A phenomenological model of active constrained layers

An analysis of interlaminar stresses in active constrained layer damping treatments

Active constrained layer damping treatments promise to be an effective means of vibration suppression in structures. Basically, the concept consists in either replacing or augmenting the constraining layer of a constrained viscoelastic material with piezoceramic actuators in an attempt to improve vibration suppression properties by capitalizing on both passive and active damping techniques. An important issue in such configurations is the concept that the actuation ability of the piezoceramic is reduced by the viscoelastic layer, rather than enhanced. On the other hand, an active constraining layer increases the shear in the viscoelastic and thus forms an effective means of enhancing the damping mechanism. Some design considerations for pure passive, pure active control, and active constrained layer damping are discussed here. Several authors have reported comparisons and formulations of active constrained layer damping techniques. The approach presented here differs in that it employs an energy principle for the equations of a beam with partial active/passive constrained layer damping treatments. To simulate a realistic design problem, the optimal sizing, length, and thickness of treatments subject to a total thickness restriction is studied for cases of active constrained layer, passive constrained layer, and pure active control. The results show that the active constrained layer damping treatment provides better vibration suppression than passive damping treatments, and it even out-performs pure active control for low-gain applications.

A new configuration of surface damping treatments, Active- Passive Hybrid Constrained Layer (HCL) damping, is analyzed and experimentally investigated. The purpose is to improve the performance of the current active constrained layer (ACL) and passive constrained layer (PCL) treatments by mixing passive and active materials in the constraining layer. In HCL, the viscoelastic material is constrained by an active-passive hybrid constraining layer -- the active part is made of PZT ceramics, and the passive part can be selected by the designer to meet different requirements, such as higher damping performance or lighter weight. The active and passive constraining parts are mechanically connected such that the displacement and force are continuous at the connecting surface, but are isolated electrically so the passive constraining part will not affect the function of its active counterpart. Following a generic study of the HCL concept by the authors earlier, the purpose of this paper is to illustrate and validate the HCL performance through both numerical and experimental investigations on a beam structure. The governing equations and boundary conditions of an HCL treated beam are derived and a finite element model is formulated. Tabletop tests with cantilever beam specimens are used for the experimental study. The new hybrid constrained layer is found to have the advantages of both ACL and PCL. By selecting a stiffer passive constraining material and an optimal active-to-passive length ratio, the HCL can achieve better closed-loop and open-loop performances than the treatment with a pure active constraining layer.

By attaching initially stressed poly vinyl chloride (PVC) layers on the flexible structures, necessary passive damping can be provided. Using passive constrained layers on these PVC layers, the efficiency can be made even better than ordinary passive constrained layer damping (PCLD) treatment. By using stressed PVC layers, a rich performance in case of circuit failure conditions is always available. An active constraining layer further enhances the damping performance of this passive technique. Precompressed layer damping treatment augmented with active constrained layer damping (ACLD) treatment has been suggested, which has many desirable features as compared to existing pretensed layer damping treatment. Such enhancement in damping performance is not possible by conventional ACLD as well as PCLD techniques. The effect of initial strain (compressive or tensile) and other parameters of the PVC layers on the vibration characteristics of flexible structure have been investigated. The Hamilton principle in conjunction with finite element method is used to derive the differential equations of motion. Using proportional feedback controllers, the complex closed loop eigenvalue problem is developed and solved numerically. The effectiveness of the proposed technique has been validated experimentally using a digital linear quadratic Gaussian controller.

In active constrained layer (ACL) damping treatments there are two distinct physical mechanisms that contribute to the damping of resonant oscillations -- increased passive damping due to increased shear in the viscoelastic material (VEM) layer, and damping due to transmission of active forces to the host structure. The present study demonstrates that the first mechanism is dominant when proportional feedback is used while the second mechanism is dominant when derivative feedback is used. In the case of proportional feedback, the shear in the VEM increases considerably so that the passive damping is significantly larger than that obtained for zero-voltage (PCL case), but the active action is actually slightly detrimental. In the case of derivative feedback, the shear strain levels in the VEM are virtually unchanged, and all of the damping augmentation is due to the active action. While previous studies have suggested that a high VEM shear modulus would enhance the active damping augmentation due to improved transmissibility of active forces from the piezoelectric layer to the host structure, voltage (or electric field) limits on the piezoelectric layer were never directly considered. In the present study it is concluded that for high VEM shear modulus the low inherent damping results in large resonant response amplitudes. In such a case, the allowable control gains (so as not to exceed the piezoelectric voltage limits) would be reduced, and the damping increases predicted previously (without considering the voltage limits) are no longer available. The present results indicate that when voltage limits are considered, the maximum damping augmentation is available in the VEM shear modulus range that provides optimal passive damping, since these allow the largest control gains.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Bending vibration of flat plates is controlled using patches of active constrained layer damping (ACLD) treatments. Each ACLD patch consists of a visco-elastic damping layer which is sandwiched between two piezo-electric layers. The first layer is directly bonded to the plate to sense its vibration and the second layer acts as an actuator to actively control the shear deformation of the visco-elastic damping layer according to the plate response. With such active/passive control capabilities the energy dissipation mechanism of the visco-elastic layer is enhanced and its damping characteristics of the plate vibration is improved. A finite element model is developed to analyze the dynamics and control of flat plates which are partially treated with multi-patches of ACLD treatments. The model is validated experimentally using an aluminum plate which is 0.05 cm thick, 25.0 cm long, and 12.5 cm wide. The plate is treated with two ACLD patches. Each of which is made of SOUNDCOAT (Dyad 606) visco- elastic layer sandwiched between two layers of AMP/polyvinylidene fluoride (PVDF) piezo- electric films. The piezo-electric axes of the patches are set at zero degrees relative to the plate longitudinal axis to control the bending mode. The effect of the gain of a proportional control action on the system performance is presented. Comparisons between the theoretical predictions and the experimental results suggest the validity of the developed finite element model. Also, comparisons with the performance of conventional passive constrained layer damping clearly demonstrate the merits of the ACLD as an effective means for suppressing the vibration of flat plates.

The layered smart composites involving a piezoelectric layer are traditionally activated by a voltage source, and the magnetic effects are totally ignored since these effects are relatively smaller in comparison to electrical and mechanical effects. However, recent results for even a single piezoelectric beam show that ignoring these effects may cause uncontrollable and unstabilizable systems. In this paper, a variational approach is used to derive a voltage-controlled Rao-Nakra type active constrained layer model. All magnetic effects due to the full set of Maxwell's equations are included. It is shown that the proposed model can be put into the semigroup formulation, i.e. ẋ = Ax + Bu; and is well-posed in the corresponding energy space. Moreover, the observed quantity due to the observation operator B* (corresponding to the control operator B with the voltage control) is totally electrical.

A vibration energy harvester harnesses the oscillatory movement and
converts it into electrical energy. On the other hand, a (dynamic) vibration absorber
dissipates the mechanical energy of a host structure (primary system). The proposal for
a harvester-absorber device (HAD), comprinsing a piezoelectric element (conventional
harvester) bonded with a viscoelastic layer and a steel constrained layer, is based on the
dual purpose of generating energy and at the same time reducing the vibratory response
of the primary system. Introducing a viscoelastic dissipative layer in a conventional
harvester, also offers the advantage of simultaneously reducing wear on the piezoelectric
element, thereby extending its lifespan and preventing fatigue-related breakage. The
paper presents a model of a harvester-absorber built from a bimorph piezoelectric
beam, a layer of viscoelastic material (E-A-R C1002-01PSA) and a beam of steel, which
acts as a constrained layer. A lumped parameter model is proposed for the theoretical
description of the HAD which is successfully used to experimentally determine its
parameters. After that, and using the equivalent stiffness concept, the HAD was
coupled to a free-free beam with two masses at its ends to study its perfomance over a
real host structure. The inertance of the composite system and voltage/force frequency
response function of the HAD were obtained and compared with experimental results.
The accuracy of the results justifies and validate the model which has the advantage
of simplicity and can contribute to reducing wear and increasing the lifespan of brittle
piezoelectric structures.

DAMPING OPTIMIZATION BY INTEGRATING ENHANCED ACTIVE CONSTRAINED LAYER AND ACTIVE-PASSIVE HYBRID CONSTRAINED LAYER TREATMENTS

The structural vibration suppression with active constrained layer damping (ACLD) was widely studied recently. However, the literature seldom concerned with the vibration control on flow-induced vibration using active constrained layer. In this paper the wind induced vibration of cantilevered beam is analyzed and suppressed by using random theory together with a velocity feedback control strategy. The piezoelectric material and frequency dependent viscoelastic layer are used to achieve effective active damping in the vibration control. The transverse displacement and velocity in time and frequency domains, as well as the power spectral density and the mean-square value of the transverse displacement and velocity, are formulated under wind pressure at variable control gain. It is observed from the numerical results that the wind induced vibration can be significantly suppressed by using a small outside active voltage on the constrained layer.

In the context of the finite elements analysis, the mechanical performance of viscoelastically bonded smart structures is investigated and analyzed. Three different models are considered and compared. In the 1st model, the actuator is glued to the host structure. On the other hand, in the two other models the actuator is glued to the bonding layer which is glued to the host structures. To explore the effect of the bonding layer characteristics on the mechanical behavior of the host structure, both elastic and viscoelastic layers are considered. The Prony’s series are utilized to simulate the viscoelastic constitutive response. The mathematical formulation of the coupled problem is presented and the dynamic finite elements equations of motion of the coupled electromechanical systems are introduced. The proposed methodology is verified by comparing the obtained results with the available results in the literature and good consentience is observed. Both static and dynamic vibration behaviors are studied incorporating the interfacial shear stresses between the bonding layer and the host structure as well as the displacements as a comparison criterion to determine the performance controlling function of the host structure. Parametric study of piezoelectric properties showed that permittivity is required in solving such systems but does not affect the performance. On the other hand, the piezoelectric characteristics have significant effects on the mechanical performance of smart structures and can be used in the optimum selection of combination just like mechanical properties and geometry. Additionally, the obtained results show that the model with viscoelastic bonding layer has an overall static performance nearly half of elastic bonding layer model while it has a slight effect on the dynamic behavior compared with the corresponding elastic bonding layer. The proposed methodology with the obtained results is supportive in the applications of structure health monitoring and dynamics of smart structural systems. The proposed procedure could be extended in a future work to include the coupled electromagnetic effects on the dynamic behavior of smart structures in hygrothermal environment.

Vibration and damping characteristics of hybrid carbon fiber composite pyramidal truss sandwich panels with viscoelastic layers

This paper proposes a new constrained viscoelastic (VE) layer treatment as a distributed supplemental damping mechanism for structural members. A steady-state solution of a cantilevered column utilizing this system is formulated under harmonic loading and validated with experimental shake table tests. Parametric studies indicated that the new treatment can reduce the elastic response of a 1/5-scale square column up to 20%, or increase the damping ratio of the column from 2% to 2.5%. They remain effective as the column begins rocking at the column-footing construction joint. The numerical results were found to be in general agreement with the shake table test data of two column specimens with and without VE layers. On the basis of the validated model, applying two VE layers of 2.38 mm-thick to cover the lower 50–90% height of a cantilevered column appears the most efficient, and can increase the damping ratio up to 12% for a full-scale column. The significant reduction in peak responses indicates that the proposed new constrained-layer system is promising for civil engineering applications.

In this paper, a computational approach is adopted to solve the optimal control and optimal parameter selection problems of a rotating flexible beam fully covered with active constrained layer damping (ACLD) treatment. The beam rotates in a vertical plane under the gravitational effect with variable angular velocity and carries an end mass. Tangent coordinate system and the moving coordinate system are used in the system modeling. Due to the highly nonlinear and coupled characteristics of the system, a relative description method is used to represent the motion of the beam and the motion equations are set up by using relative motion variables. Finite element shape functions of a cantilever beam [1] are used as the displacement shape functions in this study. Lagrangian formulation and Raleigh-Ritz approach [2] are employed to derive the governing equations of motion of the nonlinear time-varying system. The problem is posed as a continuous-time optimal control problem. The control function parameters are the control gains. The two system parameters are the thickness of the constraining layer and the viscoelastic material layer. The software package MISER3.2, which is based on the Control Parametrization and the Control Parametrization Enhancing Transform (CPET) techniques is used to solve the combined problems. The optimal solution takes the end deflection, control voltage and the total weight into account. Results show that substantial improvements are obtained with ACLD as compared to the passive constrained layer damping (PCLD) treatment.

Control of dynamic vibration is critical to the operational success of many flexible mechanism systems. This paper addresses the problem of vibration control of such mechanisms through passive damping, using constrained layer damping treatment technique. A new type of shape function for three layer frame element containing a viscoelastic layer is developed. The equations of motion of the damped flexible mechanism are derived. Modal loss factors of this kind mechanisms are predicated from undamped normal mode by means of the modal strain energy method. Comparisons between the results obtained by this paper and the results obtained by exact solution of the governing equations for a well known sandwich beam demonstrate that the method presented in this paper is correct and reliable. Application of this method in predication of modal damping ratios for damped mechanisms is discussed. It is believed that the method of this paper hold the greatest potential for optimal design of damped flexible mechanism systems.