Some diverse examples of exploiting the beneficial effects of geometric stiffness nonlinearity

Gatti, Gianluca; Brennan, M.J.; Tang, Bin

doi:10.1016/j.ymssp.2018.08.024

Cited by 60 publications

(21 citation statements)

References 78 publications

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“…Type III's isolation characteristics are of interest in this section when the stage of payload is subjected to harmonic force excitations, which could be measured by force transmissibilities or displacement-frequency responses of the payload. e isolating structures in both stages may have a hardening or softening stiffness nonlinearity which is common to a lot of classical nonlinear isolators [2,15] and can be simplified to polynomial stiffness as in a few new isolators [16][17][18][19][20][21][22]. In each stage model, there are two auxiliary lateral springs with stiffness k h1 (or k h2 ) such as a vertical spring with stiffness k v1 (or k v2 ) and a vertical linear damper with coefficient c 1 (or c 2 ) as shown in Figure 1.…”

Section: A New Type Of a Two-stage Nonlinear Isolatormentioning

confidence: 99%

Nonlinear Normal Modes in a Two‐Stage Isolator Using a Modified Finite‐Element Galerkin Method

2021

Shock and Vibration

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A modified Galerkin method is proposed to approximate the nonlinear normal modes in a new type of a two-stage isolator. Besides the displacement of payload and the force transmissibility of this typical nonlinear dynamic system, the nonlinear normal modes defined as invariant manifolds can provide more information about the nonlinear coupling between the system components when periodic motions corresponding to the normal modes of the system occur. The presented approach applies a combination of finite-element discretization and Fourier series expansion for the approximate invariant manifolds. A Galerkin projection of the governing equations for the approximate invariant manifolds yields a set of nonlinear algebraic equations in expansion coefficients, which can be solved numerically with a general choice of zero as initial guess for the cases in this work. The resultant approximate solutions for the invariant manifolds can accurately describe the nonlinear interactions between system components in periodic motions of the specific nonlinear normal modes. In addition, one can solve the invariant manifolds for an annular domain of interest directly by this method, without considering other domain that includes the origin of phase space.

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Section: A New Type Of a Two-stage Nonlinear Isolatormentioning

confidence: 99%

Nonlinear Normal Modes in a Two‐Stage Isolator Using a Modified Finite‐Element Galerkin Method

2021

Shock and Vibration

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“…e ever growing demand to enhance the performance of mechanical systems and structures has recently pushed research efforts towards the exploitation of nonlinear effects rather than to their avoidance [1,2]. New solutions and innovative designs have been investigated recently to this purpose, especially in the field of nonlinear dynamics and vibration control [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…Practical applications of the benefits that nonlinearity can introduce into a mechanical system are reported in the field of energy harvesting from vibrations [9], vibration absorbers [10], shock isolators [11], vibration isolators [12], and elastic systems for potential energy increase [13]. In some cases, a nonlinear stiffness element with a quasi-zero stiffness (QZS) characteristic [2,6,8,12,13] has been proposed to cope with the competing requirements of achieving a high-static stiffness to limit the static deflection and a low-dynamic stiffness to improve the dynamic performance. A cubic stiffness characteristic with hardening behaviour has been commonly reported, and a practical mechanical realization consists of a pair of linear springs located perpendicularly to the direction of motion, which incline as the oscillator moves [2].…”

Section: Introductionmentioning

confidence: 99%

Effect of Parameters on the Design of a Suspension System with Four Oblique Springs

Gatti

2021

Shock and Vibration

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This paper presents the fundamental static and dynamic characteristics of a suspension system consisting of four linear springs arranged in an X-shaped configuration to achieve geometric nonlinearity. The particular interest is towards the design of a softening spring geometry realizing a quasi-zero stiffness behaviour at large deflections, and the influence of the system parameters is investigated. The static performance is studied in terms of the force-deflection curve and the dynamic performance in terms of the frequency response curve. The softening-hardening behaviour of the suspension leads to a frequency response which bends to the lower frequencies reaching a well-defined minimum. It is found that both the static and dynamic behaviours may be described in terms of a single parameter, and a simple closed-form expression is determined which links the damping in the system to the excitation amplitude to achieve the lowest possible resonance frequency.

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“…Although the mechanism is mainly aimed for energy harvesting and vibration isolation research, its purpose and operating principle are the same. They can be easily adapted in the application of nonlinear dynamic vibration absorber (NDVA) [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Experimental characterization and performance of dynamic vibration absorber with tunable piecewise-linear stiffness

Mustaffer

Ramlan

Rahman

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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Dynamic vibration absorber (DVA) is one of the ways to control the level of vibration. Among many mechanisms and control strategies of the DVA, passively tuned DVA emerges as one of the most effective absorbers due to its simple mechanism. However, the performance of the passive tuned DVA suffers from narrow suppression bandwidth. This paper introduces a nonlinear dynamic vibration absorber (NDVA) with an adjustable piecewise-linear stiffness mechanism which has a characteristic almost similar to hardening stiffness to broaden the vibration suppression bandwidth. The mechanism is made of a cantilever beam constrained by two vertically and horizontally adjustable limit blocks on either side of the beam's equilibrium position. The static and dynamic properties of the proposed NDVA were first investigated for different positions of the limit blocks. Then the performance of the NDVA was compared with the linear DVA in terms of the vibration suppression bandwidth, separation of resonance frequencies and the ability to cope with mistuning. Overall, the NDVA seems to outperform the linear DVA, and it is more forgiving in the case of mistuning.

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Some diverse examples of exploiting the beneficial effects of geometric stiffness nonlinearity

Cited by 60 publications

References 78 publications

Nonlinear Normal Modes in a Two‐Stage Isolator Using a Modified Finite‐Element Galerkin Method

Nonlinear Normal Modes in a Two‐Stage Isolator Using a Modified Finite‐Element Galerkin Method

Effect of Parameters on the Design of a Suspension System with Four Oblique Springs

Experimental characterization and performance of dynamic vibration absorber with tunable piecewise-linear stiffness

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