Effects of base excitation frequency on the stability of a freestanding rigid block

Abstract

The behavior of a freestanding block subjected to base excitation is a nonlinear problem. In the past, many researchers have analyzed freestanding blocks subjected to base excitation and reported their findings. However, still more understanding is required to understand excitation frequency effects on the stability of a freestanding block. Detailed experiments and numerical analysis were performed on a parallelepiped block having an aspect ratio of four, for different values of coefficient of friction and base amplitudes. It was observed that base excitation frequency has a predominant role on the motion and hence the stability of a freestanding block. Contrary to the present understanding of the subject, it was observed that initiation of any mode of motion (like sliding, rocking) from rest depends not only on the parameters like amplitude of base excitation, coefficient of friction and aspect ratio, but also on the base excitation frequency. A freestanding system initially at rest shall remain in rest until excited by a base excitation frequency below a particular value.We numerically determined the value of this frequency (termed as cutoff frequency) for different values of coefficient of friction (0.1–1) and base amplitude (0.1–1 g) for a constant aspect ratio of four of a parallelepiped block with square base. Using data generated from numerical analysis, a three-dimensional diagram named as initiation criteria diagram was developed that identifies various regions corresponding to sliding, rocking, slide–rock and rest (no motion) phase for a freestanding block subjected to base excitation. A novel finding was the presence of a region of no motion above a frequency value for any given combination of parameters. The ratio of the amplitude of acceleration obtained at the top of the block to the amplitude of applied base acceleration (amplification factor) was calculated for different experimental cases. The dependence of the amplification factor on the base excitation frequency was also studied. Hence, it was concluded that the base excitation frequency plays an important role in determining the stability of a freestanding rigid block.