Optimizing Piecewise Linear Isolator for Steady State Vibration

In this work we have studied the effect of stoppers in quarter car model. While in rough roads these stoppers prevent the system from excessive displacement around the resonance frequency. Although stoppers prevent the undesired motion they increase the transmitted force that is undesirable in suspension systems. In order to optimize between the relative displacement and transmitted force an analytical model is considered. The piecewise linear system is the model of presented nonlinearity which cannot be considered small. Therefore standard perturbation methods are not able to provide an analytical solution. For this case we have adopted an averaging method which leads to frequency response of the piecewise linear system at resonance. In order to confirm the results obtained by averaging method an experimental device is fabricated and frequency response of the system is measured. The experimental frequency response is in very good agreement with analytical approach and numerical simulations. Sensitivity analysis methods are used to minimize the cost function of maximum relative displacement in frequency domain. The range of the parameters that minimizes the cost function where certain amount of clearance exists in the system are obtained.

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Parameter Optimizing for Piecewise Linear Isolator

Applied Mechanics ◽

10.1115/imece2004-61312 ◽

2004 ◽

Cited By ~ 1

Author(s):

A. Narimani ◽

M. F. Golnaraghi

Keyword(s):

Linear System ◽

Averaging Method ◽

Piecewise Linear ◽

Optimization Methods ◽

Relative Displacement ◽

Suspension Systems ◽

Piecewise Linear System ◽

At Resonance ◽

Transmitted Force ◽

Analytical Frequency

In this paper we have studied the effect of end stops in an isolator. While subjected to excessive base excitation the stops prevent the system from excessive relative displacement particularly around the resonance frequency. Although stoppers prevent the undesired motion they increase the transmitted force that is undesirable in suspension systems. This system is modeled as a piecewise linear system where the nonlinearity cannot be considered small. Therefore we have adopted an averaging method which leads to analytical frequency response of the piecewise linear system at resonance. Using this analytical method we are able to obtain the range of the parameters, which minimize the relative displacement of the system. Further more using the RMS optimization methods the transmitted force in the system is optimized.

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Bifurcation Induced by Mass Variation in Piecewise Linear System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.226-228.531 ◽

2012 ◽

Vol 226-228 ◽

pp. 531-535

Author(s):

Yue Hua Li ◽

Shi Dong Chen

Keyword(s):

Linear System ◽

Frequency Response ◽

Averaging Method ◽

Piecewise Linear ◽

Singularity Theory ◽

Excitation Amplitude ◽

Mass Variation ◽

Piecewise Linear System ◽

Amplitude Frequency Response ◽

Two Parameters

This paper investigates the bifurcations of the periodic solutions in the piecewise linear systems. Firstly the equation about amplitude-frequency response is deduced by the averaging method. Then the bifurcation classification is conducted by applying the singularity theory. The effects of the two parameters, the mass and the excitation amplitude, are discussed. The balance position will be changed when the quality changed, So the system is divided into two kinds of state. The results show that the parameter plane is divided into thirteen regions where bifurcation types are different. At last, discussing the amplitude- frequency response of different regions. this paper provides some theoretical guidance for system of considering load variation, and it is significant to help research the change in amplitude-frequency characteristic of piecewise linear system.

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Sensitivity Analysis of the Frequency Response of a Piecewise Linear System in a Frequency Island

Journal of Vibration and Control ◽

10.1177/1077546304032993 ◽

2004 ◽

Vol 10 (2) ◽

pp. 175-198 ◽

Cited By ~ 24

Author(s):

A Narimani ◽

M Farid Golnaraghi ◽

G Nakhaie Jazar

Keyword(s):

Frequency Response ◽

Initial Conditions ◽

Piecewise Linear ◽

Excitation Frequency ◽

Relative Displacement ◽

System Parameters ◽

Dynamical Characteristics ◽

Piecewise Linear System ◽

Amplitude Vibration ◽

Large Amplitude Vibration

In this paper, we analyze the frequency response of a piecewise linear suspension system. Dynamical characteristics of the suspension will suddenly change when its relative displacement exceeds a clearance. Piecewise linear characteristics occur, for example, wherever we use stoppers to prevent the system from excessive relative displacement. A modified averaging method is used to find the frequency response of the system to a harmonic base excitation. A frequency island is observed, which corresponds to large amplitude vibration for a certain range of system parameters. The island is an isolated region that cannot be reached by the variation of excitation frequency and depends upon initial conditions. On the frequency island, the isolator amplifies the amplitude of vibration rather than suppressing it. This will be dangerous in applications where stoppers are installed to ensure relative displacement is limited. The ranges of system parameters causing the frequency island are determined. The results obtained by an analytical method are verified using numerical simulation.

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Frequency Response of a Piecewise Linear Vibration Isolator

Journal of Vibration and Control ◽

10.1177/1077546304044795 ◽

2004 ◽

Vol 10 (12) ◽

pp. 1775-1794 ◽

Cited By ~ 46

Author(s):

A. Narimani ◽

M. E. Golnaraghi ◽

G. Nakhaie Jazar

Keyword(s):

Frequency Response ◽

Averaging Method ◽

Dominant Role ◽

Piecewise Linear ◽

Damping Ratio ◽

Vibration Isolator ◽

Linear Vibration ◽

Vibration Isolators ◽

Piecewise Linear System ◽

Response Equation

Piecewise linear vibration isolators are designed to optimally balance the competing goals of motion control and isolation. The piecewise linear system represents a hard nonlinearity, which cannot be assumed small, and hence standard perturbation methods are unable to provide a complete analytical solution. To date there is no frequency response equation reported for piecewise linear isolator systems to include both dual damping and stiffness behavior. In this investigation an averaging method was adopted to explore the frequency response of a symmetric piecewise linear isolator at resonance. The result obtained by an averaging method is in agreement with numerical simulation and experimental measurements. Preliminary sensitivity analysis is conducted to find the effect of system parameters. It appears that the damping ratio plays a more dominant role than stiffness in piecewise linear vibration isolators.

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