Bi-harmonically excited pendulum: shifted resonances and quenching the low frequency excitation

The effect of the harmonic high-frequency vibration of the suspension point on a mathematical pendulum is well known 1]. It can be described as stiffening/softening or stabilization/destabilization of the up-pointing and down-pointing equilibriums for pure vertical or pure horizontal excitation. If the excitation is tilted the effect of biasing appears in addition 2]. The effects of bi-harmonic excitation are more complex. Two of them are discussed in the recent paper. The first one occurs if one of the excitation frequencies is high and another one is low. Then the so called shifted or conjugated resonances can be observed 3]. The second one takes place if the two excitation frequencies are high but their difference is small (slowly modulated high-frequency excitation according to 4]). It is shown that in that case it is possible to choose the bi-harmonic excitation in order to quench the resonance of the pendulum without changing its basic frequency. The analysis is fulfilled both for the external and parametric excitations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)