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International Journal of Engineering & Technology Sciences
IJETS 2015, 3(2), 136-143
Free Vibration Analysis of Micro Beams Based on the Modified Couple Stress Theory, Using Approximate Methods
a Department of Engineering-Emerging Technologies, University of Tabriz, Tabriz, Iran
b Department of Mechanical engineering, University of Tabriz, Tabriz, Iran
ABSTRACT
Free vibration behaviour of micro scale Euler-Bernoulli cantilever beam carrying an attached mass is numerically investigated. This study is based on the modified couple stress elasticity theory. The non-dimensional frequency equation for the clamped- free micro beam is obtained using an approximate method for the first time. The method used in this study is the assumed modes method (Lagrange’s equations). The method is used to exerted different numbers of admissible functions and their results are compared with each other. The influence of the attached mass at the free end upon the first dimensionless natural frequency is reported so that as the mass ratio (mass of the attached substance to the micro beam mass) is increasing, the dimensionless natural frequency is decreasing. Also the frequency shift for different values of the mass ratios is investigated. It is remarkable that the different behaviour of the micro beam is due to the mass inertia of the attached mass during oscillation. Comparison with the technical other article shows the expected frequency shift and accuracy of the solution procedure used.
Assumed modes method; Attached mass; Free vibration; Fundamental frequency; Micro electro mechanical systems; Modified couple stress theory.