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On the performance of a nonlinear vibration isolator consisting of axially loaded curved beams

On the performance of a nonlinear vibration isolator consisting of axially loaded curved beams
On the performance of a nonlinear vibration isolator consisting of axially loaded curved beams
A desirable characteristic for nonlinear vibration isolators is a high static stiffness and a low dynamic stiffness. A curved beam is a possible candidate for this role provided that the amplitude of vibration about the static equilibrium position is sufficiently small. However, for large amplitude oscillations, the nonlinear dynamics may have a detrimental effect. This paper considers the force transmissibility of a single degree-of-freedom system where the stiffness element is a curved, axially loaded beam. The transmitted force is calculated by numerical time domain integration of the equations of motion. The exact force-deflection relation for the beam is used for the spring. By comparison, a frequency domain solution is sought using the Harmonic Balance (HB) method in which the system is modelled as a Duffing oscillator. It is shown that the HB and time domain solutions are in close agreement for small amplitudes of excitation and both predict advantageous performance of the nonlinear isolator compared with its equivalent linear counterpart. However, significant discrepancies occur between the two solutions for large excitation since the beam can no longer be approximated by a linear and a cubic stiffness. It is also strongly asymmetric – soft in compression but stiff in extreme extension– which gives rise to an impulse in the transmitted force in each fundamental period. This numerical problem is alleviated by inserting a linear spring in series with the beam isolator with a modest compromise in isolation performance at the excitation frequency.
vibration isolators, nonlinear vibrations, Duffing oscillator, numerical solution
Abolfathi, Ali
1872c634-797a-470d-bc31-3f3e35c146b2
Waters, Tim P.
348d22f5-dba1-4384-87ac-04fe5d603c2f
Brennan, Michael J.
87c7bca3-a9e5-46aa-9153-34c712355a13
Abolfathi, Ali
1872c634-797a-470d-bc31-3f3e35c146b2
Waters, Tim P.
348d22f5-dba1-4384-87ac-04fe5d603c2f
Brennan, Michael J.
87c7bca3-a9e5-46aa-9153-34c712355a13

Abolfathi, Ali, Waters, Tim P. and Brennan, Michael J. (2013) On the performance of a nonlinear vibration isolator consisting of axially loaded curved beams. RASD 2013, Italy. 01 - 03 Jul 2013. 11 pp .

Record type: Conference or Workshop Item (Paper)

Abstract

A desirable characteristic for nonlinear vibration isolators is a high static stiffness and a low dynamic stiffness. A curved beam is a possible candidate for this role provided that the amplitude of vibration about the static equilibrium position is sufficiently small. However, for large amplitude oscillations, the nonlinear dynamics may have a detrimental effect. This paper considers the force transmissibility of a single degree-of-freedom system where the stiffness element is a curved, axially loaded beam. The transmitted force is calculated by numerical time domain integration of the equations of motion. The exact force-deflection relation for the beam is used for the spring. By comparison, a frequency domain solution is sought using the Harmonic Balance (HB) method in which the system is modelled as a Duffing oscillator. It is shown that the HB and time domain solutions are in close agreement for small amplitudes of excitation and both predict advantageous performance of the nonlinear isolator compared with its equivalent linear counterpart. However, significant discrepancies occur between the two solutions for large excitation since the beam can no longer be approximated by a linear and a cubic stiffness. It is also strongly asymmetric – soft in compression but stiff in extreme extension– which gives rise to an impulse in the transmitted force in each fundamental period. This numerical problem is alleviated by inserting a linear spring in series with the beam isolator with a modest compromise in isolation performance at the excitation frequency.

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Published date: 2 July 2013
Venue - Dates: RASD 2013, Italy, 2013-07-01 - 2013-07-03
Keywords: vibration isolators, nonlinear vibrations, Duffing oscillator, numerical solution
Organisations: Dynamics Group

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Local EPrints ID: 355505
URI: https://eprints.soton.ac.uk/id/eprint/355505
PURE UUID: 1ad64a7f-9a20-42a9-8db1-8fc654ae3b16

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Date deposited: 02 Sep 2013 11:12
Last modified: 18 Jul 2017 03:47

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