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]

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.

scholarly journals Microstructural Topology Optimization of Constrained Layer Damping on Plates for Maximum Modal Loss Factor of Macrostructures

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhanpeng Fang ◽  
Lei Yao ◽  
Shuxia Tian ◽  
Junjian Hou
Keyword(s):  
Topology Optimization ◽  
Loss Factor ◽  
Strain Energy ◽  
Design Method ◽  
Optimization Method ◽  
Constrained Layer Damping ◽  
Viscoelastic Materials ◽  
Modal Strain Energy ◽  
Design Variables ◽  
Microstructural Topology Optimization

This paper presents microstructural topology optimization of viscoelastic materials for the plates with constrained layer damping (CLD) treatments. The design objective is to maximize modal loss factor of macrostructures, which is obtained by using the Modal Strain Energy (MSE) method. The microstructure of the viscoelastic damping layer is composed of 3D periodic unit cells. The effective elastic properties of the unit cell are obtained through the strain energy-based method. The density-based topology optimization is adopted to find optimal microstructures of viscoelastic materials. The design sensitivities of modal loss factor with respect to the design variables are analyzed and the design variables are updated by Method of Moving Asymptotes (MMA). Numerical examples are given to demonstrate the validity of the proposed optimization method. The effectiveness of the optimal design method is illustrated by comparing a solid and an optimized cellular viscoelastic material as applied to the plates with CLD treatments.

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.

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.

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 Dynamic Optimization of Constrained Layer Damping Structure for the Headstock of Machine Tools with Modal Strain Energy Method

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Yakai Xu ◽  
Weiguo Gao ◽  
Yuhan Yu ◽  
Dawei Zhang ◽  
Xiangsong Zhao ◽  
...  
Keyword(s):  
Loss Factor ◽  
Strain Energy ◽  
Dynamic Stiffness ◽  
Optimization Method ◽  
Original Structure ◽  
Damping Capacity ◽  
Machining Accuracy ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Damping Material

Dynamic stiffness and damping of the headstock, which is a critical component of precision horizontal machining center, are two main factors that influence machining accuracy and surface finish quality. Constrained Layer Damping (CLD) structure is proved to be effective in raising damping capacity for the thin plate and shell structures. In this paper, one kind of high damping material is utilized on the headstock to improve damping capacity. The dynamic characteristic of the hybrid headstock is investigated analytically and experimentally. The results demonstrate that the resonant response amplitudes of the headstock with damping material can decrease significantly compared to original cast structure. To obtain the optimal configuration of damping material, a topology optimization method based on the Evolutionary Structural Optimization (ESO) is implemented. Modal Strain Energy (MSE) method is employed to analyze the damping and to derive the sensitivity of the modal loss factor. The optimization results indicate that the added weight of damping material decreases by 50%; meanwhile the first two orders of modal loss factor decrease by less than 23.5% compared to the original structure.

Applying constrained layer damping to reduce vibration and noise from a steel-concrete composite bridge: An experimental and numerical investigation

2018 ◽  
Vol 22 (6) ◽  
pp. 1743-1769 ◽  
Author(s):  
Quanmin Liu ◽  
Xiaozhen Li ◽  
Xun Zhang ◽  
Yunlai Zhou ◽  
Y Frank Chen
Keyword(s):  
Strain Energy ◽  
Energy Analysis ◽  
Constrained Layer Damping ◽  
Statistical Energy Analysis ◽  
Train Track ◽  
Coupled Vibration ◽  
Modal Strain Energy ◽  
Composite Bridge ◽  
Track Bridge ◽  
Loss Factors

Structure-borne noise from railway bridges has become increasingly severe due to increased train speeds and axle loads. Constrained layer damping can suppress structural vibration and noise considerably across a wide frequency range by dissipating vibrational energy via damping layer shear deformation. This paper proposes a theoretical method of calculating the train-induced vibration and noise of a constrained layer damping-enhanced railway bridge based on the train–track–bridge coupled vibration, the modal strain energy method, and statistical energy analysis. First, the vibration responses of bridge decks were obtained via train–track–bridge coupled vibration calculations. Second, the constrained layer damping subsystem modal loss factors were determined via modal strain energy analysis and converted to damping loss factors in 1/3 octave band. Third, upon substituting the vibration energies of the decks and the damping loss factors of constrained layer damping subsystems into the statistical energy analysis power balance equations, the transmitted vibration energy results from various bridge subsystems were determined by solving the referenced equations. The structure-borne noise from the bridge was finally determined by analyzing the vibratory energies of all of the bridge subsystems using vibro-acoustic theory. Numerical analysis and field measurements of vibration and noise from a three-span steel–concrete composite bridge before and after constrained layer damping installation were performed. The predicted train-induced vibration and noise agreed well with the measured results. The stringer web and flange vibration velocity levels were reduced by 10.5 dB and 6.1 dB, respectively, and the sound pressure level at a measurement point 25 m (horizontal) from the track centerline and 1.5 m off the ground decreased by 4.3 dB(A).

scholarly journals Modifications to the Method of Modal Strain Energy for Improved Estimates of Loss Factors for Damped Structures

2007 ◽  
Vol 14 (5) ◽  
pp. 339-353 ◽  
Author(s):  
Peter J. Torvik ◽  
Brian Runyon
Keyword(s):  
Loss Factor ◽  
Strain Energy ◽  
Prototype System ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
High Loss ◽  
Analysis And Design ◽  
Dissipative Material ◽  
Complex Valued ◽  
Loss Factors

The method of Modal Strain Energy (MSE) enables predictions of modal loss factors for vibrating systems from finite element analyses without evaluation of a complex-valued frequency response or a complex-valued frequency. While the method is simple, some error results; especially if the dissipative material has the high loss factor characteristic of materials added to increase system damping. Several methods for reducing this error through modifications to MSE have been suggested. In this work, the exact loss factor for a simple mechanical system is found. The method of Modal Strain Energy (MSE) is then used to find the loss factor for that prototype system and errors are evaluated in terms of system parameters. Comparisons are also made to predictions with several modifications to MSE. A modification due to Rongong is found to provide significant improvement. The use of this modification together with MSE is shown to lead to lower and upper bounds for the system loss factor. As the prototype system is shown to be mechanically equivalent to constrained layer damping configurations, the findings are applicable to the analysis and design of optimized sandwich beams, plates, and damping tapes. Results are given for beams and plates with constrained layer treatments.

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