Some design considerations for active and passive constrained layer damping treatments

Vibration analysis of simply supported beams with enhanced self-sensing active constrained layer damping treatments

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 a self-sensing active constrained layer (SACL) damping treatment, the piezoelectric constraining layer is used simultaneously as both a sensor and an actuator. A variational formulation of ACL damping treatments has shown that an ACL damping treatment using a self-sensing and actuating piezoelectric element as the constraining layer in combination with rate of strain feedback as the control law will ensure that the power dissipated by the active damping always remains positive. This eliminates a major mechanism for system instability. Implementing this self-sensing actuator (SSA) as the constraining layer is made possible through the use of a bridge circuit that subtracts the strain signal from the actuator control voltage in the piezoelectric constraining layer and also differentiates the strain voltage in order to obtain the desired control law. An analytical model for ACL has been developed that can be used to predict theoretically the performance of a SACL damping treatment for a Euler - Bernoulli beam. A series of experiments studying the frequency response of an SACL test beam was performed and the results compared with the theoretical model. This theoretical model predicted the frequency of the first- and second-mode responses of the experimental beam very accurately and predicted the damping of these responses well. Therefore, this comparison indicated that the analytical model is capable of accurately predicting the frequency responses of beams treated with SACL.

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.

This paper describes the use of the multi-objective genetic algorithm (MOGA) to solve anintegrated optimization problem of a rotating flexible arm with active constrainedlayer damping (ACLD) treatment. The arm is rotating in a horizontal plane withtriangular velocity profiles. The ACLD patch is placed at the clamped end of the arm.The design objectives are to minimize the total treatment weight, the controlvoltage and the tip displacement of the arm, as well as to maximize the passivedamping characteristic of the arm. Design variables include the control gains,the maximum angular velocity, the shear modulus of the viscoelastic layer, thethickness of the piezoelectric constraining and viscoelastic layers, and the lengthof the ACLD patch. In order to evaluate the effect of different combinations ofdesign variables on the system, the finite element method, in conjunction with theGolla–Hughes–McTavish (GHM) method, is employed to model the flexible arm withACLD treatment to predict its dynamic behavior, in which the effects of centrifugalstiffening due to the rotation of flexible arm are taken into account. As a result ofoptimization, reasonable Pareto solutions are successfully obtained. It is shownthat the MOGA is applicable to the present integrated optimization problem.

A rigorous multi-objective optimization procedure, is developed to address the integrated structures/control design ofcomposite plates with surface bonded segmented active constrained layer (ACL) damping treatment. The Kresselmeier-Steinhauser function approach is used to formulate this multidisciplinary problem. The goal is to control vibration withoutincorporating a weight penalty. Objective functions and constraints include damping ratios, structural weight and naturalfrequencies. Design variables include the ply stacking sequence, dimensions and placement of segmented ACL. The optimaldesigns show improved plate vibratory characteristics and reduced structural weight. The results of the multi-objectiveoptimization problem are compared to those of a single objective optimization with vibration control as the objective.Results establish the necessity for developing the integrated structures/controls optimization procedure.Keywords: integrated design, optimization, smart composites, segmented active constrained layer, hybrid displacement field

Conventional Passive Constrained Layer Damping (PCLD) treatments with viscoelastic cores are provided with built-in sensing and actuation capabilities to actively control and enhance their vibration damping characteristics. The design parameters and control gains of the resulting Active Constrained Layer Damping (ACLD) treatments are optimally selected, in this paper, for fully-treated beams using rational design procedures. The optimal thickness and shear modulus of the passive visco-elastic core are determined first to maximize the modal damping ratios and minimize the total weight of the damping treatment. The control gains of the ACLD are then selected using optimal control theory to minimize a weighted sum of the vibrational and control energies. The theoretical performance of beams treated with the optimally selected ACLD treatment is determined at different excitation frequencies and operating temperatures. Comparisons are made with the performance of beams treated with optimal PCLD treatments and untreated beams which are controlled only by conventional Active Controllers (AC). The results obtained emphasize the potential of the optimally designed ACLD as an effective means for providing broad-band attenuation capabilities over wide range or operating temperatures as compared to PCLD treatments.

An ove lw ork demonstrates the effect of delamination in smart laminated composite beams on the performance of active constrained layer damping (ACLD) treatment. A finite element model has been derived to formulate the dynamics of the composite beams integrated with a patch of ACLD treatment and a patch of piezoelectric film acting as a distributed sensor with and without the presence of delamination at different locations. Frequency response functions of the beams have been examined to observe the effect of delamination on the performance of ACLD treatment. It has been observed that the ACLD treatment improves the active damping characteristics of the beams, even in the presence of delamination, and that the responses of the beams are sensitive to the variation of the location of delamination. The responses due to active constrained layer damping presented may provide a useful guide to detect the presence of delamination in smart composite beams by the use of the existing numerical techniques.

The vibration of a single link flexible manipulator is attenuated using the Active Constrained layer damping (ACLD) treatment. The ACLD treatment consists of a viscoelastic layer sandwiched between two piezo-electric layers acting as constraining layers with sensing and actuation capabilities. The shear deformation of the visco-elastic layer is controlled to enhance the energy dissipation mechanism and attenuate the vibration of the flexible manipulator. A finite element model is used to describe the dynamics of the system. A third order polynomial is used to describe the lateral displacement of the manipulator and a second order polynomial is used to describe the longitudinal displacements of the different layers of the manipulator. An appropriate control law is used to control the system. The Coupled Modal Strain energy technique is used to compute the equivalent viscous damping ratios for the elastic layer using the loss factor data of the material. The theoretical predictions of the model are compared with the experimental performance of a manipulator fully treated with a Dyad 606 visco-elastic layer sandwiched between two layers of polyvinylidene fluoride (PVDF) piezo-electric films. The results obtained clearly demonstrate the attenuation capabilities of the Actively-Controlled Constrained Layer Damping.

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.

Modeling and dynamics analysis of shells of revolution by partially active constrained layer damping treatment

For active/passive vibration control applications, low order models of flexible structures are always preferable. Mathematical models of passive constrained layer damping (PCLD)/active constrained layer damping (ACLD) treatment generated by energy based analytical methods are of much smaller orders as compared to finite element methods (FEM). Using these analytical methods, one can get rid of complex model reduction techniques, since these model reduction techniques are subjected to errors if applied directly to PCLD or ACLD systems. However, analytical techniques cannot be applied blindly to any PCLD system. There is significant error in loss factor prediction for certain boundary conditions. This error is also dependent on the relative thicknesses of Viscoelastic material layer, constraining layer and base beam. For certain combination of the above thicknesses and under certain boundary conditions, the models generated are useless for controller design purposes. On the other hand, FEM are highly robust and can be applied easily to any set of boundary conditions with guaranteed accuracy. Also, results predicted by this method are of high accuracy for any combinations of thicknesses of different layers. The only disadvantage of this technique is the high order of the developed model. Detailed performance comparison of both the techniques to predict the modal parameters of the PCLD treated beam is presented.

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 gravity with variable angular velocity and carries an end mass. The problem is posed as a continuous-time optimal control problem and solved via MISER3. Using the control parametrization enhancing technique (CPET), the results show that substantial improvements are obtained with ACLD as compared to the passive constrained layer damping (PCLD) treatment. In addition, accurate switching times of the system are determined. A parametric analysis is also included through simulation results.

Active control of geometrically nonlinear vibrations of doubly curved smart sandwich shells using 1–3 piezoelectric composites

ACTIVE CONSTRAINED LAYER DAMPING OF THIN CYLINDRICAL SHELLS