Convergence of an iterative solution for a class of nonlinear vibration problems

1976 ◽  
Vol 59 (5) ◽  
pp. 1180
Author(s):  
M. M. Stani?ić
Keyword(s):  
Nonlinear Vibration ◽  
Iterative Solution ◽  
Vibration Problems

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

scholarly journals Extension of method of moment equation to nonlinear deterministic vibrations

2002 ◽  
Vol 24 (3) ◽  
pp. 133-141
Author(s):  
Nguyen Dong Anh ◽  
Ninh Quang Hai
Keyword(s):  
Nonlinear Vibration ◽  
Moment Equation ◽  
Numerical Results ◽  
Equation Approach ◽  
Method Of Moment ◽  
Vibration Problems

The paper present the so-called "an extended averaged equation approach" to the investigation of nonlinear vibration problems. The numerical results in analysing the vibration systems with weak, middle and strong non-linearity show the advantages of the method.

Assessment of Solutions to Vibration Problems Involving Piecewise Constant Exertions

2000 ◽  
Author(s):  
L. Dai
Keyword(s):  
Nonlinear Vibration ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Numerical Calculations ◽  
Piecewise Constant ◽  
Truncation Errors ◽  
Piecewise Constant Argument ◽  
Vibration Problems ◽  
Linear And Nonlinear ◽  
Constant Argument

Abstract Direct analytical and numerical solutions are constructed for linear and nonlinear vibration problems involving piecewise constant exertions. Existence and uniqueness of the solutions and the truncation errors of the numerical calculations are also analysed. With the employment of a piecewise constant argument, vibration systems with piecewise constant exertions are connected with the corresponding systems with continuous exertions.

Numerical Solution of Some Three-State Random Vibration Problems

1995 ◽  
Author(s):  
S. F. Wojtkiewicz ◽  
L. A. Bergman ◽  
B. F. Spencer
Keyword(s):  
Finite Element ◽  
Random Vibration ◽  
Gaussian White Noise ◽  
Three Dimensional ◽  
Planck Equation ◽  
Iterative Solution ◽  
Response Characteristics ◽  
Solution Strategies ◽  
Gaussian White Noise Process ◽  
Vibration Problems

Abstract This paper reports some of the recent efforts by the authors to examine the random vibration of mechanical systems of large dimension. A finite element solution method for the stationary three-dimensional Fokker-Planck equation, employing sparse storage and iterative solution strategies, is outlined and then applied to several representative systems. The first of these is a linear oscillator subjected to a first order linearly filtered Gaussian white noise process. This problem is used to verify and assess the accuracy of the method. After verification, two Duffing systems are analyzed, one exhibiting unimodal and the other bimodal response characteristics. Finally, some comparisons of the finite element results with those from Monte Carlo simulation are made for the two nonlinear systems.

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