High frequency, multi-axis dynamic stiffness analysis of a fractionally damped elastomeric isolator using continuous system theory

Fredette, Luke; Singh, Rajendra

doi:10.1016/j.jsv.2016.11.025

Cited by 13 publications

(11 citation statements)

References 19 publications

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“…The modeling methods for PMS without subframe mounting system are discussed and used widely in Fredette and Singh, 5,6 Hillis. 20 The natural frequencies and decoupling ratios of the powertrain as well as the (2) The powertrain mounts in double mounting system are placed on subframe to design rigid body modes and displacements of powertrain and subframe.…”

Section: Influence Of Second Stage Mountsmentioning

confidence: 99%

“…3 The powertrain in EV generates more sever vibration excitation at high frequencies, which accounts for the necessity to reduce high frequency dynamic stiffness of mounts. 4–6 Therefore, second stage isolation is usually used for isolating vibration from the powertrain of EV to the car body at high frequencies. The widely used second stage isolation at EV is the subframe plus with the subframe mounts.…”

Section: Introductionmentioning

confidence: 99%

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Modeling and analytical methods for a mounting system with double stage isolation

Zheng

Shangguan

Kang

2021

Proceedings of the Institution of Mechanical Engineers, Part D:

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A calculation method for obtaining the displacements and rigid body modes of a Powertrain Mounting System (PMS) with double stage isolation is proposed in this paper. Firstly, the PMS with double stage isolation is modeled as a 12 Degree of Freedoms (DOFs) model, which includes six DOFs for the powertrain and the subframe respectively. The mounts are simplified as a three-dimensional spring along each axis of its Local Mount Coordinate System (LMCS), which takes the non-linear relation of the force versus the displacement of each spring into account. Secondly, the quasi-static equilibrium equation and the free vibration equation as well as the forced vibration equation of the proposed model are derived and the solutions of equations are presented. Then, the calculation and solution methods are validated by the simulation results. The differences of rigid body modes and displacements of the powertrain between single and double stage isolation are estimated, which demonstrates that the proposed model is more accurate, especially when powertrain mounts are stiff. Also, the effect of locations for powertrain mounts on car body is investigated, which shows that is beneficial for motion control of powertrain.

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Section: Influence Of Second Stage Mountsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling and analytical methods for a mounting system with double stage isolation

Zheng

Shangguan

Kang

2021

Proceedings of the Institution of Mechanical Engineers, Part D:

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“…Using a similar approach, the dynamic stiffness of a cylindrical vibration isolator was derived [ 11 ] for different pre-compressions within an audible frequency range obtaining excellent agreements with a series of experiments. To describe the audible short term response of the rubber, a fractional derivative type relaxation function was successfully adopted [ 7 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , …”

Section: Introductionmentioning

confidence: 99%

Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators

Coja

Kari

2021

Polymers

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A waveguide model for a pre-compressed cylindrical natural rubber vibration isolator is developed within a wide frequency range—20 to 2000 Hz—and for a wide pre-compression domain—from vanishing to the maximum in service, that is 20%. The problems of simultaneously modeling the pre-compression and frequency dependence are solved by applying a transformation of the pre-compressed isolator into a globally equivalent linearized, homogeneous, and isotropic form, thereby reducing the original, mathematically arduous, and complex problem into a vastly simpler assignment while using a straightforward waveguide approach to satisfy the boundary conditions by mode-matching. A fractional standard linear solid is applied as the visco-elastic natural rubber model while using a Mittag–Leffler function as the stress relaxation function. The dynamic stiffness is found to depend strongly on the frequency and pre-compression. The former is resulting in resonance phenomena such as peaks and troughs, while the latter exhibits a low-frequency magnitude stiffness increase in addition to peak and trough shifts with increased pre-compressions. Good agreement with nonlinear finite element results is obtained for the considered frequency and pre-compression range in contrast to the results of standard waveguide approaches.

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“…Visco-elastic fractional time derivative models are regularly applied, see for example Refs. [ 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 ]. Moreover, fractional time derivatives are, in addition, used for modeling chemical and physical aging of rubber [ 91 , 92 ], and in more areas, as reviewed by Machado et al.…”

Section: Introductionmentioning

confidence: 99%

Numerically Exploring the Potential of Abating the Energy Flow Peaks through Tough, Single Network Hydrogel Vibration Isolators with Chemical and Physical Cross-Links

Kari

2021

Materials

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Traditional vibration isolation systems, using natural rubber vibration isolators, display large peaks for the energy flow from the machine source and into the receiving foundation, at the unavoidable rigid body resonance frequencies. However, tough, doubly cross-linked, single polymer network hydrogels, with both chemical and physical cross-links, show a high loss factor over a specific frequency range, due to the intensive adhesion–deadhesion activities of the physical cross-links. In this study, vibration isolators, made of this tough hydrogel, are theoretically applied in a realistic vibration isolation system, displaying several rigid body resonances and various energy flow transmission paths. A simulation model is developed, that includes a suitable stress–strain model, and shows a significant reduction of the energy flow peaks. In particular, the reduction is more than 30 times, as compared to the corresponding results using the natural rubber. Finally, it is shown that a significant reduction is possible, also without any optimization of the frequency for the maximum physical loss modulus. This is a clear advantage for polyvinyl alcohol hydrogels, that are somewhat missing the possibility to alter the frequency for the maximum physical loss, due to the physical cross-link system involved—namely, that of the borate esterification.

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High frequency, multi-axis dynamic stiffness analysis of a fractionally damped elastomeric isolator using continuous system theory

Cited by 13 publications

References 19 publications

Modeling and analytical methods for a mounting system with double stage isolation

Modeling and analytical methods for a mounting system with double stage isolation

Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators

Numerically Exploring the Potential of Abating the Energy Flow Peaks through Tough, Single Network Hydrogel Vibration Isolators with Chemical and Physical Cross-Links

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