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Interaction between the elements characterizing the forced and parametric excitations
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In nonlinear systems, the first order of smallness terms of nonresonance forced and parametric excitations have no effect on the oscillation in the first approximation. However, they do interact one with another in the second approximation. | Vietnam Journal of Mechanics, NCNST of Vietnam T. XX, 1998, No 1 (9- 20) INTERACTION BETWEEN THE ELEMENTS CHARACTERIZING THE FORCED AND PARAMETRIC EXCITATIONS NGUYEN VAl':o = E cos X, 2Ra 0 sin,Po = Esinx, and therefore, cos X = 0 =? X = sin X = ±1 z,2 11" 311" , . and E .Po = ±arc sm - R , 2 ao (3.7) c) Sub case 3. .(~.8) ~· -;;::,, The resonance curve C 3 has forrri: (3.9) From the equations (2.2) we obtain O.asin,Po = Esinx, 2Ra0 cos .Po= -E cos x, and therefore, sinx=O=?x=O, cosx = ±1, 1r, . ±E 2 E2 ,P =arccos--=? a 0 > - -2 2Rao - 4R · (3.10) 3 Last two subcases show that, if x f= 0, ~, 1r, 11" , the resonance curves C2, 2 2. 3 Ca do not exist. If X == ~, 11" , then beside the resonance curve C 1 there is still 2 .