Passive Constrained Layer Damping 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.

Istraživanje stabilnosti kod unutrašnje obrade struganjem pomoću vretena bušilice sa pasivnim prigušivanjem ograničavajućim slojem

The vibrations produced in a boring tool in internal turning deteriorate the machined surface quality and reduce the tool life, which results in a massive noise during the machining. Therefore, unwanted vibrations are necessary to be eliminated by improving the boring bar's dynamic stiffness and damping capacity. This paper investigates a passive constrained layer damping (CLD) boring bar with a hybrid damping layer to study the internal turning system's stability. Initially, the dynamic models of the conventional and CLD tools are thoroughly studied using Euler-Bernoulli beam theory (EBT) and validated them with finite element modelling (FEM). The frequency response functions (FRFs) obtained from the impact hammer tests are used to estimate the modal parameters. With modal parameters, the semi-analytical stability lobe diagrams (SLDs) are plotted for the boring system with the conventional and CLD boring bar. Tool-tip responses for various cutting conditions are simulated numerically to validate and to study stability. The cutting experiments with traditional and CLD boring bar are conducted for stability analysis and compared tool-tip responses with numerical results. It is observed that both the numerical and experimental results agree with the selected cutting conditions from SLDs. It is also observed that the CLD boring bar with a hybrid damping layer reduced the vibration displacements by five times compared to the conventional one.

Passive Constrained Layer Damping: A State of the Art Review

In this paper authors discuss the advancements made over years in the passive constrained layer damping (PCLD) technique used for structural vibration control. To start with, the paper presents a brief literature survey on passive damping techniques using viscoelastic materials (VEM) emphasizing unconstrained layer damping (UCLD) followed by PCLD. The discussion on PCLD technique includes different mathematical models and experimental investigations related to it. Finally, the various design modifications proposed by the different researchers in order to improve the performance of conventional PCLD configuration in presented.

Passive vibration control of plate using nodal patterns of mode shape

Passive constrained layer damping (PCLD) is nowadays a general method for reducing vibrations. Constrained layer damping (CLD) is a very good technology in terms of reducing vibration energy. This paper deals with optimal damping of first three modes of a thin square cantilever plate by constrained viscoelastic layers which are positioned according to the nodal patterns of the mode. In essence, the CLD patches are cut according to the nodal patterns and then applied on to the bare plate. Thus, this approach uses prior information of the deformation patterns of the plate. The ABAQUS finite element analysis software was used to create viscoelastically damped plate models subjected to forced vibration. The direct steady-state dynamic analysis was used to obtain the frequency response functions from which the resonance frequencies of the models were derived. Vibration control using nodal pattern CLD patches is a better way to apply CLD treatment to a plate. This is because the mode shapes give good predictions of where the maximum strains are in the plate as well as the design and size of the damping patches required. It is believed that the methodology proposed in this research work is capable of providing good results.

Examination of the vibroacoustic behavior of a grid-stiffened panel with applied passive constrained layer damping

This paper provides a contribution to the understanding of both the vibroacoustical behavior and the influence of passive constrained layer damping (PCLD) applications on the sound radiation of a grid-stiffened panel. A test specimen is manufactured and an experimental set-up with a synthetic turbulent boundary layer excitation is developed. In addition, a numerical model is created and updated with the results of an experimental modal analysis. Further, the acoustic effect of PCLD applied to the ribs and to the skin fields of the grid panel is assessed by measurement of the radiated sound power. It is shown that the ribs are suitable for an efficient application of PCLD. Generally, additional damping of the grid panel is achieved with PCLD for frequencies above 300 Hz. By partially covering the ribs with PCLD, a reduction of the radiated sound power of up to 2 dB in third-octave bands is achieved. In case of a total coverage of the grid panel, a reduction of up to 4 dB in third-octave bands is attained.

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.

Free Vibration and Damping of Rotating Composite Shaft with a Constrained Layer Damping

The free vibration and damping characteristics of rotating shaft with passive constrained layer damping (CLD) are studied. The shaft is made of fiber reinforced composite materials. A composite beam theory taking into account transverse shear deformation is employed to model the composite shaft and constraining layer. The equations of motion of composite rotating shaft with CLD are derived by using Hamilton’s principle. The general Galerkin method is applied to obtain the approximate solution of the rotating CLD composite shaft. Numerical results for the rotating CLD composite shaft with simply supported boundary condition are presented; the effects of thickness of constraining layer and viscoelastic damping layers, lamination angle, and rotating speed on the natural frequencies and modal dampings are discussed.

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.

A unified method for the vibration and damping analysis of constrained layer damping cylindrical shells with arbitrary boundary conditions

In this paper, an accurate solution is developed for the vibration and damping characteristics of a three-layered passive constrained layer damping (PCLD) cylindrical shell with general elastically restrained boundaries. In this formulation, characteristic equations of the system are derived by using the modified Fourier–Ritz method in conjunction with Donnell shell assumptions and linear viscoelastic theory. Regardless of boundary conditions, the displacements of each layer are expanded as the linear combination of a standard Fourier series and closed-form functions introduced to eliminate all the relevant discontinuities with the displacements and derivatives at the edges. This method can be universally applicable to all classical boundaries, elastic boundaries and their combinations without any special change in the solution procedure. It provides an effective way to investigate the influence of restraints from different directions on the vibration and damping performance of PCLD shells. New results for elastic restraints and intermediate ring supports are presented, which may serve as benchmark solutions. Furthermore, the detailed effects of thickness of layers and shear parameter on natural frequencies and loss factors are also illustrated.

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.

Topology optimization of microstructures of viscoelastic damping materials for a prescribed shear modulus

Damping performance of a passive constrained layer damping (PCLD) structure mainly depends on the geometric layout and physical properties of the viscoelastic damping material. Properties such as t...

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.

Modeling of a hybrid semi-active/passive vibration control technique

In this paper a new hybrid vibration damping technique as a combination of the semi-active pulse switching technique and passive constrained layer damping is proposed as an effective vibration control method for all frequency ranges. The semi-active pulse switching technique is an effective method to damp any type of vibrations with no need for external energy sources. However, its performance in high-frequency ranges decreases. In addition, passive techniques are not so effective in low-frequency ranges, but have significant effects in high-frequency ranges. The proposed hybrid damping technique as a combination of these two control methods is a new effective control technique for all frequency ranges. It covers the weakness of the semi-active method and provides significant damping in both low and high-frequency vibrations.

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.