PARTIAL CONSTRAINED VISCOELASTIC DAMPING TREATMENT OF STRUCTURES: A MODAL STRAIN ENERGY APPROACH

2006 ◽  
Vol 06 (03) ◽  
pp. 397-411 ◽  
Author(s):  
R. A. S. MOREIRA ◽  
J. DIAS RODRIGUES
Keyword(s):  
Strain Energy ◽  
Effective Means ◽  
Thin Plates ◽  
Viscoelastic Layer ◽  
Modal Strain Energy ◽  
Structural Modifications ◽  
Target Mode ◽  
Modal Damping ◽  
The Cost ◽  
Damping Treatments

The constrained viscoelastic layer damping treatment is an effective means for the passive vibration control of plate and beam-kind structures. In order to reduce the treatment cost, while minimizing structural modifications, particularly the increase in mass, constrained viscoelastic treatments can be successfully applied in a partial and localized manner. The effectiveness of these treatments depends on their extension and relative location with respect to the target mode shape, which is not usually expeditiously established. In order to minimize the cost of the numerical optimization of the partial treatments, an efficient numerical methodology based on the ratio between the modal strain energy of the treated area and that of the structure is hereby proposed. This method is used in the analysis of the location and extension effects of partial constrained viscoelastic treatments on the modal damping of thin plates. The numerical results are verified through an experimental study on specimens with partial constrained viscoelastic layer damping treatments.

scholarly journals Dimensionless Analysis of Segmented Constrained Layer Damping Treatments with Modal Strain Energy Method

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Shitao Tian ◽  
Zhenbang Xu ◽  
Qingwen Wu ◽  
Chao Qin
Keyword(s):  
Shear Strain ◽  
Strain Field ◽  
Strain Energy ◽  
Design Parameters ◽  
Viscoelastic Layer ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Modal Strain Energy Method ◽  
Damping Treatments ◽  
Strain Energy Method

Constrained layer damping treatments promise to be an effective method to control vibration in flexible structures. Cutting both the constraining layer and the viscoelastic layer, which leads to segmentation, increases the damping efficiency. However, this approach is not always effective. A parametric study was carried out using modal strain energy method to explore interaction between segmentation and design parameters, including geometry parameters and material properties. A finite element model capable of handling treatments with extremely thin viscoelastic layer was developed based on interlaminar continuous shear stress theories. Using the developed method, influence of placing cuts and change in design parameters on the shear strain field inside the viscoelastic layer was analyzed, since most design parameters act on the damping efficiency through their influence on the shear strain field. Furthermore, optimal cut arrangements were obtained by adopting a genetic algorithm. Subject to a weight limitation, symmetric and asymmetric configurations were compared. It was shown that symmetric configurations always presented higher damping. Segmentation was found to be suitable for treatments with relatively thin viscoelastic layer. Provided that optimal viscoelastic layer thickness was selected, placing cuts would only be applicable to treatments with low shear strain level inside the viscoelastic layer.

Modal Loss Factor Predication in Flexible Mechanism Systems With Constrain Viscoelastic Layers

1998 ◽  
Author(s):  
Zhang Xianmin ◽  
Liu Jike
Keyword(s):  
Equations Of Motion ◽  
Sandwich Beam ◽  
Viscoelastic Layer ◽  
Treatment Technique ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Frame Element ◽  
Modal Damping ◽  
Flexible Mechanism ◽  
Viscoelastic Layers

Abstract 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.

Some Pitfalls of Simplified Modeling for Viscoelastic Sandwich Beams

2000 ◽  
Vol 122 (4) ◽  
pp. 434-439 ◽  
Author(s):  
Eric M. Austin ◽  
Daniel J. Inman
Keyword(s):  
Strain Energy ◽  
Large Range ◽  
Sandwich Beams ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Skew Distributions ◽  
Transverse Vibrations ◽  
Simplified Modeling ◽  
Damping Treatments

It is commonplace in academia to base models of constrained-layer damping treatments on the assumption that the facesheets displace identically during transverse vibrations. This assumption is valid for a large range of problems, particularly for problems common in the era when damping was achieved by applying foil-backed treatments to thin panels. The authors show using a very simple example that oversimplified modeling can skew distributions of modal strain energy, a common indicator of damping. [S0739-3717(00)00204-X]

Constrained Substructure Approach to Optimal Strain Energy Analysis

2000 ◽  
Vol 123 (3) ◽  
pp. 340-346 ◽  
Author(s):  
Donald J. Leo ◽  
Eric M. Austin ◽  
Christopher Beattie
Keyword(s):  
Strain Energy ◽  
Optimal Solution ◽  
Structural Elements ◽  
Trial And Error ◽  
Energy Fraction ◽  
Modal Strain Energy ◽  
The Past ◽  
Substructure Approach ◽  
A New Technique ◽  
Damping Treatments

The chief tool for design of viscoelastic-based damping treatments over the past 20 years has been the modal strain energy (MSE) approach. This approach to damping design traditionally has involved a practitioner to vary placement and stiffness of add-on elements using experience and trial and error so as to maximize the add-on element share of system MSE in modes of interest. In this paper we develop a new technique for maximizing strain energy as a function of stiffness for add-on structural elements modeled as rank r perturbations to the original stiffness matrix. The technique is based on a constrained substructure approach allowing us to parameterize strain energy in terms of the eigenvalues of the perturbed structure. An optimality condition is derived that relates the input-output response at the attachment location of the add-on elements to the maximum achievable strain energy. A realizability condition is also derived which indicates whether or not the optimal solution is achievable with passive structural elements. This method has applications in the design of structural treatments for controlling sound and vibration and promises an efficient means of determining the limits of performance of passive structural treatments. An advantage of our approach over existing methods is that the maximum achievable strain energy fraction in the add-on elements is directly computable with the realizability condition then indicating whether the optimal solution is achievable.

Modeling of Frequency-Dependent Viscoelastic Materials for Active-Passive Vibration Damping

1999 ◽  
Vol 122 (2) ◽  
pp. 169-174 ◽  
Author(s):  
M. A. Trindade ◽  
A. Benjeddou ◽  
R. Ohayon
Keyword(s):  
Control Algorithm ◽  
Time Domain Analysis ◽  
Open Loop ◽  
Modal Strain Energy ◽  
Iterative Model ◽  
Modal Reduction ◽  
Modal Damping ◽  
Viscoelastic Layers ◽  
Damping Treatments ◽  
First Time

This work intends to compare two viscoelastic models, namely ADF and GHM, which account for frequency dependence and allow frequency and time-domain analysis of hybrid active-passive damping treatments, made of viscoelastic layers constrained with piezoelectric actuators. A modal strain energy (MSE) based iterative model is also considered for comparison. As both ADF and GHM models increase the size of the system, through additional dissipative coordinates, and to enhance the control feasibility, a modal reduction technique is presented for the first time for the ADF model and then applied to GHM and MSE ones for comparison. The resulting reduced systems are then used to analyze the performance of a segmented hybrid damped cantilever beam under parameters variations, using a constrained input optimal control algorithm. The open loop modal damping factors for all models match well. However, due to differences between the modal basis used for each model, the closed loop ones were found to be different. [S0739-3717(00)01102-8]

Optimum Placement and Control of Active Constrained Layer Damping using Modal Strain Energy Approach

2002 ◽  
Vol 8 (6) ◽  
pp. 861-876 ◽  
Author(s):  
J. Ro ◽  
A. Baz
Keyword(s):  
Strain Energy ◽  
High Efficiency ◽  
Effective Means ◽  
Optimization Technique ◽  
Optimal Placement ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Damping Characteristics ◽  
Active Constrained Layer Damping ◽  
Active Constrained Layer

The Active Constrained Layer Damping (ACLD) treatment has been used successfully for controlling the vibration of various flexible structures. It provides an effective means for augmenting the simplicity and reliability of passive damping with the low weight and high efficiency of active controls to attain high damping characteristics over broad frequency bands. In this paper, optimal placement strategies of ACLD patches are devised using the modal strain energy (MSE) method. These strategies aim at minimizing the total weight of the damping treatments while satisfying constraints imposed on the modal damping ratios. A finite element model is developed to determine the modal strain energies of plates treated with ACLD. The treatment is then applied to the elements that have highest MSE in order to target specific modes of vibrations. Numerical examples are presented to demonstrate the utility of the devised optimization technique as an effective tool for selecting the optimal locations of the ACLD treatment to achieve desired damping characteristics over a broad frequency band.

A Modified MSE Method for Viscoelastic Systems: A Weighted Stiffness Matrix Approach

1995 ◽  
Vol 117 (2) ◽  
pp. 226-231 ◽  
Author(s):  
B.-G. Hu ◽  
M. A. Dokainish ◽  
W. M. Mansour
Keyword(s):  
Stiffness Matrix ◽  
Strain Energy ◽  
Real Eigenvalue ◽  
Modal Strain Energy ◽  
Modal Strain Energy Method ◽  
Damped System ◽  
Modal Damping ◽  
Weighted Matrix ◽  
Error Index

The conventional Modal Strain Energy method (MSE is briefly discussed. Several indices are proposed to characterize a viscoelastically damped system. An Overall Error Index is proposed to assess the accuracy of the solution. A Modified MSE method is developed for a better evaluation of modal damping. Instead of neglecting the damping stiffness matrix in the determination of the eigenvectors, as is the case in the conventional MSE method, the authors used a weighted matrix to solve a real eigenvalue problem. With such modification the estimation of the modal damping is often improved. Numerical simulation of multi degree-of-freedom systems are reported using the proposed Modified MSE method and the indices.

Composite Isogrid Structures With Integral Passive Damping

2000 ◽  
Author(s):  
Yu Chen ◽  
Ronald F. Gibson
Keyword(s):  
Shear Deformation ◽  
Strain Energy ◽  
Viscoelastic Layer ◽  
Damping Properties ◽  
Modal Strain Energy ◽  
Modal Strain Energy Method ◽  
Damping Material ◽  
The Face ◽  
Damping Materials ◽  
Shear Strain Energy

Abstract This paper presents preliminary results from an analysis of the damping properties of a composite isogrid panel with an embedded viscoelastic layer by means of a finite element method (FEM) implementation of the modal strain energy method (MSE). Modal analysis shows that significant shear deformation occurs in the region between the ribs and the face skin because of the stiffness mismatch between the two. Since the performance of a viscoelastic polymer damping material is optimized by subjecting the material to shear deformation, such damping materials can be placed at the interface between the ribs and the skin in order to significantly improve the damping properties of composite isogrid structures. It is shown that the shear strain energy density (energy per volume) near the edges of the panel in the damping layer is much higher than that at the center area for the first free-free vibration mode. As a first attempt at improvement of damping, the effect of using different amounts of damping materials on the loss factor of the isogrid panel is also studied.

scholarly journals Topology Optimization of Free Damping Treatments on Plates Using Level Set Method

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Jian Pang ◽  
Weiguang Zheng ◽  
Liang Yang ◽  
Yuping Wan ◽  
Qibai Huang ◽  
...  
Keyword(s):  
Finite Element ◽  
Level Set Method ◽  
Level Set ◽  
Composite Plate ◽  
Strain Energy ◽  
Base Plate ◽  
Experimental Results ◽  
Modal Strain Energy ◽  
Level Set Function ◽  
Damping Treatments

Application of level set method to optimize the topology of free damping treatments on plates is investigated. The objective function is defined as a combination of several desired modal loss factors solved by the finite element-modal strain energy method. The finite element model for the composite plate is described as combining the level set function. A clamped rectangle composite plate is numerically and experimentally analyzed. The optimized results for a single modal show that the proposed method has the possibility of nucleation of new holes inside the material domain, and the final design is insensitive to initial designs. The damping treatments are guided towards the areas with high modal strain energy. For the multimodal case, the optimized result matches the normalized modal strain energy of the base plate, which would provide a simple implementation way for industrial application. Experimental results show good agreements with the proposed method. The experimental results are in good agreement with the optimization results. It is very promising to see that the optimized result for each modal has almost the same damping effect as that of the full coverage case, and the result for multimodal gets moderate damping at each modal.

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