A Viscoelastic Sandwich Finite Element Model for the Analysis of Passive, Active and Hybrid Structures (original) (raw)
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A finite element model for the analysis of viscoelastic sandwich structures
Computers & Structures, 2011
In this work a finite element model is developed for vibration analysis of active-passive damped multilayer sandwich plates, with a viscoelastic core sandwiched between elastic layers, including piezoelectric layers. The elastic layers are modelled using the classic plate theory and the core is modelled using the Reissener-Mindlin theory. The finite element is obtained by assembly of N ''elements'' through the thickness, using specific assumptions on the displacement continuity at the interfaces between layers. The lack of finite element plate-shell models to analyse structures with passive and active damping, is the principal motivation for the present development, where the solution of some illustrative examples and the results are presented and discussed.
International Journal for Numerical Methods in Engineering, 2001
This work, in two parts, proposes, in this ÿrst part, an electromechanically coupled ÿnite element model to handle active-passive damped multilayer sandwich beams, consisting of a viscoelastic core sandwiched between layered piezoelectric faces. The latter are modelled using the classical laminate theory, whereas the face=core=face system is modelled using classical three-layers sandwich theory, assuming Euler-Bernoulli thin faces and a Timoshenko relatively thick core. The frequency-dependence of the viscoelastic material is handled through the anelastic displacement ÿelds (ADF) model. To make the control system feasible, a modal reduction is applied to the resulting ADF augmented system. Validation of the approach developed in this part is presented in Part 2 of the paper together with the hybrid damping performance analysis of a cantilever beam.
Analysis of Active-Passive Plate Structures Using a Simple and Efficient Finite Element Model
Mechanics of Advanced Materials and Structures, 2011
In this work a simple and efficient finite element model is developed for vibration analysis of active-passive damped multilayer sandwich plates, with a viscoelastic core sandwiched between elastic layers, including piezoelectric layers. The elastic layers are modeled using the classic plate theory and the core is modeled using Reddy's third-order shear deformation theory. The finite element is obtained by assembly of N "elements" through the thickness, using specific assumptions on the displacement continuity at the interfaces between layers. The finite element model is a non-conforming triangular plate/shell element with 24 degrees of freedom for the generalized displacements, and one electrical potential degree of freedom for each piezoelectric element layer, which can be surface bonded or embedded in the laminate. To achieve a mechanism for the active control of the structural dynamics response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers. To calculate the dynamic response of active-passive damped multilayer sandwich plate structures in time domain the Newmark method is considered. Frequency domain response is also calculated and compared with alternative solutions. For both responses, a finite element code is implemented. The model is applied in the solution of some illustrative examples and the results are presented and discussed.
Smart Materials and Structures, 2002
We have used quasi-static equations of piezoelectricity to derive a finite element formulation capable of modelling two different kinds of piezoelastically induced actuation in an adaptive composite sandwich beam. This formulation is made to couple certain piezoelectric constants to a transverse electric field to develop extension-bending actuation and shear-induced actuation. As an illustration, we present a sandwich model of three sublaminates: face/core/face. We develop a control scheme based on the linear quadratic regulator/independent modal space control (LQR/IMSC) method and use this to estimate the active stiffness and the active damping introduced by shear and extension-bending actuators. To assess the performance of each type of actuator, a dynamic response study is carried out in the modal domain. We observe that the shear actuator is more efficient in actively controlling the vibration than the extension-bending actuator for the same control effort.
Active control of adaptive laminated structures with bonded piezoelectric sensors and actuators
Computers & Structures, 2004
A finite element formulation for active vibration control of thin plate laminated structures with integrated piezoelectric layers, acting as sensors and actuators, is presented in this paper. The finite element model is a nonconforming single-layer triangular plate/shell element with 18 degrees of freedom for the generalized displacements and one electrical potential degree of freedom for each piezoelectric element layer. The model is based on the Kirchhoff classical laminated theory, and can be applied to plate and shell adaptive structures.
Journal of Sound and Vibration, 2005
An exact three-dimensional solution is obtained for the cylindrical bending vibration of simply supported laminated composite plates with an embedded piezoelectric shear actuator. The piezoelectric actuator, which is poled in the longitudinal direction, will induce a transverse shear strain in the hybrid laminate when it is subjected to an electric field in the thickness direction. Suitable displacement and electric potential functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the equations that govern the steady-state vibrations of the hybrid laminate to a set of coupled ordinary differential equations, which are solved by employing the power series method. Natural frequencies, mode shapes, displacements, electric potential and stresses are presented for three-layer hybrid laminates consisting of a piezoelectric shear actuator sandwiched between fiber-reinforced composite layers. Active vibration damping is implemented using either a position feedback controller or velocity feedback controller. Frequency response curves for different controller frequencies, controller damping ratio and feedback gain demonstrate that the embedded shear actuator can be used for active damping of the fundamental flexural mode. In addition, it is shown that vibration suppression of thickness modes is also feasible using a shear actuator.
Journal of Intelligent Material Systems and Structures, 2007
Piezoelectric materials are widely used as distributed means for sensing and/or actuating a structure's response, by either bonding them to a structure's surfaces or embedding them into a laminate structure. Surface-mounted actuators are normally poled in thickness direction so that they work in the extension mode, while embedded actuators are more effective when poled in the longitudinal direction and thus working in the thickness-shear mode. It has been shown that embedded shear actuators may lead to less problems of actuators damage and debonding, minor dependence on actuators position and length and smaller stresses in the actuators. It has also been observed that surface-mounted extension actuators are generally more effective for very flexible host structures while embedded shear actuators are more effective for stiffer structures. These and other distinctive features of extension and shear actuators may be exploited to study their simultaneous use and to design a combined extension-shear actuated beam. Hence, this work presents the results of a numerical investigation of active vibration control using simultaneous extension and shear piezoelectric actuation for a clamped-clamped sandwich beam. The analysis is carried out using a laminate/sandwich beam finite element model combined to an optimal control with limited input. Results show that simultaneous use of extension and shear actuators is very promising since their actuation mechanisms are complimentary. In particular, a good damping performance was obtained over an increased frequency-range with very localized actuators.
Active Control of Laminated Plates Using a Piezoelectric Finite Element
Mechanics of Advanced Materials and …, 2008
The aim of this work is to develop a simple and very efficient tool, to simulate the active control of laminated plates, and in a next step, to optimize the geometry and number of sensors and actuators. A new piezoelectric Finite Element is presented. It is an eight node plate with one electrical potential degree of freedom for each interface of piezoelectric layers. The usual FSDT theory is combined with a "field compatibility" methodology to avoid the transverse shear locking for thin plates. A LQR control method including a state observer is used to compute the control. Four examples are presented. The quasi-static correction and the use of collocated sensor/actuator are discussed.
Exact solution for rectangular sandwich plates with embedded piezoelectric shear actuators
2001
An exact solution is obtained for the three-dimensional deformations of simply supported laminated rectangular thick plates with embedded shear mode piezoelectric actuators, subjected to mechanical and electrical loading on the upper and lower surfaces. Each layer of the laminate is made of either an orthotropic elastic material or a piezoelectric material whose poling direction lies in the plane of the plate, with perfect bonding between the adjoining layers.
2020
An active method of vibration control of a smart sandwich plate (SSP) using discrete piezoelectric patches is investigated. In order to actively control the SSP vibration, the plate is equipped with three piezoelectric patches that act as actuators. Based on the classical plate theory, a finite element model with the contributions of piezoelectric sensor and actuator patches on the mass and stiffness of the sandwich plate was developed to derive the state space equation. LQR control algorithm is used in order to actively control the SSP vibration. The accuracy of the present model is tested in transient and harmonic loads. The applied piezoelectric actuator provides a damping effect on the SSP vibration. The amplitudes of vibrations and the damping time were significantly reduced when the control is ON.