Incremental Harmonic Balance Method With Multiple Time Scales for Aperiodic Vibration of Nonlinear Systems

1983 ◽  
Vol 50 (4a) ◽  
pp. 871-876 ◽  
Author(s):  
S. L. Lau ◽  
Y. K. Cheung ◽  
S. Y. Wu
Keyword(s):  
Time Scales ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Almost Periodic ◽  
Incremental Harmonic Balance Method ◽  
New Approach ◽  
Incremental Harmonic Balance

An incremental harmonic balance method with multiple time scales is presented in this paper. As a general and systematic computer method, it is capable of treating aperiodic “steady-state” vibrations such as combination resonance, etc. Moreover, this method is not subjected to the limitation of weak nonlinearity. To show the essential features of the new approach, the almost periodic free vibration of a clamped-hinged beam is computed as an example.

Low- and High-Temperature Primary Resonance in Shape Memory Oscillator Observed by Multiple Time Scales and Harmonic Balance Method

2019 ◽  
Vol 14 (11) ◽  
Author(s):  
Andrzej Weremczuk ◽  
Joanna Rekas ◽  
Rafal Rusinek
Keyword(s):  
Shape Memory ◽  
Time Scales ◽  
Harmonic Balance ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Multiple Time Scales ◽  
Practical Implementation ◽  
Multiple Time ◽  
Fifth Order

Abstract This paper focuses on the primary resonance of a one degree-of-freedom (1DOF) oscillator with a spring made of shape memory alloy (SMA). The primary resonance is analyzed using the multiple time scales method (MTSM) and the harmonic balance method (HBM). The shape memory spring is described by a fifth-order polynomial function. The solutions are analyzed along with the results reported by another authors, and compared with numerical simulations. Three ranges of temperature are analyzed. Finally, the practical implementation aspect of the harmonic balance and MTSMs are discussed.

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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