Nonlinear and Time-Varying Dynamics of High-Dimensional Models of a Translating Beam With a Stationary Load Subsystem

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
G. Y. Xu ◽  
W. D. Zhu
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
High Dimensional ◽  
Structural Systems ◽  
Time Varying ◽  
Incremental Harmonic Balance Method ◽  
Included Trial ◽  
Incremental Harmonic Balance ◽  
Dimensional Models ◽  
Low Dimensional

Nonlinear vibration and dynamic stability analyses of distributed structural systems have often been conducted for their low-dimensional spatially discretized models, and the results obtained from the low-dimensional models may not accurately represent the behaviors of the distributed systems. In this work the incremental harmonic balance method is used to handle a variety of problems pertaining to determining periodic solutions of high-dimensional models of distributed structural systems. The methodology is demonstrated on a translating tensioned beam with a stationary load subsystem and some related systems. With sufficient numbers of included trial functions and harmonic terms, convergent and accurate results are obtained in all the cases. The effect of nonlinearities due to the vibration-dependent friction force between the translating beam and the stationary load subsystem, which results from nonproportionality of the load parameters, decreases as the number of included trial functions increases. A low-dimensional spatially discretized model of the nonlinear distributed system can yield quantitatively and qualitatively inaccurate predictions. The methodology can be applied to other nonlinear and/or time-varying distributed structural systems.

Nonlinear and Time-Varying Dynamics of High-Dimensional Models of a Translating Beam With a Stationary Load Subsystem

2008 ◽  
Author(s):  
G. Y. Xu ◽  
W. D. Zhu
Keyword(s):  
High Dimensional ◽  
Structural Systems ◽  
Nonlinear Frequency ◽  
Time Varying ◽  
Included Trial ◽  
Frequency Responses ◽  
Linear And Nonlinear ◽  
Dimensional Models ◽  
Low Dimensional

Nonlinear vibration and dynamic stability analyses of distributed structural systems have often been conducted for their low-dimensional spatially-discretized models, and the results obtained from the low-dimensional models may not accurately represent the behavior of the distributed systems. In this work the incremental harmonic balance method is used for the first time to handle a variety of problems for high-dimensional models of distributed structural systems, including determination of linear and nonlinear frequency responses, optimization of system parameters, determination of simple parametric instability region boundaries, analysis of parametrically-excited nonlinear systems, and determination of linear and nonlinear frequency responses under combined parametric and forcing excitations. The methodology is demonstrated on a translating tensioned beam with a stationary load subsystem and some related systems. With sufficient numbers of included trial functions and harmonic terms, convergent and accurate results are obtained in all the cases. The effect of nonlinearities due to the vibration-dependent friction force between the translating beam and the stationary load subsystem, which results from non-proportionarity of the load parameters, decreases as the number of included trial functions increases. A low-dimensional spatially-discretized model of the nonlinear distributed system can yield quantitatively and qualitatively inaccurate predictions. The methodology can be applied to other nonlinear and/or time-varying distributed structural systems.

An Optimized Efficient Galerkin Averaging-Incremental Harmonic Balance Method for High-Dimensional Spatially Discretized Models of Continuous Systems Based on Parallel Computing

2021 ◽  
Author(s):  
Ren Ju ◽  
Weidong Zhu
Keyword(s):  
Parallel Computing ◽  
Harmonic Balance ◽  
Parallel Implementation ◽  
Nonlinear Dynamic Analysis ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
High Dimensional ◽  
Continuous Systems ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance

Abstract Modern computers are generally equipped with multi-core central processing units (CPUs). There has been great interest to introduce a parallelized harmonic balance method to make full use of computing resources and improve the efficiency in dealing with nonlinear dynamic analysis of high-dimensional spatially discretized models of continuous systems. In this work, an optimized efficient Galerkin averaging-incremental harmonic balance method for solving high-dimensional models of continuous systems based on parallel computing is introduced. Optimized parallel implementation based on tensor contraction is introduced in time-domain series calculations and the quasi-Newton method is used in the iteration procedure, which greatly accelerate computational speeds of both serial and parallel implementations. Especially, the parallel implementation achieves high parallel efficiency when multiple CPU cores are used. Due to its high computational efficiency and good robustness, the proposed method has the potential to be used as a powerful universal solver and analyzer for general types of continuous systems.

scholarly journals Comparison of Common Methods in Dynamic Response Predictions of Rotor Systems with Malfunctions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongliang Yao ◽  
Qian Zhao ◽  
Qi Xu ◽  
Bangchun Wen
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Newmark Method ◽  
Incremental Harmonic Balance Method ◽  
Rotor Systems ◽  
Double Frequency ◽  
Frequency Domain Methods ◽  
Incremental Harmonic Balance

The efficiency and accuracy of common time and frequency domain methods that are used to simulate the response of a rotor system with malfunctions are compared and analyzed. The Newmark method and the incremental harmonic balance method are selected as typical representatives of time and frequency domain methods, respectively. To improve the simulation efficiency, the fixed interface component mode synthesis approach is combined with the Newmark method and the receptance approach is combined with the incremental harmonic balance method. Numerical simulations are performed for rotor systems with single and double frequency excitations. The inherent characteristic that determines the efficiency of the two methods is analyzed. The results of the analysis indicated that frequency domain methods are suitable single and double frequency excitation rotor systems, whereas time domain methods are more suitable for multifrequency excitation rotor systems.

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