Modeling of finite amplitude acoustic waves in closed cavities using the Galerkin method

2003 ◽  
Vol 113 (4) ◽  
pp. 1863-1870 ◽  
Author(s):  
Robert R. Erickson ◽  
Ben T. Zinn
Keyword(s):  
Galerkin Method ◽  
Acoustic Waves ◽  
Finite Amplitude ◽  
The Galerkin Method

Nonlinear Finite-Amplitude Dynamics

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Linear Model ◽  
Finite Amplitude ◽  
Numerical Code ◽  
Spectral Space ◽  
Simple Geometry ◽  
Nonlinear Simulations ◽  
The Galerkin Method

This chapter modifies the numerical code by adding the nonlinear terms to produce finite-amplitude simulations. The nonlinear terms are calculated using a Galerkin method in spectral space. After explaining the modifications to the linear model, the chapter shows how to add the nonlinear terms to the code. It also discusses the Galerkin method, the strategy of computing the contribution to the nonlinear terms for each mode due to the binary interactions of many other modes. The Galerkin method works fine as far as calculating the nonlinear terms is concerned because of the simple geometry and convenient boundary conditions. The chapter concludes by showing how to construct a nonlinear code and performing nonlinear simulations.

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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