Nonlocal Size Dependence of a Softness Nanobeam with Large Axial Tension under Various Boundary Conditions

Abstract

The transverse dynamical behaviors of softness Euler-Bernoulli nanobeams subjected to a biggish initial axial force based on nonlocal elasticity theory are investigated in this paper. The size-dependent theory is considered and a small intrinsic length scale parameter unavailable in classical continuum mechanics is adopted into the problem model as a size parameter. The linear partial differential governing equation is derived from the Newton’s second law and the ordinary equation and its dispersion relation are gained from by the method of separation of variables. Five sets of supporting conditions are presented respectively including simply supported, fully clamped, flexible fixed ends, sliding supports ends and completely free ends. Vibration frequencies are obtained approximately and correlations between the natural frequency and the dimensionless small scale parameter are also analyzed and discussed in detail. It shows that an increase in small scale parameter and dimensionless initial axial tension causes natural frequency to increase, while an increase in the dimensionless stiffness of nanostructures causes natural frequency to decrease, or the nanostructural bending stiffness is enhanced when nonlocal effects are considered.