Forced Vibration of Continuous System With Nonlinear Boundary Conditions

1978 ◽  
Vol 100 (3) ◽  
pp. 487-491 ◽  
Author(s):  
T. Watanabe
Keyword(s):  
Boundary Conditions ◽  
Nuclear Power ◽  
Power Plants ◽  
Nonlinear Boundary ◽  
Continuous System ◽  
Approximate Solutions ◽  
Nonlinear Boundary Conditions ◽  
Mechanical Equipment ◽  
Single Degree Of Freedom ◽  
Piping Systems

This paper deals with the nonlinear vibration problem concerning mechanical equipment-piping systems in nuclear power plants and others. An analytical method by approximate solutions is introduced for these systems as a continuous system with nonlinear boundary conditions, and some numerical examples are shown. Finally some numerical results obtained as a continuous system are compared with those of a single-degree-of-freedom system.

Longitudinal Stress Due to Sustained Loads in a Nonlinear World

2006 ◽  
Author(s):  
David W. Diehl
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Longitudinal Stress ◽  
Current Definition ◽  
Common Practices ◽  
Piping Systems ◽  
Sustained Loads ◽  
Consistent Method

This paper reviews the current definition and common practices for evaluating longitudinal stresses due to sustained loads in piping systems and focuses on an ambiguity that may occur in these calculations where nonlinear boundary conditions (e.g. resting support liftoff) exist. Author then introduces and demonstrates a convenient and consistent method for calculating these stresses in the presence of these nonlinear boundary conditions.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

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