Approximate Methods for Analysing Nonlinear Structures

Neild, Simon A

doi:10.1007/978-3-7091-1187-1_2

Cited by 18 publications

(29 citation statements)

References 20 publications

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“…(18) shows that the systems of concern in this work frequently encounter steady-state responses with significant components that are time-constant (in addition to the termẐ c calculated already), and also at double the excitation frequency. These steady state solutions are found analytically with a Normal Forms (NF) method for second order differential equations [22,23,24,25]. This method transforms Eq.…”

Section: Overview Of Methodsmentioning

confidence: 99%

Relieving the effect of static load errors in nonlinear vibration isolation mounts through stiffness asymmetries

Shaw

Neild²,

Friswell

2015

Journal of Sound and Vibration

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High Static Low Dynamic Stiffness (HSLDS) mounts consist of nonlinear springs that support a high static load with low static displacement, whilst maintaining locally low stiffness near equilibrium, to give a low natural frequency and consequently good isolation properties. Recent analysis has investigated such devices when the force-displacement relationship is an odd function about the equilibrium position, and analysed the consequences of different shapes of these functions. However many devices that have the HSLDS characteristic do not meet the assumptions of this analysis, in that the force-displacement relationship is generally asymmetric about equilibrium. Furthermore, even devices that do meet this assumption may be subject to significant adjustment error, particularly in the context of air vehicles where manoeuvres such as banked turns can cause an apparent variation in gravitational acceleration, and a consequent variation in the weight of the payload. This change in static load moves the payload away from its intended region of low stiffness. The current paper provides analysis of these situations, and shows that the performance of a mount with a symmetric stiffness-displacement relationship is highly sensitive to errors in the static loading. It is then shown that a mount with an asymmetric stiffnessdisplacement function can offer significant performance advantages when there are adjustment errors in the loading of the mount.

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Section: Overview Of Methodsmentioning

confidence: 99%

Relieving the effect of static load errors in nonlinear vibration isolation mounts through stiffness asymmetries

Shaw

Neild²,

Friswell

2015

Journal of Sound and Vibration

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“…Please see [18,19,21] for more details of the derivation. Here we use the already defined ω a parameter such that, either ω an = ω γn if no detuning is applied or ω an = ω rn for the detuning case.…”

Section: Nonlinear Near-identity Transformation: V → Umentioning

confidence: 99%

“…option N2, (27), must be applied). From β 1 it can be seen that the resonant terms are [1,2], [1,4], [1,5], [1,9], [1,12] and [1,15] for mode 1 and [2, 1], [2,6], [2,7], [2,11], [2,18] and [2,19] for mode 2. Applying option N2 to these terms gives the transformed equations of motionü…”

Section: A Two-degree-of-freedom Oscillatormentioning

confidence: 99%

“…These expressions have come from terms [1,1] and [1,11] in β 1 for mode 1 (note that terms [1,6], [1,7], [1,18] and [1,19] also result in a response at 3Ω however the corresponding terms in n * u1 are zero) and terms [2,2], [2,4], [2,5], [2,9], [2,12] and [2,15] for mode 2. The resulting amplitudes of these sinusoidal responses are X 1,3Ω and X 2,Ω respectively, where to calculate X 2,Ω (54) is used.…”

Section: A Two-degree-of-freedom Oscillatormentioning

confidence: 99%

“…Normal forms is usually applied to first-order nonlinear oscillator equations and an assessment of their accuracy is given in [17]. Here we consider a recently developed formulation that can be applied directly to second-order nonlinear oscillators directly, termed second-order normal forms [18,19]. The second-order normal form technique has the useful property that the nonlinear transform removes non-resonant terms for each mode, rather than for each state, as is the case using the first-order formulation.…”

Section: Introductionmentioning

confidence: 99%

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A generalized frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness

Neild

Wagg

2013

Nonlinear Dyn

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In this paper we derive a frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness. This approach includes a matrix of detuning parameters which are used to model the amplitude dependent variation in resonant frequencies for the system. As a result, we compare three different approximations for modelling the affect of the nonlinear stiffness on the linearized frequency of the system. In each case the response of the primary resonances can be captured with the same level of accuracy. However harmonic and subharmonic responses away from the primary response are captured with significant differences in accuracy. The detuning analysis is carried out using a normal form technique, and the analytical results are compared with numerical simulations of the response. Two examples are considered, the second of which is a two degree-of-freedom oscillator with cubic stiffnesses.

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Approximate Methods for Analysing Nonlinear Vibrations

Wagg

Neild

2014

Nonlinear Vibration With Control

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Approximate Methods for Analysing Nonlinear Structures

Cited by 18 publications

References 20 publications

Relieving the effect of static load errors in nonlinear vibration isolation mounts through stiffness asymmetries

Relieving the effect of static load errors in nonlinear vibration isolation mounts through stiffness asymmetries

A generalized frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness

Approximate Methods for Analysing Nonlinear Vibrations

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