Comparison of Exact and Approximate Frequency Response of a Piecewise Linear Vibration Isolator

Jazar, Reza N.; Mahinfalah, M.; Aagaah, M. Rastgaar; Nazari, G. H.

doi:10.1115/detc2005-84522

Cited by 3 publications

(3 citation statements)

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“…and applying averaging method [25,26] leads to the Fig. 1 Mechanical model of the bi-linear system and representation of the stiffness and damping following descriptions for frequency and phase responses.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The piecewise linear vibration system when studied analytically, numerically, and experimentally [24][25][26][27][28][29][30][31] showed an interesting behaviour known as jump. When the excitation frequency is gradually increased at constant excitation amplitude, there comes a point where a sudden drop in relative displacement amplitude is observed.…”

Section: The Phenomenon Of Jump and Condition For Jump Avoidancementioning

confidence: 99%

“…A more detailed study was undertaken by Narimani et al [24] in 2004, and a frequency response equation was presented for symmetric piecewise linear systems with dual damping and stiffness behaviour, using a modified averaging method. Piecewise linear vibration isolator has been analysed in a vast amount of investigations considering time response, frequency response, jump condition, and frequency island appearance [25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

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Design of a piecewise linear vibration isolator for jump avoidance

Jazar

Mahinfalah

Deshpande

2007

Proceedings of the Institution of Mechanical Engineers, Part K:

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Piecewise linear isolators are smart passive vibration isolators that provide effective isolation for high frequency/low amplitude excitation. This can be done by introducing a soft primary suspension and a relatively damped secondary suspension. Such a piecewise isolator prevents the system from a high relative displacement in low frequency/high amplitude excitation. By employed an averaging method it is possible to obtain an implicit function for frequency response of a symmetric bilinear vibration isolator system under steady-state harmonic excitation. This function is examined for jump avoidance. A condition is derived which when met ensures that the undesirable phenomenon of ‘jump’ does not occur and the system response is functional. The jump avoidance and sensitivity of the condition are examined and investigated as the dynamic parameters vary. The results of this investigation can be directly employed in design of effective piecewise linear vibration isolators. A linear vibration system is defined as one in which the quantities of mass (or inertia), stiffness, and damping are linear in behaviour and do not vary with time [1]. Although mathematical models employing a linear ordinary differential equation with constant coefficients portray a simple and manageable system for analytical study, in most cases they are an incomplete representation simplified for the sake of analysis. Most real physical vibration systems are more accurately depicted by non-linear governing equations, in which the non-linearity may stem from structural constraints causing a change in stiffness and damping characteristics, or from inherent non-linear behaviour of internal springs and dampers. This paper focuses on a general form of such a non-linear system. This study of piecewise-linear systems will allow hazardous system behaviour over operating frequency ranges to be gauged and controlled in order to avoid premature fatigue damage, and prolong the life of the system.

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Section: Mathematical Modelmentioning

confidence: 99%

Section: The Phenomenon Of Jump and Condition For Jump Avoidancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design of a piecewise linear vibration isolator for jump avoidance

Jazar

Mahinfalah

Deshpande

2007

Proceedings of the Institution of Mechanical Engineers, Part K:

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Frequency Island and Nonlinear Vibrating Systems

Marzbani

Quốc

et al. 2018

Smart Innovation, Systems and Technologies

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Sensitivity of Jump Avoidance Condition of Piecewise Linear Vibration Isolator to Dynamical Parameters

Deshpande

Mehta

Jazar

2005

Design Engineering, Parts a and B

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An adapted averaging method is employed to obtain an implicit function for frequency response of a bilinear vibration isolator system under steady state. This function is examined for jump-avoidance and a condition is derived which when met ensures that the undesirable phenomenon of ‘Jump’ does not occur and the system response is functional and unique. The jump avoidance and sensitivity of the condition are examined and investigated as the dynamic parameters vary. The results of this investigation can be directly employed in design of effective piecewise linear vibration isolators. A linear vibration system is defined as one in which the quantities of mass (or inertia), stiffness, and damping are linear in behavior and do not vary with time [1]. Although mathematical models employing a linear ordinary differential equation with constant coefficients portray a simple and manageable system for analytical scrutiny, in most cases they are an incomplete representation simplified for the sake of study. Most real physical vibration systems are more accurately depicted by non-linear governing equations, in which the non-linearity may stem from structural constraints causing a change in stiffness and damping characteristics, or from inherent non-linear behavior of internal springs and dampers. This paper focuses on a general form of such a non-linear system. This study of piecewise-linear systems will allow hazardous system behavior over operating frequency ranges to be gauged and controlled in order to avoid premature fatigue damage, and prolong the life of the system.

show abstract

Comparison of Exact and Approximate Frequency Response of a Piecewise Linear Vibration Isolator

Cited by 3 publications

References 0 publications

Design of a piecewise linear vibration isolator for jump avoidance

Design of a piecewise linear vibration isolator for jump avoidance

Frequency Island and Nonlinear Vibrating Systems

Sensitivity of Jump Avoidance Condition of Piecewise Linear Vibration Isolator to Dynamical Parameters

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