Finite Element Modeling for Vibration Analysis of Constrained Layer Damping Treated Structures

2000 ◽  
Author(s):  
Yanchu Xu ◽  
Dennis Chen
Keyword(s):  
Single Element ◽  
Element Formulation ◽  
Constrained Layer Damping ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Element Density ◽  
Compound Plate ◽  
Kinetic And Potential Energies ◽  
Structure Layer ◽  
Base Structure

Abstract A compound plate element is presented for modeling all layers of the damped structure into a single element. By associating deformations of the damping layer to those of base structure layer and constraining layer, the kinetic and potential energies of the damping layer as well as those of base and constraining layers can be derived. Then the element mass and stiffness matrices can be obtained for all layers as a whole. The newly derived element formulation results in significant simplification of constrained layer modeling and dramatic reduction of element density while maintaining the desired accuracy. The use of the element also allows direct and more accurate calculation of structural modal damping in modal analysis.

Structural Modification Software Development for Design Optimization

1995 ◽  
Author(s):  
Xiaoye Gu ◽  
Alison B. Flatau
Keyword(s):  
Structural Response ◽  
Acoustic Power ◽  
Modal Parameters ◽  
Constrained Layer Damping ◽  
Experimental Frequency ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Structural Responses ◽  
Damping Materials ◽  
Modal Mass

Abstract This paper presents a method for obtaining structural matrices from experimental frequency response function (FRF) data and using these structural matrices to predict the response of the structure to modifications at various locations. The approach taken is designed for subsequent use in optimizing structural modifications to efficiently reduce radiated acoustic power. A series of programs were written for identifying the structural matrices (mass matrices, stiffness matrices and damping matrices) from the measured FRF data. These matrices are used to obtain the modified response of the structure resulting from adding linear springs at different locations on the structure. Experimental results from a beam are presented to verify these programs. Work is in progress on extending this method to incorporate modifications to the structure produced by constrained-layer damping materials. The programs for obtaining the structural matrices and the structural response are composed of approaches used by several prior authors. Potter and Richardson’s [1,2] method is used for obtaining the relative modal parameters (modal mass, modal stiffness and modal damping). Luk and Mitchell’s [3,4] pseudo-inverse method is employed to obtain the structural matrices for cases when the number of modes measured is much less than the number of test points. A method for deriving the absolute value of modal parameters from the measured FRF data is also developed using modal analysis theory. Linear springs are added at various positions to modify the structure. The structural matrices are used to predict the modified structural responses scaled to displacement per unit force. A series of linear spring modifications are modeled and implemented experimentally to verify these programs.

A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate

2006 ◽  
Vol 128 (4) ◽  
pp. 477-488 ◽  
Author(s):  
A. Chakraborty ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Shear Deformation ◽  
Mechanical Response ◽  
Laminated Composite ◽  
Wave Number ◽  
Single Element ◽  
Element Formulation ◽  
Frequency Wave ◽  
Spectral Finite Element

A new spectral plate element (SPE) is developed to analyze wave propagation in anisotropic laminated composite media. The element is based on the first-order laminated plate theory, which takes shear deformation into consideration. The element is formulated using the recently developed methodology of spectral finite element formulation based on the solution of a polynomial eigenvalue problem. By virtue of its frequency-wave number domain formulation, single element is sufficient to model large structures, where conventional finite element method will incur heavy cost of computation. The variation of the wave numbers with frequency is shown, which illustrates the inhomogeneous nature of the wave. The element is used to demonstrate the nature of the wave propagating in laminated composite due to mechanical impact and the effect of shear deformation on the mechanical response is demonstrated. The element is also upgraded to an active spectral plate clement for modeling open and closed loop vibration control of plate structures. Further, delamination is introduced in the SPE and scattered wave is captured for both broadband and modulated pulse loading.

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.

scholarly journals A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

2016 ◽  
Vol 35 (23) ◽  
pp. 1696-1711 ◽  
Author(s):  
Danilo S Victorazzo ◽  
Andre De Jesus
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Composite Beam ◽  
Linear Equations ◽  
Beam Theory ◽  
Element Formulation ◽  
Compliance Matrix ◽  
Asymmetric System ◽  
Anisotropic Composite ◽  
Stiffness Matrices

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

Symmetric Model Correction of Mechanical Systems

1993 ◽  
Author(s):  
Marca Lam ◽  
Daniel J. Inman ◽  
Andreas Kress
Keyword(s):  
Analytical Model ◽  
Model Updating ◽  
Symmetric Model ◽  
Simple Method ◽  
Modal Data ◽  
Model Correction ◽  
Systems Model ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Damped Systems

Abstract This work examines the model updating problem for simple nonconservative proportionally damped systems. Model correction, also called model updating, refers to the practice of adjusting an analytical model until the model agrees with measured modal data. The specific case examined here assumes that natural frequencies and modal damping ratios are available from vibration tests and that the measured data disagrees in part with the modal data predicted by an analytical model. Most model correction schemes tend to produce updated damping and stiffness matrices which are asymmetric. The simple method presented here focuses on retaining the desired symmetry in the updated model.

Constrained Layer Damping Treatments for Microstructures

2002 ◽  
Vol 124 (4) ◽  
pp. 612-616 ◽  
Author(s):  
Yi-Chu Hsu ◽  
I. Y. Shen
Keyword(s):  
Laser Doppler Vibrometer ◽  
Viscoelastic Layer ◽  
Constrained Layer Damping ◽  
Element Analysis ◽  
Resonance Modes ◽  
Thick Photoresist ◽  
Measured Frequency Response ◽  
Damping Treatments ◽  
Base Structure ◽  
Silicon Beams

This paper presents a bulk micromachining process to fabricate micro-constrained layer treatments (MCLT) on a microstructure to increase its damping, and demonstrates the damping improvement through calibrated experiments. MCLT consists of a silicon base structure (e.g., beams or plates), a viscoelastic photoresist layer, and an aluminum constraining layer. Silicon base beams and plates are fabricated from {100} wafer through Ethylene-Diamine-Pyrocatechol etch and buffered oxide etch. A 4.5-μm thick photoresist AZ4620 is spun on the silicon base beam as the viscoelastic layer. Finally, an aluminum layer is deposited through low-pressure vapor deposition as the constraining layer. To evaluate damping performance of MCLT, silicon beams with and without MCLT are subjected to swept-sine excitations by PZT from 0 to 100 kHz. In addition, a laser Doppler vibrometer and a spectrum analyzer measured frequency response functions (FRF) of the specimen. A finite element analysis identifies the resonance modes measured in FRF. Experimental results confirm that MCLT can increase damping of silicon beams by at least 40%. Significantly better damping performance is expected, if the loss factor of the viscoelastic layer is increased.

A four-node quadrilateral element for vibration and damping analysis of sandwich plates with viscoelastic core

2017 ◽  
Vol 21 (3) ◽  
pp. 1072-1118 ◽  
Author(s):  
Shanhong Ren ◽  
Guozhong Zhao
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Complex Eigenvalue ◽  
Constrained Layer Damping ◽  
Quadrilateral Element ◽  
Frequency Dependent ◽  
Viscoelastic Core ◽  
Rectangular Element

Constrained layer damping treatments have been widely used as an effective way for vibration control and noise reduction of thin-walled plates and shells. Despite extensive application in vibration and damping analysis of sandwich plates with viscoelastic core, the rectangular element is challenged by irregular structural forms in practical engineering. In this paper, a three-layer four-node quadrilateral element with seven degrees of freedom at each node is presented. Compared with classical rectangular element, the four-node quadrilateral element has stronger adaptability in complex structural forms and boundary conditions. Based on the layer-wise theory where the constrained layer and the base layer meet Kirchhoff theory and the viscoelastic layer satisfies first-order shear deformation theory, the finite element formulation of the sandwich plate with viscoelastic core is derived by the Hamilton principle in variational form and based on the generalization of the discrete Kirchhoff Quadrilateral plate element. The complex modulus model is employed to describe the viscoelastic core of sandwich plates, allowing for the material’s frequency dependent characteristics. The natural frequencies and associated modal loss factors are computed based on the complex eigenvalue problems. The frequency dependent characteristic of the viscoelastic core is considered and an iterative procedure is introduced to solve the nonlinear eigenvalue problem. At last, six verification numerical examples that include three sandwich beam-plates and three sandwich plates are provided to compare present method with experiment, analytical method, Galerkin method, finite element methods and commercial software (NASTRAN). The results show that the proposed finite element can accurately and efficiently simulate the sandwich plates treated with constrained layer damping with a variety of structural forms and boundary conditions.

Finite Element Formulation for Linear Stability Analysis of Axially Functionally Graded Nonprismatic Timoshenko Beam

2019 ◽  
Vol 19 (02) ◽  
pp. 1950002 ◽  
Author(s):  
Masoumeh Soltani ◽  
Behrouz Asgarian
Keyword(s):  
Stability Analysis ◽  
Power Series ◽  
Linear Stability ◽  
Timoshenko Beam ◽  
Linear Stability Analysis ◽  
Functionally Graded ◽  
Element Formulation ◽  
Variable Cross ◽  
Timoshenko Beams ◽  
Stiffness Matrices

An improved approach based on the power series expansions is proposed to exactly evaluate the static and buckling stiffness matrices for the linear stability analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section and fixed–free boundary condition. Based on the Timoshenko beam theory, the equilibrium equations are derived in the context of small displacements, considering the coupling between the transverse deflection and angle of rotation. The system of stability equations is then converted into a single homogeneous differential equation in terms of bending rotation for the cantilever, which is solved numerically with the help of the power series approximation. All the mechanical properties and displacement components are thus expanded in terms of the power series of a known degree. Afterwards, the shape functions are gained by altering the deformation shape of the AFG nonprismatic Timoshenko beam in a power series form. At the end, the elastic and buckling stiffness matrices are exactly determined by the weak form of the governing equation. The precision and competency of the present procedure in stability analysis are assessed through several numerical examples of axially nonhomogeneous and homogeneous Timoshenko beams with clamped-free ends. Comparison is also made with results obtained using ANSYS and other solutions available, which indicates the correctness of the present method.

Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation

1985 ◽  
Vol 52 (4) ◽  
pp. 897-906 ◽  
Author(s):  
D. F. Golla ◽  
P. C. Hughes
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Mass Density ◽  
Viscoelastic Damping ◽  
Element Formulation ◽  
Elastic Structures ◽  
Element Analysis ◽  
Modal Damping ◽  
Computer Based ◽  
Finite Element Formulations

Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M, K” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.

scholarly journals Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach

2011 ◽  
Vol 18 (1-2) ◽  
pp. 221-244 ◽  
Author(s):  
Zheng Ling ◽  
Xie Ronglu ◽  
Wang Yi ◽  
Adel El-Sabbagh
Keyword(s):  
Topology Optimization ◽  
Energy Dissipation ◽  
Design Variable ◽  
Optimization Design ◽  
Damping Ratio ◽  
Design Tool ◽  
Optimization Approach ◽  
Constrained Layer Damping ◽  
Modal Damping Ratio ◽  
Modal Damping

Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA) is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an invaluable design tool.

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