Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

In this research, vibration and wave propagation analysis of a twisted micro- beam on Pasternak foundation is investigated. The strain-displacement relations （kine-matic equations） are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory （SGT） is used to implement the size dependent effect at micro-scale. Finally, using an energy method and Hamilton＇s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave prop- agation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is in- versely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.

Ground-borne vibration generated by high-speed train viaduct systems in soft-upper/hard-lower rock strata

An experimental study and theoretical analysis were carried out to explore the ground-borne vibration generated by elevated high-speed railway in rock strata.Taking a typical rail line constructed on rock area in China as the research object,a set of field tests was performed on Rizhao-Lankao High-Speed Railway,the bridge and ground vibrations were measured as trains passed at 330−340 km/h,then the transferring law and spatial distribution under individual frequencies were investigated.The experiment results indicate that the bridge frequency spectrum exhibited relatively high-frequency vibration peaks caused by short-wavelength irregularity;ground vibration farther than 30 m away can be amplified with a higher frequency and numerous components.Furthermore,the wave propagation equation of a stratified rock strata was established based on direct-stiffness method to explore the vibration attenuation rules via frequency-domain analysis.It is found that the rock area has a weaker correlation between vibration transmissibility and frequency,thicker and harder rock strata loss their vibration attenuation capacity.It can be concluded that the high-speed railways induced vibration on rock strata shows a wide frequency band and large amplitude,the design of reducing vibration aimed at specific frequency is important according to next more detailed numerical study.