Free vibration of axially functionally graded nanobeam with an attached mass based on nonlocal strain gradient theory via new ADM numerical method

Document Type : Research Article

Authors

1 Mech. Eng., Zanjan University

2 Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran

3 University of Zanjan

Abstract

The purpose of this paper is to study the free vibrations along a longitudinal line of a targeted graded nano beam with an attached mass based on the theory of nonlocal strain gradient theory using the asymptotic development method. nowadays due to the importance and usage of nano structures, investigation and recognition of their mechanical and mechanical properties seem necessary. Due to its small size and behavior depending on its size and the inability of classical theories to predict dependant mechanical behaviors, non-classical theories have been used. The governing equations and boundary condition relations of targeted graded nano beam with five boundary conditions simplesimple, clamped-free, clamped-clamped, clampedsimple, and clamped-attached mass have derived by using Hamiltonian principle. Then differential equation is solved analytically to obtain the frequency equations for the five boundary conditions. In the following, dimensionless frequencies by using the solving zero and the first order of numerical asymptotic development method have derived. Advantage of this method is simplicity, noncomplex mathematical relations and proper coding execution time. Eventually, the effect of nonlocal parameters, material length scale, type of material, the ratio of length to thickness, and mode number on free vibration nano beam has been investigated.

Keywords

Main Subjects

References

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Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 2 (Special Issue)
May 2021
Pages 1159-1178

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