A Modified Couple Stress Elasticity for Non-Uniform Composite Laminated Beams Based on the Ritz Formulation

Abstract

Due to the large application of tapered beams in smart devices, such as scanning tunneling microscopes (STM), nano/micro electromechanical systems (NEMS/MEMS), atomic force microscopes (AFM), as well as in military aircraft applications, this study deals with the vibration behavior of laminated composite non-uniform nanobeams subjected to different boundary conditions. The micro-structural size-dependent free vibration response of composite laminated Euler–Bernoulli beams is here analyzed based on a modified couple stress elasticity, which accounts for the presence of a length scale parameter. The governing equations and boundary conditions of the problem are developed using the Hamilton’s principle, and solved by means of the Rayleigh–Ritz method. The accuracy and stability of the proposed formulation is checked through a convergence and comparative study with respect to the available literature. A large parametric study is conducted to investigate the effect of the length-scale parameter, non-uniformity parameter, size dimension and boundary conditions on the natural frequencies of laminated composite tapered beams, as useful for design and optimization purposes of small-scale devices, due to their structural tailoring capabilities, damage tolerance, and their potential for creating reduction in weight.

Analytical Solution for Bending and Free Vibrations of an Orthotropic Nanoplate based on the New Modified Couple Stress Theory and the Third-order Plate Theory

“…Many theories of the static and dynamic behavior of nanoplates have already been developed and some theories are still under development [15][16][17][18]. The nonlocal continuum model for the biaxial buckling analysis of composite nanoplates with shape memory alloy nanowires is presented in [19].…”