bending-shear couplings at the field interpolation level itself. The proposed formulation proves to be the fastest converging FSDT-based extension mode smart beam formulation.

Geometric Effects on the Accuracy of Euler-Bernoulli Piezoelectric Smart Beam Finite Elements

Numerical analysis of piezoelectric smart beams plays an important role in the design of smart beam based control systems. In general, smart beams are thin and Euler-Bernoulli piezoelectric beam element is widely used for their structural analysis. Accuracy of Euler-Bernoulli piezoelectric beam element depends on the appropriate assumptions for electric potential involved in the formulation. Most of the Euler-Bernoulli piezoelectric beam finite elements available in the literature assume linear through-thickness potential distribution. It is shown that the accuracy of these conventional formulations varies with relative proportion of piezoelectric material in the total beam cross-section. This is attributed to the effect of the induced potential due to electromechanical coupling. The use of a number of sublayers in the mathematical modeling of each piezoelectric physical layer is shown to improve accuracy, at the cost of additional computational effort due to increased number of nodal electrical degrees of freedom. A more efficient way to handle the effects of induced potential is to use a consistent through-thickness electric potential derived from the electrostatic equilibrium equation. In addition to the conventional linear terms, this field consists of a higher order coupled term which effectively takes care of the geometric effects and produce accurate results, without the use of sublayers in modeling.

Design of Simultaneous Periodic Output Feedback Control for Smart Structures

This paper presents the problem of modelling simultaneous periodic output feedback control design to control the first two vibration modes of a flexible smart cantilever beam. The entire structure is modeled by finite element method using a piezoelectric beam element which includes a piezoelectric sensor and actuator dynamics. Simulation results demonstrate that a single controller can be employed to control the first two vibration modes for six different sensor/actuator locations along the beam. Application of simultaneous control introduces a redundancy in smart structure control.

Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators

Finite element modelling of laminated structures with distributed piezoelectric sensor and actuator layers and control electronics is considered in this paper. Beam, plate and shell type elements have been developed incorporating the stiffness, mass and electromechanical coupling effects of the piezoelectric laminates. The effects of temperature on the electrical and mechanical properties and the coupling between them are also taken into consideration in the finite element formulation. The piezoelectric beam element is based on Timoshenko beam theory. The plate/shell element is a nine-noded field-consistent element based on first order shear deformation theory. Constant-gain negative velocity feedback, Lyapunov feedback as well as a linear quadratic regulator (LQR) approach have been used for active vibration control with the structures subjected to impact, harmonic and random excitations. The influence of the pyroelectric effects on the vibration control performance is also investigated. The LQR approach is found to be more effective in vibration control with lesser peak voltages applied in the piezo actuator layers as in this case the control gains are obtained by minimizing a performance index. The application of these elements in high-performance, light-weight structural systems is highlighted.