Static Bending and Vibration of Composite Nanobeams Taking Into the Effect of Geometrical Imperfection

This work is the first to use the finite element technique to analyze the vibrational and static bending responses of multi-layer composite nanobeams. Each layer is made from microporous material and has variable mechanical properties.

The formulae for the calculations are derived from the enhanced third-order shear strain theory, which accounts for the impact of size effects and the imperfections in the initial shape. Because of its dependability in demonstrating the validity of the theory of computing, the two-node element is chosen to implement the solution.

Numerical computations are performed to provide commentary on the effect of certain geometrical factors and bonding circumstances on the vibrational and static bending responses of nanobeams. Research has shown that the mechanical response of multi-layer beams also depends greatly on the shape of the interface between the layers.

Some main points in this work are concluded as follows: the natural frequency of the beams will drop if the values of k₀ and V₀ are raised in either direction. When k₀ has a small value, if V₀ increases, the maximum deflection of the beam increases, but when k₀ has a large value, if V₀ increases, the deflection of the beam decreases. There is a nonlinear relationship between the parameter N and the beams’ maximum deflection as well as their natural frequencies. It is able to find a suitable value of N that allows for the beam rigidity to be at both its maximum and its lowest. These are useful results for the practical design of multi-layer beam structures.