Design and Optimization of Broadband Vibration Absorbers for Noise Control

2001 ◽  
Author(s):  
Emily S. Heinze ◽  
Michael D. Grissom ◽  
Ashok Belegundu
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Analysis Algorithm ◽  
Design And Optimization ◽  
Forcing Function ◽  
Modal Model ◽  
Practical Design ◽  
Base Structure

Abstract A general and practical approach is presented for optimizing structural additions to a base structure for broadband dynamic objectives when the base structure is excited by an arbitrary forcing function. The mode shapes and natural frequencies of the base structure are first found using a commercial finite element code or an experimental modal analysis. The mode shapes are used as basis shapes to reduce the size of the equations. The structural additions are then added as impedances into the reduced modal model. An efficient analysis algorithm is presented to reduce the computational burden for broadband analysis and optimization loops. The power transferred into a Broadband Vibration Absorber (BBVA) from a base structure is maximized as an example application. The numerical results are experimentally verified demonstrating the practical design capabilities of the method.

scholarly journals Stochastic Modal Models of Slender Uncertain Curved Beams Preloaded Through Clamping

2012 ◽  
Author(s):  
Javier Avalos ◽  
Lanae A. Richter ◽  
X. Q. Wang ◽  
Raghavendra Murthy ◽  
Marc P. Mignolet
Keyword(s):  
Stochastic Model ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Simulated Data ◽  
Mode Shapes ◽  
Curved Beams ◽  
Shape Information ◽  
Final Shape ◽  
Modal Model ◽  
Clamped Beams

This paper addresses the stochastic modeling of the stiffness matrix of slender uncertain curved beams that are forced fit into a clamped-clamped fixture designed for straight beams. Because of the misfit with the clamps, the final shape of the clamped-clamped beams is not straight and they are subjected to an axial preload. Both of these features are uncertain given the uncertainty on the initial, undeformed shape of the beams and affect significantly the stiffness matrix associated with small motions around the clamped-clamped configuration. A modal model using linear modes of the straight clamped-clamped beam with a randomized stiffness matrix is employed to characterize the linear dynamic behavior of the uncertain beams. This stiffness matrix is modeled using a mixed nonparametric-parametric stochastic model in which the nonparametric (maximum entropy) component is used to model the uncertainty in final shape while the preload is explicitly, parametrically included in the stiffness matrix representation. Finally, a maximum likelihood framework is proposed for the identification of the parameters associated with the uncertainty level and the mean model, or part thereof, using either natural frequencies only or natural frequencies and mode shape information of the beams around their final clamped-clamped state. To validate these concepts, a simulated, computational experiment was conducted within Nastran to produce a population of natural frequencies and mode shapes of uncertain slender curved beams after clamping. The application of the above concepts to this simulated data led to a very good to excellent matching of the probability density functions of the natural frequencies and the modal components, even though this information was not used in the identification process. These results strongly suggest the applicability of the proposed stochastic model.

A Unified Frequency Equation and the Motion Analysis of a Moving Flexible Beam Carrying a Concentrated Mass

1999 ◽  
Author(s):  
S. Park ◽  
J. W. Lee ◽  
Y. Youm ◽  
W. K. Chung
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Open Loop ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Forcing Function ◽  
The Mathematical Model

Abstract In this paper, the mathematical model of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying an intermediate lumped mass is derived. The equations of motion of the beam-mass-cart system is analyzed utilizing unconstrained modal analysis, and a unified frequency equation which can be generally applied to this kind of system is obtained. The change of natural frequencies and mode shapes with respect to the change of the mass ratios of the beam, the lumped mass and the cart and to the position of the lumped mass is investigated. The open-loop responses of the system by arbitrary forcing function are also obtained through numerical simulations.

Exact Nonlinear Dynamic Analysis of a Beam With a Nonlinear Vibration Absorber and With Various Boundary Conditions

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Mohammad Bukhari ◽  
Oumar Barry
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Nonlinear Dynamic ◽  
Microelectromechanical Systems ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Vibration Absorber ◽  
Nonlinear Frequency ◽  
Nonlinear Vibration Absorber ◽  
Various Boundary Conditions

Abstract We study the nonlinear vibration of a beam with an attached grounded and ungrounded nonlinear vibration absorber (NVA) using the exact natural frequencies and mode shapes of the loaded beam. The nonlinearity in the beam is due to midplane stretching and that in the NVA is of cubic stiffness nonlinearity. We consider various boundary conditions and derive their closed-form characteristic equations and mode shapes. The method of multiple scales (MMS) is directly applied to the nonlinear partial differential equations of motion to obtain explicit expressions of the nonlinear frequency, modulation, and loci of the saddle-node bifurcation equations. Our analytical approach is validated using direct numerical simulation. Parametric studies demonstrate that the performance of the NVA does not only depend on its key design variables and location, but also on the boundary conditions, midplane stretching of the beam, and type of configuration (i.e., grounded NVA versus ungrounded NVA). Our analysis also indicates that the use of common approach such as employing approximate modes in estimating the nonlinear response of a loaded beam produces significant error (i.e., up to 1200% in some case). These observations suggest that the exact modes shape and natural frequencies are required for a precise investigation of the nonlinear dynamic of loaded beams. These findings could contribute to the design improvement of NVAs, microelectromechanical systems (MEMS), energy harvesters, and metastructures.

Implementation of a Nonlinear Torsional Vibration Absorber for Suppression of Vibrations in Rotating Machinery

2013 ◽  
Author(s):  
Ammaar Bin Tahir ◽  
Oleg Shiryayev ◽  
Nader Vahdati ◽  
Hamad Karki
Keyword(s):  
Nonlinear Vibration ◽  
Torsional Vibration ◽  
Vibration Suppression ◽  
Nonlinear Energy Sink ◽  
Modal Parameters ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Modal Model ◽  
Linear Spring

Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is tuned for a specific resonant frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies. Vibrations dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. Experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, we carry out the design optimization of the nonlinear torsional vibration absorber using an equivalent 2-DOF modal model. A linear vibration absorber is developed in parallel. Subsequently, both absorbers will be manufactured, assembled and mounted on the system to evaluate their vibration suppression capabilities.

Study of Passive Vibration Absorbers Attached on Beam Structure

2014 ◽  
Vol 660 ◽  
pp. 511-515 ◽  
Author(s):  
Izzuddin Zaman ◽  
Muhammad Mohamed Salleh ◽  
Maznan Ismon ◽  
Bukhari Manshoor ◽  
Amir Khalid ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Natural Frequency ◽  
Structural Vibration ◽  
Mode Shapes ◽  
Small Scale ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Element Analysis ◽  
Structural Dynamic

Structural vibration is undesirable, wasting energy and possibly leading to excessive deflections and structure and machine’s failure. In order to reduce structural vibration, one of the common way is considering vibration absorber system attach to the structure. In this study, a vibration absorber is developed in a small scale size. The host structure selected for the study is a fixed-fixed ends beam. The effectiveness of vibration absorbers attached to a beam is investigated through experimental study. In prior to experiment, a finite element analysis of Solidworks® and analytical equations of Matlab® are produced in order to determine the structural dynamic response of the beam, such as the natural frequency and mode shapes. The preliminary results of finite element analysis demonstrate that the first five natural frequency of fixed-fixed end beam are 17Hz, 46Hz, 90Hz, 149Hz and 224Hz, and these results are in agreement with the beam’s analytical equations. However, there are slight discrepancies in experiment result due to noise and error occurred during the setup. In the later stage, the experimental works of beam are performed with attached vibration absorber. Result shows that the attachment of vibration absorber produces better outcome, which is about 45% vibration reduction. It is expected that by adding more vibration absorber to the structure, the vibration attenuation can significant.

Design of Vibration Absorbers for Structures Subject to Multiple-Tonal Excitations

2005 ◽  
Vol 128 (1) ◽  
pp. 106-114 ◽  
Author(s):  
P. W. Wang ◽  
C. C. Cheng
Keyword(s):  
Natural Frequencies ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Systematic Method ◽  
Rotating Speed ◽  
Rotary Machine ◽  
Eccentric Rotor ◽  
Vibration Attenuation ◽  
Impedance Technique ◽  
Multiple Frequencies

The purpose of this paper is to introduce a systematic method of designing a vibration absorber that affects vibration attenuation at multiple frequencies. This vibration absorber is a nonprismatic beam with natural frequencies intentionally designed to coincide with the frequencies of excitation, e.g., the rotating speed of a rotary machine and its harmonic orders. Therefore, it can reduce the vibration response due to rotor eccentric, rotor shaft bending, mechanical looseness, etc. The thickness profile of the nonprismatic beam can be approximated discretely by a large amount of block masses. Each block mass behaves as an elastic structure member, and its thickness can be determined systematically using the impedance technique proposed in this paper. A design is given to demonstrate the methodology, and the result is experimentally validated.

scholarly journals Research on the dynamics of railway car construction

2019 ◽  
Vol 20 (1-2) ◽  
pp. 142-146
Author(s):  
Jarosław Bednarz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Model ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Structural Models ◽  
Transformation Model ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Modal Model

Nowadays, one of the basic criteria of the design of mechanical structures are dynamic properties of the object. They have a significant effect on the vibration, emitted noise, fatigue strength, controllability and stability of the structure. The structural models are most often use to describe the dynamics of the structures. These models are built in accordance with the principles of the finite element method . Structural model can be used to determine the modal model which is a collection of natural frequencies and corresponding mode shapes by an appropriate coordinate transformation model. The construction pro-cess is called the modal analysis . The article presented a method of conducting the experimental modal studies of railway car. The aim of the study was to identify the dynamic properties including the frequency and mode shapes of the object..

scholarly journals Optimizations of distributed dynamic vibration absorbers for suppressing vibrations in plates

2018 ◽  
Vol 37 (4) ◽  
pp. 1188-1200 ◽  
Author(s):  
Xuezhi Zhu ◽  
Zhaobo Chen ◽  
Yinghou Jiao
Keyword(s):  
Vibration Control ◽  
Optimization Problems ◽  
Mode Shapes ◽  
Vibration Absorber ◽  
Superposition Method ◽  
Vibration Absorbers ◽  
Dynamic Vibration Absorber ◽  
Plate Structures ◽  
Dynamic Vibration ◽  
Dynamic Vibration Absorbers

Dynamic vibration absorber is an ideal device for vibration control at specific frequencies. In order to get a robust vibration control performance, multiple or distributed dynamic vibration absorbers are usually used for suppressing vibrations in plate structures. Optimization methods for the single dynamic vibration absorber in various vibration systems had been proposed many years ago. However, the analytical optimization solutions with respect to the distributed dynamic vibration absorbers for the plate structures have not been found. In this paper, the optimization problems of the distributed dynamic vibration absorbers for suppressing vibrations in plates are studied. Vibration equations of the plate carrying distributed dynamic vibration absorbers are established using modal superposition method. The similarities of vibration shapes of the dynamic vibration absorbers and mode shapes of the plate are revealed. According to the characteristics of the vibration shapes of dynamic vibration absorbers, the vibration equations of the plate carrying distributed dynamic vibration absorbers are transformed into a form of equations of a two degree of freedom system. The analytical optimization formulas of the distributed dynamic vibration absorbers for suppressing vibrations in plates are derived by applying the fixed-points theory. The effectiveness of the optimization formulas is verified through numerical simulations. The simulation results also show that a brilliant multi-mode vibration control can be realized by using the optimized distributed dynamic vibration absorbers.

An Inverse Approach on Load Identification From Optimally Placed Accelerometers

2013 ◽  
Author(s):  
Deepak K. Gupta ◽  
Anoop K. Dhingra
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Load Identification ◽  
Acceleration Response ◽  
Inverse Approach ◽  
Modal Damping ◽  
Modal Model ◽  
Load Transducer ◽  
Modal Coordinates ◽  
Selection Of

This paper presents an inverse approach for estimating dynamic loads acting on a structure from acceleration time response measured experimentally at finite number of optimally placed accelerometers on the structure. The structure acts as its own load transducer. The approach is based on the standard equilibrium equation of motion in modal coordinates. Modal model of a system is defined by its modal parameters — natural frequencies, corresponding mode shapes and modal damping factors. These parameters can be estimated experimentally from measured data, analytically for simple problems, or from finite element method. For measurement of the acceleration response, there can be a large number of combinations of locations on the structure where the accelerometers can be mounted and the results may be quite sensitive to the locations selected for accelerometer placements. In fact, the precision with which the applied loads are estimated from measured acceleration response depends on the number of accelerometers utilized and their location on the component. Implementation of a methodology to determine the optimum set of accelerometer locations, based on the construction of D-optimal design, is presented to guide the selection of number and locations of accelerometers that will provide the most precise load estimates. A technique based on model reduction is proposed to reconstruct the input forces accurately. A numerical validation that helps to understand the main characteristics of the proposed approach is also presented. The numerical results reveal the effectiveness and utility of the technique.

The Effect of Close or Repeated Eigenvalues on the Updating of Model Parameters from FRF Data

1992 ◽  
Vol 114 (4) ◽  
pp. 514-520 ◽  
Author(s):  
M. I. Friswell ◽  
J. E. T. Penny
Keyword(s):  
Natural Frequencies ◽  
Analytical Models ◽  
Mode Shapes ◽  
Model Parameters ◽  
Finite Element Models ◽  
Reduced Order ◽  
Vibration Data ◽  
Modal Model ◽  
Equation Error ◽  
Error Method

Methods to update the parameters of finite element models using measured vibration data usually use the experimentally derived modal model, that is, the system natural frequencies, damping coefficients, and mode shapes. Alternatively the frequency response functions have been used directly to update condensed analytical models and so avoid the sometimes difficult step of deriving the modal model. Previously the authors suggested an algorithm using FRF data that is basically a weighted equation error method based on a reduced order model. This paper investigates the performance of the algorithm for systems with closely coupled or repeated natural frequencies or eigenvalues.

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