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.

Characteristics of Vibrational Wave Propagation and Attenuation in Submarine Fluid-Filled Pipelines

As an important part of lifeline engineering in the development and utilization of marine resources, the submarine fluid-filled pipeline is a complex coupling system which is subjected to both internal and external flow fields. By utilizing Kennard＇s shell equations and combining with Helmholtz equations of flow field, the coupling equations of submarine fluid-filled pipeline for n=0 axisymmetrical wave motion are set up. Analytical expressions of wave speed are obtained for both s=1 and s=2 waves, which correspond to a fluid-dominated wave and an axial shell wave, respectively. The numerical results for wave speed and wave attenuation are obtained and discussed subsequently. It shows that the frequency depends on phase velocity, and the attenuation of this mode depends strongly on material parameters of the pipe and the internal and the external fluid fields. The characteristics of PVC pipe are studied for a comparison. The effects of shell thickness/radius ratio and density of the contained fluid on the model are also discussed. The study provides a theoretical basis and helps to accurately predict the situation of submarine pipelines, which also has practical application prospect in the field of pipeline leakage detection.

Train-induced vibration on elevated railway station

Results of in-situ vibration measurement carried out at Tianjin West Elevated Railway Station which has the trains running on the station structure were reported. The main excitation source is the train passing through the station. Vibration measurements were recorded in the vertical direction of the supporting track beam, the platform and the steel truss beam of the waiting hall, as well as in the vertical, longitudinal and transverse directions of the roof arch base of the station. Acceleration time responses were obtained. The maximum value, vibration level and one-third octave band RMS spectra of the measured accelerations were studied. The propagation of vibration in different structural floors was discussed. The influence of train speed, distance to the vibration source and the type of train on the structural vibration were analyzed. Results show that the vibration level increases with the train speed, while it attenuates with the distance to the track. Furthermore, the vibration responses of different structural floors were compared, and it is noted that the vertical vibration of the bottom slab of the platform is most severe and the transverse vibration of the roof arch base is the smallest. The results provide reference on the vibration characteristics and vibration energy distribution of this type of "Train on building frame" system used as an elevated railway station.