Dynamic effects of the ratio of applied/natural frequency on the amplitudes of joint displacements of MDOF frames

Abstract

This paper examined the effects of the various ratios of applied/natural frequency on the amplitude of joint displacements of any given undamped MDOF frame for a given forcing frequency. Three different models were used to carry out dynamic analyses on a chosen MDOF frame subjected to constant dynamic load with forcing frequencies varying from zero to outside the range of the natural frequencies. Amplitudes of joint displacements were first determined from the equations of motion for forced vibration and secondly by applying the frequency ratios to the conventional expression of dynamic magnification factor for SDOF systems. The results show that, for a given forcing frequency, the displacements obtained by applying the Maximum Frequency Ratio to the conventional expression of the dynamic magnification factor agree with that obtained by direct analysis and that significant displacement occur when this ratio lies in the range of 0.58 to 1.29. The other frequency ratios, so long as they are not unity, have little or no effects on the displacements. The ideas developed here could be used in practice as a control for deflection results obtained from rigorous dynamic analysis of MDOF frames.