Determination of nonlinear vibration of 2DOF system with an asymmetric piecewise-linear compression spring using incremental harmonic balance method

Ranjbarzadeh, Hossein; Kakavand, Farshad

doi:10.1016/j.euromechsol.2018.07.005

Cited by 13 publications

(3 citation statements)

References 16 publications

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“…Dynamic analysis of piecewise systems can be conducted using different methods. For example, Ranjbarzadeh and Kakavand [25] utilized the incremental harmonic balance method to analyze the dynamic response of a symmetrical piecewise nonlinear system. Wang et al [26] used a hyperbolic tangent function to represent the piecewise restoring force and investigated the vibration reduction of a piecewise linear system using the harmonic balance method (HBM).…”

Section: Introductionmentioning

confidence: 99%

A Method for Stabilizing the Vibration Amplitude of a Flip-Flow Vibrating Screen Using Piecewise Linear Springs

Lin,

Wang,

et al. 2024

Minerals

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The flip-flow vibrating screen (FFVS) is a novel multi-body screening equipment that utilizes vibrations to classify bulk materials in the field of screening machinery. The relative amplitude of FFVSs determines the tension and ejection intensity of elastic flip-flow screen panels, which is a critical operating parameter affecting the screening performance. However, FFVSs generally suffer from large variations of relative amplitude caused by the loading of materials and the changes in shear spring stiffness (the temperature changes of the shear springs lead to their stiffness changes), which significantly reduce the screening efficiency and lifespan of FFVSs. To address this problem, this paper proposes a nonlinear stiffness-based method for stabilizing the vibration amplitude of FFVSs using piecewise linear springs. By introducing these springs between the two frames, the sensitivity of the relative amplitude to shear spring stiffness is reduced, thereby achieving the stabilization of the relative amplitude of FFVSs. In this study, the variations of the vibration amplitude of the FFVS due to the loading of materials and the changes in shear spring stiffness were first demonstrated in a reasonable operating frequency range. Then the reasonable operating frequency range and dynamics of the resultant nonlinear flip-flow vibrating screen (NFFVS) with piecewise linear springs were investigated using the harmonic balance method (HBM) and the Runge–Kutta numerical method. The operating frequency region for the NFFVS lies between the critical frequency ωcs and the frequency ωlb corresponding to the saddle-node bifurcation point. Finally, a test rig was designed to validate the theoretical predictions. Theoretical and experimental results demonstrate that piecewise linear springs can effectively stabilize the relative amplitude of the FFVS.

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Section: Introductionmentioning

confidence: 99%

A Method for Stabilizing the Vibration Amplitude of a Flip-Flow Vibrating Screen Using Piecewise Linear Springs

Lin,

Wang,

et al. 2024

Minerals

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“…Other solutions methods for nonlinear systems with piecewise functions include Harmonic Balance Method [27][28][29], coordinate transformations [30][31][32], and path-following continuation methods [1,2,33]. For the last category, authors generally resort to Numerical Continuation toolboxes, like MatCont [34], COCO [35] and AUTO-07 [36].…”

Section: Introductionmentioning

confidence: 99%

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

2023

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In the industry field, the increasingly stringent requirements of lightweight structures are exposing the ultimately nonlinear nature of mechanical systems. This is extremely true for systems with moving parts and loose fixtures which show piecewise stiffness behaviours. Nevertheless, the numerical solution of systems with ideal piecewise mathematical characteristics is associated with time-consuming procedures and a high computational burden. Smoothing functions can conveniently simplify the mathematical form of such systems, but little research has been carried out to evaluate their effect on the mechanical response of multi-degree-of-freedom systems. To investigate this problem, a slightly damped mechanical two-degree-of-freedom system with soft piecewise constraints is studied via numerical continuation and numerical integration procedures. Sigmoid functions are adopted to approximate the constraints, and the effect of such approximation is explored by comparing the results of the approximate system with the ones of the ideal piecewise counter-part. The numerical results show that the sigmoid functions can correctly catch the very complex dynamics of the proposed system when both the above-mentioned techniques are adopted. Moreover, a reduction in the computational burden, as well as an increase in numerical robustness, is observed in the approximate case.

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“…Vibration system with nonlinear coupling is analysed in [39]. Nonlinear vibrations of a system with piecewise linear spring are investigated in [40]. Nonlinear vibrations of piezoelectric plates are analysed in [41].…”

Section: Introductionmentioning

confidence: 99%

Vibroimpact mechanism in one separate case

Ragulskis¹,

Ragulskis²

2019

Math. models, eng.

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It is known that in the vibroimpact system at the chosen values of parameters linear relationship between impact velocities and eigenfrequencies may exist. The purpose of this paper is to reveal the qualities of the systems of this type. Investigations are performed by analytical and numerical methods. It is determined that in the systems of this type nonlinear solutions with infinite series of harmonics exist. Multivalued stable and unstable regimes do not exist in the systems. The obtained analytical relationships enabled to reveal new qualities of the systems and to make useful conclusions. Keywords: characteristics of impact velocity and eigenfrequencies, free and decaying vibrations, phase trajectories of motions, harmonics of motions up to infinity.

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Determination of nonlinear vibration of 2DOF system with an asymmetric piecewise-linear compression spring using incremental harmonic balance method

Cited by 13 publications

References 16 publications

A Method for Stabilizing the Vibration Amplitude of a Flip-Flow Vibrating Screen Using Piecewise Linear Springs

A Method for Stabilizing the Vibration Amplitude of a Flip-Flow Vibrating Screen Using Piecewise Linear Springs

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

Vibroimpact mechanism in one separate case

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