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

The response of a two-degree-of-freedom system with quadratic coupling under a modulated amplitude sinusoidal excitation is studied. The obj ective of this research is to study the effect of the modulation on th e system performance. The case of periodic response is studied in the present paper; chaotic response of the same system under similar excit ation 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 sta tionary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in the (F-1, F-0) parameter space which are useful in predicting jumps from one branch to another and bifurcations. The study shows that bot h F-1 (the modulation amplitude) and omega (the modulation frequency) have great effects on the stability boundaries, and that (i) the stabl e area is greatly expanded by the modulation, (ii) the stationary bifu rcation point itself can be exceeded (F-0 > F-2) without loss of stab ility, (iii) decreasing omega can make the stability boundary very com plicated and, finally, (iv) for very small omega the response can make periodic jumps back and forth between the two (pseudo-) stationary so lutions. (C) 1996 Academic Press Limited