On the Accuracy of the Galerkin Method for a Nonlinear Dynamic Beam Equation

2011 ◽  
Vol 34 (14) ◽  
pp. 1725-1732
Author(s):  
J. Peradze
Keyword(s):  
Galerkin Method ◽  
Nonlinear Dynamic ◽  
Beam Equation ◽  
The Galerkin Method

scholarly journals A Numerical Algorithm for a Kirchhoff-Type Nonlinear Static Beam

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Jemal Peradze
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problem ◽  
Galerkin Method ◽  
Numerical Algorithm ◽  
Boundary Value ◽  
Iteration Process ◽  
Beam Equation ◽  
Nonlinear Static ◽  
The Galerkin Method ◽  
Nonlinear Iteration

A boundary value problem is posed for an integro-differential beam equation. An approximate solution is found using the Galerkin method and the Jacobi nonlinear iteration process. A theorem on the algorithm error is proved.

Nonlinear Dynamic Stability of an Electrically Actuated Microbeam Structure in MEMS

2011 ◽  
Author(s):  
Changping Chen ◽  
Yejie Jiang ◽  
Li Hong ◽  
Liming Dai
Keyword(s):  
Numerical Calculation ◽  
Galerkin Method ◽  
Dynamic Stability ◽  
Axial Force ◽  
Nonlinear Dynamic ◽  
Piezoelectric Effect ◽  
Electrically Actuated ◽  
Nonlinear Dynamic Stability ◽  
Principal Region ◽  
The Galerkin Method

In this article, based on the Euler-Bernoulli hypothesis and the Galerkin method, ananalysis of the nonlinear dynamic stability for a clamped-guided piezoelectric laminated microbeam under both a periodic axial force and a symmetric electrostatic load is presented. By using the incremental harmonic balanced method (IHBM), the boundary of the principal region of instability is got. In the numerical calculation, the effect of the environmental damping, geometric nonlinear, piezoelectric effect and the symmetric electrostatic load on the principal region of instability is discussed.

Non-Newtonian oscillatory layer flow, approximate solution

1979 ◽  
Vol 44 (10) ◽  
pp. 2908-2914 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Galerkin Method ◽  
Horizontal Plane ◽  
Oscillatory Flow ◽  
Oscillatory Boundary Layer ◽  
Layer Flow ◽  
Pseudoplastic Liquid ◽  
The Galerkin Method

The problem of the oscillatory flow of pseudoplastic liquid in vicinity of the infinitely long horizontal plane is formulated in stresses. For Re i.e. for conditions of oscillatory boundary layer the problem is solved approximately by the Galerkin method.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

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