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

2013 ◽  
Vol 774-776 ◽  
pp. 3-6
Author(s):  
Ying Feng Lei ◽  
Wei Guang Zheng ◽  
Qi Bai Huang ◽  
Chuan Bing Li
Keyword(s):  
Topology Optimization ◽  
Numerical Study ◽  
Harmonic Excitation ◽  
Surface Velocity ◽  
Viscoelastic Layer ◽  
Constrained Layer Damping ◽  
Objective Functions ◽  
Normal Surface ◽  
Simple Interface ◽  
Passive Constrained Layer Damping

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.

scholarly journals Topology Optimization of Passive Constrained Layer Damping with Partial Coverage on Plate

2013 ◽  
Vol 20 (2) ◽  
pp. 199-211 ◽  
Author(s):  
Weiguang Zheng ◽  
Yingfeng Lei ◽  
Shande Li ◽  
Qibai Huang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Objective Function ◽  
Optimization Procedure ◽  
Constrained Layer Damping ◽  
Flat Plates ◽  
Modal Strain Energy ◽  
Partial Coverage ◽  
Material Interpolation ◽  
Passive Constrained Layer Damping

The potential of using topology optimization as a tool to optimize the passive constrained layer damping (PCLD) layouts with partial coverage on flat plates is investigated. The objective function is defined as a combination of several modal loss factors solved by finite element-modal strain energy (FE-MSE) method. An interface finite element is introduced to modeling the viscoelastic core of PCLD patch to save the computational space and time in the optimization procedure. Solid isotropic material with penalization (SIMP) method is used as the material interpolation scheme and the parameters are well selected to avoid local pseudo modes. Then, the method of moving asymptote (MMA) is employed as an optimizer to search the optimal topologies of PCLD patch on plates. Applications of two flat plates with different shapes have been applied to demonstrate the validation of the proposed approach. The results show that the objective function is in a steady convergence process and the damping effect of the plates can be enhanced by the optimized PCLD layouts.

Optimization of Plate with Partial Constrained Layer Damping Treatment for Vibration and Noise Reduction

2011 ◽  
Vol 138-139 ◽  
pp. 20-26 ◽  
Author(s):  
Shou Wu Hou ◽  
Ying Hou Jiao ◽  
Xin Wang ◽  
Zhao Bo Chen ◽  
Yong Bo Fan
Keyword(s):  
Sandwich Plate ◽  
Vibrational Energy ◽  
Added Mass ◽  
Transverse Force ◽  
Viscoelastic Layer ◽  
Sound Power ◽  
Constrained Layer Damping ◽  
Simply Supported ◽  
Passive Constrained Layer Damping ◽  
Lagrange’S Method

To efficiently reduce vibration and noise of a plate, an optimization of passive constrained layer damping (CLD) is presented. The dynamic equation of a sandwich plate with CLD treatment is derived using Lagrange’s method. The assumed modes method is employed to solve the equation and obtain the vibrational energy and sound power, which are used as the objective of optimal design. A genetic algorithm of big mutation is employed to search for the optimum of the location of CLD treatment, the thicknesses of both the constraining layer and the viscoelastic layer and the shear modulus of the viscoelastic material with the restriction of added mass of the total CLD treatment. Numerical results show that for a simply-supported plate with a transverse force (1Hz~200Hz) applied at (0.8La, 0.8Lb), the optimized CLD significantly reduce the vibrational energy and sound power.

Optimum Layout of Passive Constrained Layer Damping Treatment Using Genetic Algorithms

2010 ◽  
Author(s):  
S. W. Hou ◽  
Y. H. Jiao ◽  
Z. B. Chen
Keyword(s):  
Shear Modulus ◽  
Viscoelastic Material ◽  
Large Scale ◽  
Vibration Suppression ◽  
Flexible Structures ◽  
Wide Frequency Range ◽  
Viscoelastic Layer ◽  
Constrained Layer Damping ◽  
Passive Constrained Layer Damping ◽  
Loss Factors

The passive constrained layer damping (CLD) treatments have been used widely for vibration suppression of various flexible structures. Fully covered CLD treatment is extensively used to depress the vibration over a wide frequency range in engineering applications. In most of these treatments it is required that the CLD treatment should not significantly increase the weight or volume. This paper focuses on damping optimization of fully coating beam with a constrained viscoelastic layer. The governing equation of motion of a CLD covered beam is derived using an energy approach and Lagrange’s method. The assumed modes method is employed in solving the equation to obtain the modal loss factors which are used as the objective of optimal layout. A genetic algorithm with large-scale mutation method is employed to search for the optima of the thicknesses of both the constraining layer (CL) and the viscoelastic layer (VL) and the shear modulus of the viscoelastic material (VEM) with the restriction of added volume of the total CLD treatment. Numerical results show that the optima of three design variables, the thicknesses of the CL and the VL and the shear modulus of its viscoelastic material, are highly relevant to each other. The softer or thinner constraining layer requires a softer viscoelastic material for an optimal damping treatment, and high value of the elastic modulus of the base beam matches high shear modulus of the viscoelastic material. The variation of the CL thickness decreases slowly and that of the VL thickness increases with the increase of the thickness of the CLD treatment. Stiffer constraining layer assure greater modal loss factors.

Experimental and Finite Element Analysis of Stand-Off Layer Damping Treatments for Beams

2007 ◽  
Author(s):  
Jessica M. H. Yellin ◽  
I. Y. Shen ◽  
Per G. Reinhall
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Frequency Response ◽  
Viscoelastic Layer ◽  
Constrained Layer Damping ◽  
Response Functions ◽  
Element Analysis ◽  
Frequency Response Functions ◽  
Damping Treatments ◽  
Passive Constrained Layer Damping

Passive stand-off layer (PSOL) and slotted stand-off layer (SSOL) damping treatments are presently being implemented in many commercial and defense designs. In a PSOL damping treatment, a stand-off or spacer layer is added to a conventional passive constrained layer damping treatment. In an SSOL damping treatment, slots are included in the stand-off layer. A set of experiments using PSOL and SSOL beams in which the geometric properties of the stand-off layer were varied was conducted to analyze the contribution of the stand-off layer to the overall system damping. This set of experiments measured the frequency response functions for a series of beams in which the total slotted area of the stand-off layer was held constant while the number of slots in the stand-off layer was increased for a constant stand-off layer material. Finite element analysis models were developed in ANSYS to compare the predicted frequency response functions with the experimentally measured frequency response functions for the beams treated with PSOL and SSOL damping treatments. In these beams, the bonding layers used to fabricate these treatments were found to have a measurable and significant effect on the frequency response of the structure. The finite element model presented here thus included an epoxy layer between the base beam and the stand-off layer, a contact cement layer between the stand-off layer and the viscoelastic layer, and a method for modeling delamination.

Modeling Vibration-Induced Tire-Pavement Interaction Noise in the Mid-frequency Range

2020 ◽  
Author(s):  
Sterling McBride ◽  
Ricardo Burdisso ◽  
Corina Sandu
Keyword(s):  
Sound Intensity ◽  
Element Model ◽  
Dominant Frequency ◽  
Contact Forces ◽  
Surface Velocity ◽  
New Wave ◽  
Normal Surface ◽  
Radiated Noise ◽  
Physical Effects ◽  
Effects Of Rotation

ABSTRACT Tire-pavement interaction noise (TPIN) is one of the main sources of exterior noise produced by vehicles traveling at greater than 50 kph. The dominant frequency content is typically within 500–1500 Hz. Structural tire vibrations are among the principal TPIN mechanisms. In this work, the structure of the tire is modeled and a new wave propagation solution to find its response is proposed. Multiple physical effects are accounted for in the formulation. In an effort to analyze the effects of curvature, a flat plate and a cylindrical shell model are presented. Orthotropic and nonuniform structural properties along the tire's transversal direction are included to account for differences between its sidewalls and belt. Finally, the effects of rotation and inflation pressure are also included in the formulation. Modeled frequency response functions are analyzed and validated. In addition, a new frequency-domain formulation is presented for the computation of input tread pattern contact forces. Finally, the rolling tire's normal surface velocity response is coupled with a boundary element model to demonstrate the radiated noise at the leading and trailing edge locations. These results are then compared with experimental data measured with an on-board sound intensity system.

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.

Numerical Study of an Impact Oscillator

1995 ◽  
Author(s):  
Kannan Marudachalam ◽  
Faruk H. Bursal
Keyword(s):  
Dynamical Systems ◽  
Numerical Algorithm ◽  
Initial Conditions ◽  
Numerical Study ◽  
Harmonic Excitation ◽  
General Purpose ◽  
Constrained Systems ◽  
Global Dynamics ◽  
Impact Oscillator ◽  
Stick Slip

Abstract Systems with discontinuous dynamics can be found in diverse disciplines. Meshing gears with backlash, impact dampers, relative motion of components that exhibit stick-slip phenomena axe but a few examples from mechanical systems. These form a class of dynamical systems where the nonlinearity is so severe that analysis becomes formidable, especially when global behavior needs to be known. Only recently have researchers attempted to investigate such systems in terms of modern dynamical systems theory. In this work, an impact oscillator with two-sided rigid constraints is used as a paradigm for studying the characteristics of discontinuous dynamical systems. The oscillator has zero stiffness and is subjected to harmonic excitation. The system is linear without impacts. However, the impacts introduce nonlinearity and dissipation (assuming inelastic impacts). A numerical algorithm is developed for studying the global dynamics of the system. A peculiar type of solution in which the trajectories in phase space from a certain set of initial conditions merge in finite time, making the dynamics non-invertible, is investigated. Also, the effect of “grazing,” a behavior common to constrained systems, on the dynamics of the system is studied. Based on the experience gained in studying this system, the need for an efficient general-purpose numerical algorithm for solving discontinuous dynamical systems is motivated. Investigation of stress, vibration, wear, noise, etc. that are associated with impact phenomena can benefit greatly from such an algorithm.

Hybrid Control of Rotating Beams Using Pattern Search Based Optimization Technique

2018 ◽  
Author(s):  
Rajiv Kumar Vashisht ◽  
Qingjin Peng
Keyword(s):  
Smart Materials ◽  
Optimization Technique ◽  
Flexible Structures ◽  
Pattern Search ◽  
Feedback Controller ◽  
Structural Vibration ◽  
Flexible Beam ◽  
Constrained Layer Damping ◽  
Rotating Beams ◽  
Passive Constrained Layer Damping

Rotating beams are quite common in rotating machinery e.g. fans of compressors in an airplane. This paper presents the experimental, hybrid, structural vibration control of flexible structures to enhance the vibration behavior of rotating beams. Smart materials have been used as sensors as well as actuators. Passive constrained layer damping (PCLD) treatment is combined with stressed layer damping technique to enhance the damping characteristics of the flexible beam. To further enhance the damping parameters, a closed form robust feedback controller is applied to reduce the broadband structural vibrations of the rotating beam. The feed forward controller is designed by combing with the feedback controller using a pattern search based optimization technique. The hybrid controller enhances the performance of the closed loop system. Experiments have been conducted to validate the effectiveness of the presented technique.

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