Passive Constrained Layer Damping Treatment Research Articles

Vibration control of piezoelectric beams with active constrained layer damping treatment using LADRC algorithm

Active constrained layer damping (ACLD) treatment has become an important smart structure for vibration suppression due to its ability to achieve enhanced damping effects through real-time control. The control algorithm is a critical factor that determines the damping performance of the ACLD treatment. In this work, we utilize the linear active disturbance rejection control (LADRC) algorithm for the first time in the vibration suppression of beams with the ACLD treatment by compensating for the disturbance. To optimize vibration suppression, we also propose an efficient parameter tuning approach by analyzing the effects of controller bandwidth, control gain, and observer bandwidth on vibration suppression performance. Firstly, the dynamic model of elastic beams with the ACLD treatment is established and the LADRC algorithm is designed. Subsequently, the accuracy of the model is verified by comparing it with open literature and experiments. Then, the influences of the control parameters and different positions of the ACLD treatment on the vibration suppression performance are studied. Finally, the vibration suppression effects of LADRC and traditional PID algorithms are compared. The results indicate that the vibration suppression performance of the ACLD treatment is better than that of the passive constrained layer damping (PCLD) treatment. Setting the controller bandwidth to a small value and then adjusting other control parameters can effectively reduce the difficulty of parameter tuning while achieving superior vibration suppression performance. Appropriately increasing the observer bandwidth or reducing the control gain is beneficial for enhancing the suppression efficiency. The parameter tuning approach in this study provides vital guidance for the application of the LADRC algorithm in structural vibration suppression.

Dynamics of viscoelastic material sandwich beam

ABSTRACT In this study, the non-linear dynamics of a horizontal motioned hub-beam system with passive constrained layer damping treatment are presented. The beam is constructed with three layers, viz., the host layer and the constrained layer with isotropic material, and the core layer of viscoelastic material. The system is non-linear due to coupling between the rigid motion of hub and flexible motion of the beam and also due to consideration of the beam curvature effect of bending. The equations of motion are derived using Hamilton’s principle based on expressing the kinetic energy and potential energy of the manipulator system in terms of generalised coordinates. The problem is approached by the finite element method, and the Newmark’s beta time integration scheme is adopted. Numerical simulations show that the viscoelastic material not only reduces the amplitude of elastic deflection but also quickly attenuates the vibration to zero. The results are evaluated for different values of thickness of the constrained layer, viscoelastic layer, payloads, and elastic modulus of each layers. It is observed that the vibration amplitude could be controlled through the use of the passive layer of damping.

Free vibration and damping characteristics study of doubly curved sandwich shell panels with viscoelastic core and isotropic/laminated constraining layer

Abstract In this work, a shear deformable viscoelastic sandwich shell element is proposed for doubly curved sandwich shell panels with passive constrained layer damping (PCLD) treatment. The transverse displacements of the constraining layer and base layer are considered to be independent, besides the in-plane displacements . The transverse and in-plane displacements of the viscoelastic core are considered to be varying linearly through the thickness. Shear as well as normal deformations of the core are included in the analysis. The equation of motion of the doubly curved sandwich shell panel under free vibration is derived via Hamilton's principle . The modal frequencies and modal loss factors of the Isotropic elastic-Viscoelastic-Isotropic elastic (IVI) sandwich shell panel and Laminated elastic-Viscoelastic-Laminated elastic (LVL) sandwich panel are obtained from numerical solutions, using finite element method in conjunction with Hamilton's principle. Parametric studies are carried out to ascertain the effects of shell geometries, aspect ratio, orthotropicity of the skins, core layer thickness, constraining layer thickness, core loss factor on the natural frequencies and system loss factors under different boundary conditions.

Optimization of Constrained Layer Damping Parameters in Beam Using Taguchi Method

This paper presents a study in which an attempt has been made to find out the maximum damping capacity of passive constrained layer damping treatments by optimizing the parameters of the treatment using the Taguchi method. Passive constrained layer damping treatment is one where two layers such as viscoelastic layer and constraining layer are attached on the surface of the structure so as to enhance the damping capacity of the structure. The performance of the constrained layer damping (CLD) parameters is evaluated in terms of its thickness of viscoelastic, constraining layer and coverage of the treatment over the surface of the beam. An orthogonal array, main effect, signal-to-noise ratio and analysis of variance are employed to analyze the effect of CLD parameters on the damping behavior and first natural frequency. The analysis of the results gives the optimal combination of thicknesses of different layers and coverage area of the treatment. Finally, it is demonstrated by conducting confirmation experiments that the predicted results obtained using regression equations are consistent with experimental observations.

Topology optimization of PCLD on plates for minimizing sound radiation at low frequency resonance

Topology optimization of passive constrained layer damping (PCLD) treatment patched on thin plates with respect to sound radiation at low frequency resonance is investigated. An extended solid isotropic material with penalization (SIMP) model is described using an interface finite element model for viscoelastic layer. Then the given FE mesh for base structure can remain the same during the optimization process. The objective function, radiated sound power, is simplified by using sound radiation mode and modal strain energy method, the merit of which is the complex dynamic equations of the composite plate need not to be solved and only modal analyses for the associated undamped modal equations are required. Numerical and experimental results show that significant reductions of the sound power are achieved. Two optimal topologies of the PCLD patches are analyzed. It's shown that to minimize the sound radiation power at low frequency, not only the structural damping but also the volume velocity should be concerned.

Microstructural topology optimization of viscoelastic materials for maximum modal loss factor of macrostructures

The geometric layout and physical properties of a viscoelastic damping material have a significant influence on the damping performance of a passive constrained layer damping (PCLD) structure. This paper presents a two-scale optimization method and aims to find the optimal microstructural configuration of the viscoelastic material (i.e., the optimal effective properties of the material) with maximum modal loss factors of the macrostructures. The modal loss factor is obtained by using the Modal Strain Energy (MSE) method. The material microstructure is assumed to be homogeneous in the macro-scale, i.e., the macrostructure is composed of periodic unit cells (PUC). In the optimization formulation, the relative densities are introduced as the design variables for the material microstructure design, based upon the idea of the Solid Isotropic Material with Penalization (SIMP) method of topology optimization. The modal loss factor of the structure is assigned as the objective function. All the sensitivities of the modal loss factor with respect to the design variables are derived analytically and the optimization problem is solved by Method of Moving Asymptote (MMA) method. Several examples of the design optimization of viscoelastic cellular materials are presented to demonstrate the validity of the method. The effectiveness of the design method is illustrated by comparing a solid and an optimized cellular viscoelastic material as applied to a cantilever beam with the PCLD treatment.

Vibration and damping characteristics of sandwich plates with viscoelastic core

As an effective approach to suppress vibrations and noise, passive constrained layer damping (PCLD) treatments are widely used in engineering practice. However most of the studies concentrate on the one-dimensional beams with active/passive constrained damping layer, the analysis on the two-dimensional plates are relatively small. This research proposes an efficient sandwich modeling technique to deal with the vibration and damping characteristics of the PLCD plate structure. A type of three-layer four-node rectangular element with seven degrees of freedom on every node is used to simulate the PLCD plate structure. The displacement relationships of each layer are obtained based on the first-order shear deformation theory. The finite element equations of motions are derived by the Hamilton principle in variation form. The natural frequency and loss factor are discussed based on the eigenvalue problems. Numerical examples are provided to verify the accuracy and efficiency of the present finite element method. Finally, the influences of the layer thickness, the loss factors of the viscoelastic cores on the natural frequencies and loss factors of the PLCD plate structure are discussed as well.

Damping Analysis of Multilayer Passive Constrained Layer Damping on Cylindrical Shell Using Transfer Function Method

Based on the Donnell assumptions and linear viscoelastic theory, the constitutive relations for the multilayer passive constrained layer damping (PCLD) cylindrical shell are described. In terms of energy, the motion equations and boundary conditions of the cylindrical shell with multilayer PCLD treatment are derived by the Hamilton principle. After trigonometric series expansion and Laplace transform, the state vector is introduced and the dynamic equation in state space is established. The transfer function method is used to solve the state equation. The dynamic performance including the natural frequency, the loss factor, and the frequency response of the multilayer PCLD cylindrical shell is obtained. The results show that with more layers, the more effective in suppressing vibration and noise, if the same amount of visco-elastic and constrained material is applied. It demonstrates a potential application of multilayer PCLD treatment in some critical structures, such as cabins of aircrafts, hulls of submarines, and bodies of rockets and missiles.

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

A new model for a smart shell of revolution treated with active constrained layer damping (ACLD) is developed, and the damping effects of the ACLD treatment are discussed. The motion and electric analytical formulation of the piezoelectric constrained layer are presented first. Based on the authors' recent research on shells of revolution treated with passive constrained layer damping (PCLD), the integrated first-order differential matrix equation of a shell of revolution partially treated with ring ACLD blocks is derived in the frequency domain. By virtue of the extended homogeneous capacity precision integration technology, a stable and simple numerical method is further proposed to solve the above equation. Then, the vibration responses of an ACLD shell of revolution are measured by using the present model and method. The results show that the control performance of the ACLD treatment is complicated and frequency-dependent. In a certain frequency range, the ACLD treatment can achieve better damping characteristics compared with the conventional PCLD treatment.

Topology Optimization of Passive Constrained Layer Damping on Plates with Respect to Noise Control

The square of normal surface velocity of a thin plate with a harmonic excitation is minimized by optimizing the topologies of attached passive constrained layer damping (PCLD) treatments. An extended solid isotropic material with penalization model for topology optimization is introduced based on a simple interface finite element modeling for viscoelastic layer of PCLD patch. For the purpose of illustrating the proposed method, a clamped square plate is used in the numerical study. Significant reductions of the objective functions are achieved by the optimal distributions.

Transfer function method for frequency response and damping effect of multilayer PCLD on cylindrical shell

Based on the Donnell assumptions and linear visco-elastic theory, the constitutive equations of the cylindrical shell with multilayer Passive Constrained Layer Damping (PCLD) treatments are described. The motion equations and boundary conditions are derived by Hamilton principle. After trigonometric series expansion and Laplace transform, the state vector is introduced and the dynamic equations in state space are established. The transfer function method is used to solve the state equation. The dynamic performance including the natural frequency, the loss factor and the frequency response of clamped-clamped multi-layer PCLD cylindrical shell is obtained. The results show that multi-layer PCLD cylindrical shell is more effective than the traditional three-layer PCLD cylindrical shell in suppressing vibration and noise if the same amount of material is applied. It demonstrates a potential application of multi-layer PCLD treatments in many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles.

Theoretical and experimental vibration analysis of rotating beams with combined ACLD and Stressed Layer Damping treatment

Active constrained layer damping (ACLD) treatment increases the efficiency of passive constrained layer damping (PCLD) treatment, but in case of circuit failure, only the decreased efficiency of PCLD treatment is available. The efficiency of the ordinary PCLD treatment can be enhanced by adding a stressed poly vinyl chloride (PVC) layers on the base beam instead of using viscoelastic materials. Hamilton Principle in conjunction with finite element method is used to derive the non-linear differential equations of motion for a rotating beam. Using proportional feedback controllers, the complex closed loop eigenvalue problem is developed and solved numerically. The effect of rotational speed of the beam, initial strain and other parameters of the PVC layer is investigated. To prove the effectiveness of the new technique, experimental investigations have also been carried out.

Vibration control of curved panel using smart damping

Damping designs with active piezoelectric materials and passive viscoelastic materials combine the advantages of both active and passive constrained layer damping (ACLD/PCLD) treatments. Present study is aimed to examine through experiments, vibration control of curved panel treated with optimally placed active or passive constrained layer damping patches. Placement strategies of constrained layer patches are devised using the modal strain energy method. The optimum location for the application of ACLD/PCLD patches are found for specific modes and the information for different modes is then collated to get the best locations for control of multiple modes. The treatments are then applied to the elements target specific modes of vibrations as well as for control of multiple modes. Extensive experiments are conducted by using number of samples of ACLD and PCLD patches for each configuration to control different modes simultaneously or independently. The results demonstrate the utility of the technique for selecting the locations of the ACLD treatments to achieve desired damping characteristics over a broad frequency range. Experiment results well corroborates with theoretical predictions.

Damping Characteristics of a Cantilever Plate Using Permanent Magnetic Constrained Layer Damping Strip Treatment

Significant improvement of damping characteristics can be achieved by using the new class of magnetic constrained layer damping treatment (MCLD). This paper presents the damping properties of the first and second torsional mode for a five-layer cantilever rectangular plate treated with partial MCLD. The Rayleigh-Ritz method and Hamilton’s principle are employed in the analysis. We have chosen both single and segmented patches with different sizes. It can be observed that for the two modes single-patched MCLD treatment induces less improvement of damping characteristics especially for the short patch. The effects of calculation of parameters like placement strategies of discrete patches, the length of patches are analyzed and discussed. The results obtained from analytical show that the optimum location of the patch, for the torsional mode, is at edge of the plate. Favorable comparisons with the conventional passive constrained layer damping treatment (PCLD) on various special cases of the problem are obtained. The results demonstrate MCLD treatment still improvements over PCLD in damping structural vibrations.

Damping Characteristics of a Cantilever Plate Using Permanent Magnetic Constrained Layer Damping Strip Treatment

Significant improvement of damping characteristics can be achieved by using the new class of magnetic constrained layer damping treatment (MCLD). This paper presents the damping properties of the first and second torsional mode for a five-layer cantilever rectangular plate treated with partial MCLD. The Rayleigh-Ritz method and Hamilton’s principle are employed in the analysis. We have chosen both single and segmented patches with different sizes. It can be observed that for the two modes single-patched MCLD treatment induces less improvement of damping characteristics especially for the short patch. The effects of calculation of parameters like placement strategies of discrete patches, the length of patches are analyzed and discussed. The results obtained from analytical show that the optimum location of the patch, for the torsional mode, is at edge of the plate. Favorable comparisons with the conventional passive constrained layer damping treatment (PCLD) on various special cases of the problem are obtained. The results demonstrate MCLD treatment still improvements over PCLD in damping structural vibrations.

Active Vibration Control of Beams By Combining Precompressed Layer Damping and ACLD Treatment: Theory and Experimental Implementation

Abstract 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.

Enhanced ACLD treatment using stand-off-layer: FEM based design and experimental vibration analysis

The main disadvantage of active constrained layer damping treatment is the reduced transmissibility of active forces. This problem can be solved up to certain extent by using edge anchors. These edge anchors or stiffeners increase the transmissivity of forces only at very high feedback gains but decrease the effectiveness of passive constrained layer damping (PCLD) treatment. The efficiency of the passive constrained layer damping treatment can be improved drastically by adding the stand-off-layer (SOL) between the viscoelastic layer and the base beam. This technique has additional advantages as well. Firstly, it increases the viscoelastic strain so that more energy is dissipated via viscoelastic layer. Secondly, it enhances the effect of active forces and moments even without using edge anchors because the shear modulus of the SOL is in the range 10 8–10 9 N/m 2. Hamilton’s principle in conjunction of finite element method is used to derive the equations of motion. The complex eigenvalue is developed and solved numerically by using simple proportional feedback control strategy. Results are compared with ordinary active constrained layer damping (ACLD) treatment in order to highlight the effectiveness of the proposed technique. Validity of the proposed treatment has also been verified experimentally.

An Experimental and Analytical Vibration Study of a Thin Cylindrical Shell Treated with Constrained Layer Damping

This paper presents a experimental optimization method for a thin cylindrical shell with a partially passive constrained layer damping (PCLD) treatment. Vibration level difference theory is employed to evaluate damping effect of PCLD structures which the thicknesses of damping layer and constrained layer are different.

Spectral Finite Element Modeling of Cylindrical Shells with Passive Constrained Layer Damping

This paper presents a spectral finite element method for a cylindriacl shell with a passive constrained layer damping treatment. A thin shell theory based on Donnell-Mushtari-Vlasov assumption is employed. The equation of spectral unit and the method of determination of natural frequency and modal loss factor are presented.

Kinetic Analysis of a Cylindrical Shell Partially Treated with Constrained Layer Damping

This paper presents a transfer function method for a cylindrical shell with a partially passive constrained layer damping (PCLD) treatment. A thin shell theory based on Donnell-Mushtari-Vlasov assumption is employed to yield a mathematical model. The equation of motion and boundary conditions of a cylindrical shell with partially PCLD are derived. The paper provides theory supports for PCLD structure’s engineering applications in submarine weapon field.