INTERNAL RESONANCE OF AN L-SHAPED BEAM WITH A LIMIT STOP .2. FORCED VIBRATION

A limit stop is placed at the elbow of an L-shaped beam whose linear n atural frequencies are nearly commensurable. As a result of this harde ning device the non-linear system exhibits multiple internal resonance s, which involve various degree of coupling between the first five mod es of the beam in free vibration. A point load is so placed as to exci te several modes and the resulting forced vibration is examined. In th e undamped case, three in-phase and two out-of-phase solution branches have been found. The resonance curve is extremely complicated, with m ultiple branches and interactions between the first four modes. The am plitudes of the higher harmonics are highly influenced by damping, the presence of which can effectively attenuate internal resonances. Cons equently parts of the resonance curve may be eliminated, with the resu lting response comprising different distinctive branches. (C) 1996 Aca demic Press Limited