Resonance frequencies of functionally graded nanocantilevers subjected to nonlinear spring constraint and attached nanoparticle

Nowadays, thousands of studies have looked into the nonlinear vibration analysis of micro/nanostructures by solving nonlinear partial differential equations; however, there is almost no focus on the solution of the nonlinear boundary condition problems in the micro/nanoscale literature. This work pr...

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Bibliographic Details
Published in:Acta mechanica 2023-03, Vol.234 (3), p.991-1007
Main Authors: Bahrami, Arian, Zargaripoor, Ali, Khojastehnezhad, Vahid M., Pourasl, Hamed H., Hashemipour, Majid
Format: Article
Language:English
Subjects:
Analysis
Boundary conditions
Classical and Continuum Physics
Control
Differential equations
Dynamical Systems
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Euler-Bernoulli beams
Free vibration
Heat and Mass Transfer
Mathematical analysis
Mechanical engineering
Nanoelectromechanical systems
Nanoparticles
Nonlinear differential equations
Original Paper
Parameters
Partial differential equations
Resonance
Solid Mechanics
Spring constant
Theoretical and Applied Mechanics
Vibration
Vibration analysis
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Summary:Nowadays, thousands of studies have looked into the nonlinear vibration analysis of micro/nanostructures by solving nonlinear partial differential equations; however, there is almost no focus on the solution of the nonlinear boundary condition problems in the micro/nanoscale literature. This work presents the free vibration of a nonlocal functionally graded Euler–Bernoulli beam with a tip nanoparticle and a nonlinear spring constraint using Eringen’s nonlocal theory. It is assumed that there is a nonlinear/linear spring and a nanoparticle at one end of the beam while the other is clamped. The effect of various parameters, such as the nonlocal parameter, the nanoparticle mass, and the nonlinear/linear spring constant on the resonance frequencies, is demonstrated and discussed in detail. The presented benchmark tables can be used as an appropriate resource to validate analytical or approximate solutions in future works. Furthermore, the presented results can be useful for those designing micro/nano-electromechanical devices.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-022-03427-9