Vibration Analysis of micro Euler- Bernoulli beams with loading based on the strain gradient theory

Sajad Esmailpour Hamedani¹

1) MSc in Mechanical Engineering

Publication : 4th International Congress on Engineering, Technology and Applied Science - Auckland University of Technology(etas2019.com)
Abstract :
In this paper, Nonlinear Vibration Analysis of micro Euler- Bernoulli beams with loading based on the strain gradient theory investigated. Studying and analyzing micro beams with loading can be an important step for studying the vibration of micro structures like micro turbines. Of course, it must be said there has not been much researches on it so far. For this purpose, the strain energy and kinetic energy and external force relations are attained and put in to the Hamilton s Principle to obtain the equations of motion for the micro beam. Then the non-dimensional equations are formed with the help of dimensionless parameters. Finally, by applying Galerkin approach, axial and flapping natural frequencies are extracted. In this paper, first the effects of varying the thickness to the material length scale parameter ratio on the flapping and axial natural frequencies are calculated and results for the strain gradient theory and the modified couple stress theory are compared. In the continue, the first fourth axial and flapping mode shapes were obtained. The results of this research can be used in various industrial applications or for use in other researches.
Keywords : Vibrations Micro Beams Galerkin Approach MEMS