The Multi-Mode Response between Deflectional and Torsional Modes in a Beam : Series C : Vibration, Control Engineering, Engineering for Industry

Deflectional and torsional modes of a beam may be coupled by nonlinear terms for large amplitudes. As a problem of deflectional-torsional vibrations coupled by nonlinear terms, the dynamic response of a beam with a thin rectangular cross section subjected to harmonic excitation in the lateral direction is taken up. The possibility of a multi-mode response between deflectional and torsional modes is discussed theoretically. For this, first a general analysis is given. Then, a typical case is taken up in which the natural frequency of the second deflectional mode coincides with that of the first torsional one, and a numerical calculation is conducted near the primary resonance point. It is shown that, in addition to the usual harmonic oscillation, two types of oscillations accompanying torsional modes are possible, whose amplitudes decrease in one type and increase in the other, as the excitation frequency increases. In this way the occurrence of the multi-mode response is ascertained. An experimental analysis is also conducted, which confirms the validity of the theoretical analysis.