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

چکیده مقاله

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