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NON-STATIONARY RESPONSES OF A NONLINEARLY COUPLED PITCH-ROLL SHIP MODEL UNDER MODULATED EXCITATION

NON-STATIONARY RESPONSES OF A NONLINEARLY COUPLED PITCH-ROLL SHIP MODEL UNDER MODULATED EXCITATION,10.1006/jsvi.1996.0213,Journal of Sound and Vibrati

NON-STATIONARY RESPONSES OF A NONLINEARLY COUPLED PITCH-ROLL SHIP MODEL UNDER MODULATED EXCITATION   (Citations: 4)
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The response of a two-degree-of-freedom system with quadratic coupling under a modulated amplitude sinusoidal excitation is studied. The objective of this research is to study the effect of the modulation on the system performance. The case of periodic response is studied in the present paper; chaotic response of the same system under similar excitation is reported in a subsequent paper.Several approximate solutions are obtained and compared. The stability of an exact solution with one mode having zero amplitude is studied. Loss of stability in this case involves either a rapid transition from one of two stable (in the stationary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in the (F1,F0) parameter space which are useful in predicting jumps from one branch to another and bifurcations. The study shows that bothF1(the modulation amplitude) and ο (the modulation frequency) have great effects on the stability boundaries, and that (i) the stable area is greatly expanded by the modulation, (ii) the stationary bifurcation point itself can be exceeded (F0>F2*) without loss of stability, (iii) decreasing ο can make the stability boundary very complicated and, finally, (iv) for very small ο the response can make periodic jumps back and forth between the two (pseudo-) stationary solutions.
Journal: Journal of Sound and Vibration - J SOUND VIB , vol. 192, no. 3, pp. 669-699, 1996
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