scholarly journals Solution of Wave Equation in Radial Form by VIM

2012 ◽  
Vol 2012 ◽  
pp. 1-3
Author(s):  
Hossein Aminikhah
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Analytic Approximation ◽  
Variational Iteration ◽  
Initial And Boundary Conditions

An analytic approximation to the solution of wave equation is studied. Wave equation is in radial form with indicated initial and boundary conditions, by variational iteration method it has been used to derive this approximation and some examples are presented to show the simplicity and efficiency of the method.

scholarly journals Approximate analytical solution of buckling of multi-damaged column-like structures using a continuous diffused crack model by variational iteration method

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Xingzhuang Zhao
Keyword(s):  
Boundary Conditions ◽  
Iteration Method ◽  
Ritz Method ◽  
Variational Iteration Method ◽  
Static Stability ◽  
Crack Model ◽  
Buckling Loads ◽  
Buckling Modes ◽  
Different Boundary Conditions ◽  
Variational Iteration

AbstractCompressive structural members can be locally damaged by overloading, corrosion, car crash and fire. In this work, a continuous diffused crack model is proposed to study the static stability of Euler–Bernoulli rectangular column-like structures under different boundary conditions. The governing differential equation is formulated by adopting a diffused crack model. The powerful variational iteration method is implemented to find the approximate analytical buckling modes and buckling loads based on the buckling response of the intact column. A novel generalized Lagrange multiplier is derived. The proposed method incorporates the effects of the crack width into consideration when deriving the buckling modes. The stability equation allows addressing the influences of multiple damages and can be applied to both concentrated and distributed cracks. The famous Rayleigh–Ritz method is utilized to verify the computed buckling loads. The proposed diffused crack model and the application with VIM is efficient and accurate for handling buckling problems of cracked columns under different boundary conditions.

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