1997
DOI: 10.1007/978-94-015-8847-8
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Applied Asymptotic Methods in Nonlinear Oscillations

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Cited by 66 publications
(45 citation statements)
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“…Engineers are generally more concerned about subcritical (hard) bifurcations as a small perturbation around the equilibrium position can lead the system to large amplitude vibration states, which the structure may not tolerate [5]. A number of authors have studied the "Mass-on-moving-Belt" model ("MB model" in the following), Tondl [6], Hetzler et al [7], Hetzler [8], Won and Chung [9], Nayfeh and Mook [10], Mitropolskii and Van Dao [11], Popp [12], Popp et al [13], Hinrichs et al [14], Andreaus and Casini [15], Awrejcewicz and Holicke [16], Awrejcewicz et al [17], which present various types of analysis of a mass-on-belt system with various kinds of friction laws, and provide in some cases, analytical expressions for the change between stick-slip and pure-slip oscillations. Many authors have attempted to use fast vibrations which in some respects seems to transform classical Coulomb friction into viscous-like damping ( [5,18]).…”
Section: Introductionmentioning
confidence: 99%
“…Engineers are generally more concerned about subcritical (hard) bifurcations as a small perturbation around the equilibrium position can lead the system to large amplitude vibration states, which the structure may not tolerate [5]. A number of authors have studied the "Mass-on-moving-Belt" model ("MB model" in the following), Tondl [6], Hetzler et al [7], Hetzler [8], Won and Chung [9], Nayfeh and Mook [10], Mitropolskii and Van Dao [11], Popp [12], Popp et al [13], Hinrichs et al [14], Andreaus and Casini [15], Awrejcewicz and Holicke [16], Awrejcewicz et al [17], which present various types of analysis of a mass-on-belt system with various kinds of friction laws, and provide in some cases, analytical expressions for the change between stick-slip and pure-slip oscillations. Many authors have attempted to use fast vibrations which in some respects seems to transform classical Coulomb friction into viscous-like damping ( [5,18]).…”
Section: Introductionmentioning
confidence: 99%
“…It is supposed that v is close to the natural frequency w, namely: v2 = w2 + c:6. , (1.1) here 6. is a detuning parameter and c is a small positive one. Applying to (0.1) the asymptotic method [2] and using the amplitude and phase variables (a,()) given by we have…”
Section: Summary Of the Case Of Small Parametersmentioning
confidence: 99%
“…The opposite case will be investigated in the next section. The smallness of parameters is characterized by introducing a small positive parameter E. For this case the asymptotic method of Krylov -Bogoliubov -Mitropolskii (K-B-M) [1,2] is used to seek the approximate solutions aud to study their stability.…”
Section: The Case Of Small Parametersmentioning
confidence: 99%