Vibration Transmission Through an Isolator Modelled by Continuous System Theory

Kim, S.; Singh, Rajendra

doi:10.1006/jsvi.2001.3852

Cited by 24 publications

(25 citation statements)

References 12 publications

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“…In order to include internal resonances and anti-resonances, a multi-dimensional mass-spring system [28] and classical, essentially one-dimensional waveguides [20][21][22] may be applied. However, the wavelength in rubber is generally short within the audible frequency range resulting in a break down of the assumption on which the classical, essentially one-dimensional waveguides methods rely on, thus requiring more elaborated methods such as waveguide methods derived from the full-wave equations that are also valid for short wavelengths [7,15,16,19,34,35] and are essentially based on the possible eigenmodes found in the Pochhammer-Chree solution for waves in infinite solid cylinders [6,26].…”

Section: Kari (B)mentioning

confidence: 99%

Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range: Part 2—waveguide solution

Kari

2017

Continuum Mech. Thermodyn.

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The dynamic stiffness of a chemically and physically ageing rubber vibration isolator in the audible frequency range is modelled as a function of ageing temperature, ageing time, actual temperature, time, frequency and isolator dimension. In particular, the dynamic stiffness for an axially symmetric, homogeneously aged rubber vibration isolator is derived by waveguides where the eigenmodes given by the dispersion relation for an infinite cylinder satisfying traction free radial surface boundary condition are matched to satisfy the displacement boundary conditions at the lateral surface ends of the finite rubber cylinder. The constitutive equations are derived in a companion paper (Part 1). The dynamic stiffness is calculated over the whole audible frequency range 20-20,000 Hz at several physical ageing times for a temperature history starting at thermodynamic equilibrium at +25 • C and exposed by a sudden temperature step down to −60 • C and at several chemical ageing times at temperature +25 • C with simultaneous molecular network scission and reformation. The dynamic stiffness results are displaying a strong frequency dependence at a short physical ageing time, showing stiffness magnitude peaks and troughs, and a strong physical ageing time dependence, showing a large stiffness magnitude increase with the increased physical ageing time, while the peaks and troughs are smoothed out. Likewise, stiffness magnitude peaks and troughs are frequency-shifted with increased chemical ageing time. The developed model is possible to apply for dynamic stiffness prediction of rubber vibration isolator over a broad audible frequency range under realistic environmental condition of chemical ageing, mainly attributed to oxygen exposure from outside and of physical ageing, primarily perceived at low-temperature steps.

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Section: Kari (B)mentioning

confidence: 99%

Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range: Part 2—waveguide solution

Kari

2017

Continuum Mech. Thermodyn.

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“…In our study, we examine this issue and the characteristic mobilities are obtained for a semi-infinite elastomeric beam. Detailed mathematical treatment is given in the recent journal article we wrote [20]. It is assumed that the shear modulus (G) is very low that is true for a rubber-like material.…”

Section: Mobilities Of Timoshenko Beammentioning

confidence: 99%

“…Note that the frequency response characteristics of a Timoshenko beam changes at the transition frequency ( T ω ). Details are given in reference [20]. It is observed from Figure 2 that the inclusion of shear deformation increases the magnitudes of force and moment mobilities.…”

Section: Mobilities Of Timoshenko Beammentioning

confidence: 99%

Vibration Power Transmission Through Multi-Dimensional Isolation Paths Over High Frequencies

Kim

Singh

2001

SAE Technical Paper Series

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In many vibration isolation problems, translational motion has been regarded as a major contributor to the energy transmitted from a source to a receiver. However, the rotational components of isolation paths must be incorporated as the frequency range of interest increases. This article focuses on the flexural motion of an elastomeric isolator but the longitudinal motion is also considered. In this study, the isolator is modeled using the Timoshenko beam theory (flexural motion) and the wave equation (longitudinal motion), and linear, timeinvariant system assumption is made throughout this study. Two different frequency response characteristics of an elastomeric isolator are predicted by the Timoshenko beam theory and are compared with its subsets. A rigid body is employed for the source and the receiver is modeled using two alternate formulations: an infinite beam and then a finite beam. Power transmission efficiency concept is employed to quantify the isolation achieved. Further, vibration power components are also examined. The roles of isolator parameters such as the static stiffness ratios, shape factors and material properties are investigated.

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“…Force or velocity effectiveness term, the ratio of transmitted force or velocity with an isolator to the one without the isolator, has also been employed [1,2]. Those concepts are extended to a multi-dimensional problem [3,4] but the incompatible units of off-diagonal terms hinder the further application of such measures [5]. For this reason, the concept of vibration power, with compatible units for both translational and rotational motions, has been used to assess transmission to receivers [6].…”

Section: Introductionmentioning

confidence: 99%

Structure-Borne Noise Measures and Their Correlation to Sound Radiation over a Broad Range of Frequencies

Kim

Singh

2003

SAE Technical Paper Series

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Structure-borne noise within vehicle structures is often transmitted in a multi-dimensional manner and thus the vibro-acoustic model(s) of automotive powertrain or chassis must incorporate longitudinal and transverse (flexural) motions as well as their couplings. In this article, we employ the continuous system theory to model a typical vibration isolator (say the engine mounting system) and a compliant receiver that could simulate the body structure. The powertrain source is however assumed to be rigid, and both harmonic force and moment excitations are considered. Our analysis is limited to a linear time-invariant system, and the frequency domain based mobility method is utilized to synthesize the overall system. Contributions of both inplane and flexural motions to structure-borne and radiated noise are incorporated. Two examples are considered to illustrate the methodology. First, multidimensional transmissibility and effectiveness terms are analytically and comparatively evaluated along with vibration power-based measures for an inverted 'L' beam receiver and selected source configurations. Further, free field sound pressures are calculated and correlated with structure-borne power transmitted to the receiver. Second, sound measurements and predictions for an experimental inverted 'L' plate receiver demonstrate that a rank order based on free field sound pressures may be regarded as a measure of structureborne noise reduction. Measured insertion losses for sound pressure match well with those computed. VIBRATION ISOLATION MEASURES USING TRANSMISSIBILITY AND EFFECTIVENESS SYSTEM WITH AN INVERTED 'L' BEAM RECEIVER: Various vibration isolation measures are examined for an analytical isolation system with an inverted 'L' beam

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Vibration Transmission Through an Isolator Modelled by Continuous System Theory

Cited by 24 publications

References 12 publications

Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range: Part 2—waveguide solution

Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range: Part 2—waveguide solution

Vibration Power Transmission Through Multi-Dimensional Isolation Paths Over High Frequencies

Structure-Borne Noise Measures and Their Correlation to Sound Radiation over a Broad Range of Frequencies

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