Interaction of Higher Modes in Nonlinear Free Vibration of Stiffened Rectangular Plates

2017 ◽  
Author(s):  
Saman Farhangdoust ◽  
Davood Younesian ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Free Vibration ◽  
Nonlinear Differential Equations ◽  
Free Vibration Analysis ◽  
Variational Iteration Method ◽  
Sensitivity Study ◽  
Solution Technique ◽  
Rectangular Plates ◽  
Nonlinear Free Vibration ◽  
Frequency Responses ◽  
Stiffened Steel

Nonlinear free vibration analysis of stiffened plates is presented in this paper. The von Karman theory is employed to model the rectangular stiffened steel plate. The first two symmetric and asymmetric modes are taken into consideration and the coupled nonlinear differential equations of system are derived using the Galerkin approach. The Variational Iteration Method (VIM) is considered as the solution technique and an integral iterative formulation is presented to obtain the nonlinear natural frequencies. Subsequently a parametric sensitivity study is carried out and the effect of different initial amplitudes on the frequency responses is investigated.

Application of Variational Iteration Method in Nonlinear Free Vibration Analysis of Multi-Layered Nano-Scale Graphene Sheets

2014 ◽  
Author(s):  
Mehran Sadri ◽  
Davood Younesian ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Free Vibration ◽  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Free Vibration Analysis ◽  
Variational Iteration Method ◽  
Graphene Sheets ◽  
Geometrical Parameters ◽  
Nonlinear Free Vibration ◽  
Variational Iteration ◽  
Nano Scale

The nonlinear free vibration of multi-layered nano-scale graphene sheets is studied. Using the von Kármán and nonlocal continuum theories, large amplitude of vibration is included in the analysis as well as the size effect of nano-structure. The SSSS boundary condition is considered for the multi-layered graphene sheet and coupled nonlinear differential equations of motion of layers are taken into account based on Galerkin method. Variational iteration method (VIM) is employed as the solution procedure and nonlinear natural frequencies of the system are analytically determined. Two different geometries are taken into account and the analytical results are compared with frequencies obtained by numerical method. Finally, influence of geometrical parameters and amplitude of vibration on nonlinear frequencies of the system is examined.

Nonlinear Free Vibration Analysis of a Fluid-Conveying Microtube

2014 ◽  
Author(s):  
Shamim Mashrouteh ◽  
Mehran Sadri ◽  
Davood Younesian ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Variational Iteration Method ◽  
Solution Technique ◽  
Nonlinear Free Vibration ◽  
Nonlinear Equations Of Motion ◽  
Analytical Expressions

Nonlinear free vibration of a microstructure has been analyzed in this study. A fluid-conveying microtube is mathematically modeled using non-classical beam theory. Partial differential equation of the model is considered in non-dimensional form. Simply-supported boundaries are taken into account and assuming three vibrating modes, an analytical method is employed to obtain the nonlinear equations of motion. Variational iteration method has been utilized as an analytical solution technique. In order to obtain the nonlinear natural frequencies of the system, analytical expressions are found based on this method. A parametric study is also carried out to investigate the effect of different parameters on the vibration characteristics of the microstructure.

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