Vibrations of Bernoulli-Euler beams using the two-phase nonlocal elasticity theory

Mechanical Properties Analysis of Bilayer Euler-Bernoulli Beams Based on Elasticity Theory

This paper analyzes the effects of structures and loads on the static bending and free vibration problems of bilayer beams. Based on static mechanical equilibrium and energy equilibrium, the static and dynamic governing equations of bilayer beam are established. It is found that the value of the thickness ratio has a significant effect on the static and dynamic responses of the beam, and the st...

Axial and Torsional Free Vibrations of Elastic Nano-Beams by Stress-Driven Two-Phase Elasticity

Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. A new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. The proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter...

Surface Effects on Free Vibration Analysis of Nanobeams Using Nonlocal Elasticity: A Comparison Between Euler-Bernoulli and Timoshenko

In this paper, surface effects including surface elasticity, surface stress and surface density, on the free vibration analysis of Euler-Bernoulli and Timoshenko nanobeams are considered using nonlocal elasticity theory. To this end, the balance conditions between nanobeam bulk and its surfaces are considered to be satisfied assuming a linear variation for the component of the normal stress thr...

Vibration Analysis of a Rotating Nanoplate Using Nonlocal Elasticity Theory

The nanostructures under rotation have high promising future to be used in nano-machines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scale-dependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and b...

Non-symmetric and chaotic vibrations of Euler- Bernoulli beams under harmonic and noisy excitations