Experimental Study of Non-Linear Transient Motion Confinement in a System of Coupled Beams

Aubrecht, Johannes; Vakakis, Alexander F.; Tsao, Tsu-Chin; Bentsman, Joseph

doi:10.1006/jsvi.1996.0451

Cited by 14 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A jump occurs at point (C) (M 8.58 Hz) labeled as jump I in Figures 6 and 7, and the system settles into a nonlinear localized steady state motion where most of the vibrational energy is confined to the directly excited beam. On the localized branch (KE) the two beams vibrate nearly in anti-phase, in full agreement with theoretical and experimental predictions of previous works [8,11,12]. By further increasing the frequency, the nonlinear steady state localization is eliminated by jump I1 (at M 8.84 Hz) and the system settles into a linear, out-of-phase periodic response with no vibro-impacts.…”

Section: Theoretical Steady State Impactsupporting

confidence: 89%

Numerical and Experimental Study of Nonlinear Localization in a Flexible Structure with Vibro‐Impacts

1997

View full text Add to dashboard Cite

In this work a numerical and experimental study of nonlinear motion confinement phenomena in a nonlinear flexible assembly with vibro‐impacts is carried out. The assembly consists of two coupled cantilever beams whose motion is constrained by rigid barriers. In the theoretical model the impact nonlinearities are simulated by clearance nonlinearities with steep stiffness characteristics; special care is taken to model energy dissipation due to inelastic impacts. The theoretical results confirm that the vibro‐impact system possess motion confinement properties. Both transient and steady state motions are studied, and it is shown that under certain conditions the vibrational energy of the system is passively confined to only one of the two beams. These essentially nonlinear responses exist inspite of direct coupling between the two beams, and have no analogs in linear theory. The experimental results confirm the theoretical predictions both in the transient and steady state regimes. The passive nonlinear motion confinement phenomena reported in this and previous works can be utilized to enhance the controllability of flexible structures with symmetries, and to improve current shock and vibration isolation designs of such systems.

show abstract

Section: Theoretical Steady State Impactsupporting

confidence: 89%

Numerical and Experimental Study of Nonlinear Localization in a Flexible Structure with Vibro‐Impacts

1997

View full text Add to dashboard Cite

show abstract

“…Previous authors studied localised buckling phenomena in forced non-linear elastic systems [52][53][54]. In the works by Vakakis and co-workers, non-linear localisation in discrete [34,55,56] and continuous [38][39][40][41][42][57][58][59][60] periodic systems with stiffness non-linearities were studied. A main result of these works is that, in contrast to linear periodic systems where structural disorder and weak substructure coupling are required for mode localisation, non-linear mode localisation can occur in perfectly symmetrical non-linear systems (i.e.…”

Section: Non-linear Localisation and Motion Confinementmentioning

confidence: 99%

NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW

Vakakis

1997

Mechanical Systems and Signal Processing

Self Cite

234

137

View full text Add to dashboard Cite

The concept of 'non-linear normal mode' (NNM) is discussed. After providing some introductory definitions, the applications of NNMs to vibration theory are considered. In particular, it is shown how this concept can be used to study forced resonances of non-linear systems and non-linear localisation of vibrational energy in symmetric systems. NNMs can provide a valuable tool for understanding certain essentially non-linear dynamic phenomena that have no counterparts in linear theory and that cannot be analysed by conventional linearised methods. Additional applications of NNMs to modal analysis, model reduction, vibration and shock isolation designs, and the theory of non-linear oscillators are also discussed.

show abstract

“…They have been extensively studied [4][5][6][7][8] and have been proposed to theoretically exist in diverse systems such as in spin wave modes of antiferromagnets [9], DNA denaturation [10], and the dynamics of Josephson-junction networks [11,12]. Also, they have been shown to be important in the dynamics of mechanical engineering systems [13,14]. Although a number of experiments have been proposed, discrete breathers have yet to be experimentally generated and measured.In this Letter, we present, to our knowledge, the first experimental study of discrete breathers in a spatially extended system.…”

mentioning

confidence: 99%

Discrete Breathers in Nonlinear Lattices: Experimental Detection in a Josephson Array

2000

View full text Add to dashboard Cite

We present an experimental study of discrete breathers in an underdamped Josephson-junction array. Breathers exist under a range of dc current biases and temperatures, and are detected by measuring dc voltages. We find the maximum allowable bias current for the breather is proportional to the array depinning current while the minimum current seems to be related to a junction retrapping mechanism. We have observed that this latter instability leads to the formation of multi-site breather states in the array. We have also studied the domain of existence of the breather at different values of the array parameters by varying the temperature.Discrete breathers are a new type of excitation in nonlinear lattices. They are characterized by an exponential localization of the energy. This localization does not occur in linear systems and it is different from Anderson localization, which is due to the presence of impurities. Thus, discrete breathers are also known as intrinsic localized modes.Breathers have been proven to be generic solutions for the dynamics of nonlinear coupled oscillator systems [1,2] by the use of the novel mathematical technique of the anti-integrable limit [3]. They have been extensively studied [4][5][6][7][8] and have been proposed to theoretically exist in diverse systems such as in spin wave modes of antiferromagnets [9], DNA denaturation [10], and the dynamics of Josephson-junction networks [11,12]. Also, they have been shown to be important in the dynamics of mechanical engineering systems [13,14]. Although a number of experiments have been proposed, discrete breathers have yet to be experimentally generated and measured.In this Letter, we present, to our knowledge, the first experimental study of discrete breathers in a spatially extended system. We have designed and fabricated an underdamped Josephson-junction ladder which allows for the existence of breathers when biased by dc external currents. We have developed a method for exciting breathers and explored their existence domain and instability mechanisms with respects to the junction parameters and the applied current.A Josephson junction consists of two superconducting leads separated by a thin insulating barrier. Due to the Josephson effect, it behaves as a solid-state nonlinear oscillator and is usually modeled by the same dynamical equations that govern the motion of a driven pendulum [15,16]: i =φ + Γφ + sin ϕ. The response of the junction to a current is measured by the voltage of the junction which is given by v = (Φ 0 /2π)dϕ/dt. By coupling junctions it is possible to construct solid-state physical realizations of different models such as the Frenkel- Moreover, since the parameters, such as Γ(T ), vary with temperature, a range of parameter space can be studied easily with each sample.The inset of Fig. 1 shows a schematic of the anisotropic ladder array. The junctions are fabricated using a NbAl 2 O x -Nb tri-layer technology with a critical current density of 1000 A/cm 2 . The current is injected and extracted through bias resisto...

show abstract

Experimental Study of Non-Linear Transient Motion Confinement in a System of Coupled Beams

Cited by 14 publications

References 0 publications

Numerical and Experimental Study of Nonlinear Localization in a Flexible Structure with Vibro‐Impacts

Numerical and Experimental Study of Nonlinear Localization in a Flexible Structure with Vibro‐Impacts

NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW

Discrete Breathers in Nonlinear Lattices: Experimental Detection in a Josephson Array

Contact Info

Product

Resources

About