INTERNAL RESONANCE OF AN L-SHAPED BEAM WITH A LIMIT STOP .1. FREE-VIBRATION

Real-life structures often possess piecewise stiffness because of clea rances or interference between subassemblies. Such an aspect can alter a system's fundamental free vibration response and leads to complex m ode interaction. The free vibration behaviour of an L-shaped beam with a limit stop is analyzed by using the frequency response function and the incremental harmonic balance method. The presence of multiple int ernal resonances, which involve interactions among the first five mode s and are extremely complex, have been discovered by including higher harmonics in the analysis. The results show that mode interaction may occur if the higher harmonics of a vibration mode are close to the nat ural frequency of a higher mode. The conditions for the existence of i nternal resonance are explored, and it is shown that a prerequisite is the presence of bifurcation points in the form of intersecting backbo ne curves. A method to compute such intersections by using only one ha rmonic in the free vibration solution is proposed. (C) 1996 Academic P ress Limited