|
Advances in Aircraft and Spacecraft Science Volume 10, Number 3, May 2023 , pages 257-279 DOI: https://doi.org/10.12989/aas.2023.10.3.257 |
||
|
Free vibration analysis of nonlocal viscoelastic nanobeam with holes and elastic foundations by Navier analytical method |
||
Ola A. Siam, Rabab A. Shanab, Mohamed A. Eltaher and Norhan A. Mohamed
|
||
| Abstract | ||
| This manuscript is dedicated to deriving the closed form solutions of free vibration of viscoelastic nanobeam embedded in an elastic medium using nonlocal differential Eringen elasticity theory that not considered before. The kinematic displacements of Euler-Bernoulli and Timoshenko theories are developed to consider the thin nanobeam structure (i.e., zero shear strain/stress) and moderated thick nanobeam (with constant shear strain/stress). To consider the internal damping viscoelastic effect of the structure, Kelvin/Voigt constitutive relation is proposed. The perforation geometry is intended by uniform symmetric squared holes arranged array with equal space. The partial differential equations of motion and boundary conditions of viscoelastic perforated nonlocal nanobeam with elastic foundation are derived by Hamilton principle. Closed form solutions of damped and natural frequencies are evaluated explicitly and verified with prestigious studies. Parametric studies are performed to signify the impact of elastic foundation parameters, viscoelastic coefficients, nanoscale, supporting boundary conditions, and perforation geometry on the dynamic behavior. The closed form solutions can be implemented in the analysis of viscoelastic NEMS/MEMS with perforations and embedded in elastic medium. | ||
| Key Words | ||
| analytical solutions; dynamic analysis; elastic foundations; Kelvin/Voigt model; perforated nanostructure | ||
| Address | ||
| Ola A. Siam, Rabab A. Shanab: Engineering Mathematics Department, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt Mohamed A. Eltaher: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia; Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt Norhan A. Mohamed: Engineering Mathematics Department, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt | ||
