Nonlinear free vibration of a cantilever nanobeam with surface effects: Semi-analytical solutions

2016 ◽  
Vol 113 ◽  
pp. 184-195 ◽  
Author(s):  
Demin Zhao ◽  
Jianlin Liu ◽  
Lin Wang
Keyword(s):  
Free Vibration ◽  
Analytical Solutions ◽  
Surface Effects ◽  
Nonlinear Free Vibration

Nonlinear free vibration of piezoelectric nanobeams incorporating surface effects

2014 ◽  
Vol 23 (3) ◽  
pp. 035012 ◽  
Author(s):  
Shahrokh Hosseini-Hashemi ◽  
Iman Nahas ◽  
Mahmood Fakher ◽  
Reza Nazemnezhad
Keyword(s):  
Free Vibration ◽  
Surface Effects ◽  
Nonlinear Free Vibration

Nonlocal nonlinear free vibration of nanobeams with surface effects

2015 ◽  
Vol 52 ◽  
pp. 44-53 ◽  
Author(s):  
Shahrokh Hosseini-Hashemi ◽  
Reza Nazemnezhad ◽  
Hossein Rokni
Keyword(s):  
Free Vibration ◽  
Surface Effects ◽  
Nonlinear Free Vibration ◽  
Nonlocal Nonlinear

Surface effects on nonlinear free vibration of nanobeams

2011 ◽  
Vol 42 (4) ◽  
pp. 934-937 ◽  
Author(s):  
Behnam Gheshlaghi ◽  
Seyyed M. Hasheminejad
Keyword(s):  
Free Vibration ◽  
Surface Effects ◽  
Nonlinear Free Vibration

scholarly journals Theoretical Analysis on the Nonlinear Free Vibration of a Tri-Cross String

2017 ◽  
Vol 2017 ◽  
pp. 1-17
Author(s):  
Bo Pan ◽  
Jingda Tang ◽  
Ryuichi Tarumi ◽  
Fulin Shang ◽  
Yanbo Wang ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Theoretical Analysis ◽  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Vibration Amplitude ◽  
Natural Frequencies ◽  
Geometrical Nonlinearity ◽  
Governing Equations ◽  
Nonlinear Free Vibration

Here we present a theoretical analysis on the nonlinear free vibration of a tri-cross string system, which is an element of space net-antennas. We derived the governing equations from Hamilton’s principle and obtained a linearized solution by the standard perturbation method. The semi-analytical solutions of the governing equations have not been provided referring to the solution of plate vibrating problem. This analysis revealed that natural frequencies of the tri-cross string depend on the vibration amplitude due to the geometrical nonlinearity in the constitutive equation. The geometric parameters, such as the diameters and the lengths of the constituent strings, also affect the frequency through the nonlinearity of the tri-cross string. The nonlinear natural frequency shows coupled characteristic; that is, the natural frequency of the tri-cross string varies with that of the constituent strings, but the contribution of each constituent string to the natural frequency is in different proportions.

Analytical Solutions for Nonlinear Free Vibration of Micro-Scale Timoshenko Beams

2016 ◽  
Author(s):  
Zia Saadatnia ◽  
Ebrahim Esmailzadeh ◽  
Davood Younesian
Keyword(s):  
Free Vibration ◽  
Analytical Solutions ◽  
Equations Of Motion ◽  
Variational Iteration Method ◽  
Strain Gradient Theory ◽  
Physical Parameters ◽  
Gradient Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Nonlinear Free Vibration

Nonlinear free vibration of micro-beams based on the Timoshenko beam model is studied. The governing equations of motion using the strain gradient theory, Von Kármán strain tensors and Hamiltonian principle, are developed. The Galerkin method is applied to the governing equations and the coupled nonlinear ordinary differential equations of system are obtained. The variational iteration method is utilized to determine the time responses of the micro-beam and also a close form expression for the frequency-amplitude is found. The analytical solutions obtained for different values of parameters are compared with those found from different numerical methods. The effects of geometrical and physical parameters on the dynamics of micro-beam are also examined. Moreover, the analytical formulation for frequency ratio, i.e., the ratio of nonlinear natural frequency to the linear one is obtained and the sensitivity of this ratio to the variations of various parameters is evaluated. It is proved that the proposed solution methods and the results obtained are accurate and reliable when dynamics of such micro structures are studied.

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