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Journal of Vcibration Testing and System Dynamics 4(2) (2020) 173--181 | DOI:10.5890/JVTSD.2020.06.004

Z.C. Feng

Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA

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Abstract

This work is motivated by finding dynamic quantities by which some insects are able to sense the direction of vibration sources. Many insects communicate by substrate vibrations alone. We introduce a two-degree-of-freedom dynamic model with time delay in the inputs to the system. Through frequency response functions we obtain surprisingly simple results with regard to the vibrational responses to waves from two opposite directions. The two-degree-of-freedom systems are divided into two types. For those whose rotational resonance frequency is lower than the translational resonance frequency, type I, the vibration on the side toward the wave source is larger than the back side for all wave frequencies. This difference in vibration amplitudes reverses for those systems whose rotational resonance frequency is above the translational resonance frequency { type II. This directional dependence is further demonstrated by numerical simulations of bandlimited random input. Our results provide the basic principle guiding the reconstruction of "Seismoscope" that was recorded to have been invented by Zhang Heng in ancient China before 132AD.

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