An dynamical evaluation of size-dependent weakened nano-beam based on the nonlocal strain gradient theory

Abstract

This paper examines the free lateral vibration of a cracked nano-beam based on Euler-Bernoulli beam theory and nonlocal strain gradient theory (NSGT). Due to the importance and application of nanostructures, their mechanical and mechanical properties are essential. The governing equations and boundary conditions related to using the Hamilton principle have been extracted. The beam separation with the nano-beams division into two parts attached to the Torsion spring is modeled. The model calls the excess strain energy due to crack and increases the discontinuity in the deflection slope. This study investigated the effects of crack propagation, crack intensity, material length scale parameter, and various nonlocal parameters. A comparison of previous studies has been published, where a good agreement is observed. The results show that the parameters mentioned above play an important role in dynamical behavior.

A complex solution on the dynamic response of sandwich graphene‐reinforced aluminum‐based composite beams with copper face sheets under two moving constant loads on an elastic foundation

“…Therefore, this study is important in exploring the dynamic response of a graphene‐reinforced aluminum‐based composite (GRAC) sandwich beam on an elastic foundation using an analytical solution. The investigation considers various parameters such as the percentage of graphene, the spring constant, the speed ratio, the moving load speed, and the distribution pattern 1–7 …”