Static stability and free vibration characteristics of a micro laminated beam under varying axial load using modified couple stress theory and Ritz method

This paper explores the buckling and free vibration behaviors of micro laminated composite beams (MLCBs) exposed to varying axial loads using the modified couple stress theory (MCST), with arbitrary boundary conditions and layups. The size effect is captured in MCST by taking into account the material length scale parameters. In the axial direction, the applied load has either constant, linear, or parabolic variations. The equilibrium equations are derived and solved using Hamilton's principle and Ritz method respectively. The size effect is observed to be more pronounced when the thickness of the beam is similar to the material length scale parameter, and it nearly vanishes as the beam thickness increases. The small size effect variation is different for different boundary conditions. For parabolically increasing loading case, the rate of reduction of the fundamental frequency with an increase in applied load intensity is greater compared to other loadings.

Automated summary

This paper investigates the buckling and free vibration behaviors of micro laminated composite beams under varying axial loads using the modified couple stress theory, capturing the size effect by considering material length scale parameters and exploring different boundary conditions and layups. The observed size effect is more significant when the beam thickness is similar to the material length scale parameter and diminishes as the thickness increases. Different boundary conditions result in varying small size effect variations, with the fundamental frequency decreasing more rapidly under parabolic loading compared to other loading types.