Study of the frequency response of the block–rock mass with bimodulus characteristics

Abstract The pendulum-type wave phenomenon is a unique mechanical phenomenon in deep rock mass. It propagates at low frequencies and low speeds in the rock mass, and can cause deep rock engineering disasters such as rockbursts. For determining the low-frequency characteristics of a pendulum-type wave, the frequency response of the pendulum-type wave in block-rock mass with bimodulus characteristics is studied under a half-sine impact load. The dynamic pendulum-type wave model in a block–rock mass is used to determine the low frequency characteristics of the wave. The improved central difference method is applied, and the influence of the modulus ratio on frequency response is analyzed. Furthermore, the natural frequency of the system is inverted, through the frequency response of the block, and its correctness is verified. The results show that a decrease in the modulus ratio causes an obvious increase in the number of frequency response peaks of the block. The amplitude of the frequency response peaks decreases and the position of peaks moves to a low frequency range. The low-frequency characteristics of the pendulum-type wave in the block–rock mass with bimodulus characteristics are more obvious. The natural frequency of the system can be inverted by the fact that it corresponds to the peak frequencies of the frequency response. This approach provides a new method for the determination and measurement of the natural frequency of nonlinear systems.