On the jump-up and jump-down frequencies of the Duffing oscillator

Brennan, M.J.; Kovacic, Ivana; Carrella, A.; Waters, T.P.

doi:10.1016/j.jsv.2008.04.032

Cited by 229 publications

(124 citation statements)

References 5 publications

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“…Although the jump phenomena are usually seen as undesirable, this study is to show how one can benefit from knowing the values of the frequencies when these jumps appear. The results presented are the continuation of recent investigations concerned with the derivation of the expressions for the jump-up and jump-down frequencies for externally excited Duffing oscillators [10] and their use for the estimation of certain system parameters in such systems [11], while in this work, these expressions, experimental verification and numerical comparisons are given for a base-excited Duffing oscillator. …”

Section: Introductionmentioning

confidence: 61%

Exploiting knowledge of jump-up and jump-down frequencies to determine the parameters of a Duffing oscillator

Ramlan

Brennan

Kovacic

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. roszaidi@utem.edu.my Abstract:This work concerns the novel application of certain non-linear phenomenajump frequencies in a base-excited Duffing oscillator. First, approximate analytical expressions are derived for the relationships between the jump-up and jump-down frequencies, the damping ratio and the cubic stiffness coefficient. Then, experimental results, accompanied with the results of numerical simulations, are presented to show how one can benefit from knowing these frequencies.

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Section: Introductionmentioning

confidence: 61%

Exploiting knowledge of jump-up and jump-down frequencies to determine the parameters of a Duffing oscillator

Ramlan

Brennan

Kovacic

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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“…Such systems are well-studied and discussed lucidly in [13] and in [14]. They are often considered paradigms for nonlinear vibration.…”

Section: Appendix a The Softening Duffing Oscillatormentioning

confidence: 99%

On the nonlinear dynamics and quasi-statics of tape joined structures.

Segalman¹,

Starr²

2012

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Tape joints have been a key tool in assembly of nuclear weapons for almost 40 years. In that time sufficient experience has been gained to have confidence on the robustness of this technology within established design constraints; the structural dynamics of systems assembled by tape joints are much less well understood. Though there is lore that tape joined structures behave linearly in the axial direction, even that is contradicted by the literature, where such structures are found to be bi-linear (nonlinear) in axial modes. Experimental results presented here show much more significant nonlinearity when such systems vibrate in such a way that there is bending across the joint cross-section.In addition, it will be difficult to understand the nonlinear structural dynamics before the pre-loads on the tape joints is known. Therefore, a strategy to deduce the joint pre-loads from surface strain measurements has been developed. This technique exploits finite element analysis to generate an approximate Green's function to map tape loads to surface strain and employs numerical optimization to solve an inverse problem. This technique is demonstrated on the same test specimen employed in the dynamics experiments. 3 AcknowledgmentThe authors thank Chi S. ("David") Lo and Jeff Payne for their continued support and patience with respect to the analytic portion of this work. Laura Jacobs-O'Malley is thanked for funding the experimental portion of this work.Michael Jew designed the test specimen employed in this study, but was drawn off by other urgencies before he could perform the tests. That work fell into the hands of Everest Sewell who took the data, Todd Simmermacher who supervised, and Brandon Zwink who helped translate it to Matlab readable form.The authors especially appreciate some very useful suggestions made by Randall Mayes and Michael Ross with respect to the preparation of this report.4

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“…A further increase of the exciting frequency makes the value of the transmissibility ratio less than one. A sudden jump in the amplitude of the steady-state response is a typical phenomenon in systems with a hardening or softening stiffness [7,17]. In this paper, the lowest exciting frequency that causes such a jump phenomenon is referred to as the jump frequency.…”

Section: Displacement Transmissibility Ratiomentioning

confidence: 99%