Thermal Postbuckling and Free Vibration of Extensible Microscale Beams Based on Modified Couple Stress Theory

• Published in: Journal of mechanics 2015-02, Vol.31 (1), p.37-46
• Main Authors: Wang, Y.-G., Lin, W.-H., Zhou, C.-L., Liu, R.-X.
• Format: Article
• Language: English
• Subjects: Analysis; Boundary value problems; Euler-Bernoulli beams; Free vibration; Joining; Mathematical analysis; Mathematical models; Mechanics; Microbeams; Postbuckling; Resonant frequency; Stresses; Studies; Vibration
• ISSN: 1727-7191; 1811-8216
• DOI: 10.1017/jmech.2014.47

This paper presents a mathematical model and a computational approach for the thermal post-buckling and free vibration in the vicinity of the buckled equilibrium position of microbeams based on the modified couple stress Euler-Bernoulli beam theory and geometrically accurate relation. The governing equations for the whole analysis are established with a intrinsic material length scale parameter to capture the size effect. These equations, in conjunction with the corresponding boundary conditions, are decomposed into two two-point boundary value problems, which are solved using the shooting method. For static deformation, the geometric nonlinearity is involved and the size dependent postbuckling configuration is obtained as a function of temperature rise. For dynamic one, the small amplitude free vibration about the prebuckled position is developed following an assumed harmonic time mode, and the length scale and temperature rise dependent fundamental natural frequency is presented. Numerical computations are executed to illustrate the size dependency in the thermal postbuckling behaviors and fundamental frequency of the vibration around the buckled configuration of microbeams.