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.

Vibration Analysis of a Shape Memory Oscillator by Harmonic Balance Method Verified Numerically

2019 ◽  
Vol 29 (03) ◽  
pp. 1930007 ◽  
Author(s):  
Rafal Rusinek ◽  
Joanna Rekas ◽  
Krzysztof Kecik
Keyword(s):  
Shape Memory ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
System Parameters ◽  
Irregular Motion

This paper focuses on periodic solutions for a one-degree-of-freedom oscillator with a spring made of shape memory alloy (SMA). However, when periodic solutions are unstable, irregular motion is identified numerically. The shape memory spring is described by a polynomial characteristic in this model. The harmonic balance method (HBM) is employed to find periodic solutions near the primary resonance. The solutions are confronted with results obtained by the multiple time scales method and numerical simulations. Finally, the effect of system parameters and temperature on the system dynamics is discussed.

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.

Non-Stationary Oscillations at Slow Transitions Across Instabilities

2007 ◽  
Author(s):  
Rudolf R. Pusˇenjak ◽  
Maks M. Oblak ◽  
Jurij Avsec
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Time Scales ◽  
Primary Resonance ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Excitation Parameter ◽  
Linear Dynamical Systems ◽  
Weakly Nonlinear ◽  
Non Linear

The paper presents the study of non-stationary oscillations, which is based on extension of Lindstedt-Poincare (EL-P) method with multiple time scales for non-linear dynamical systems with cubic non-linearities. The generalization of the method is presented to discover the passage of weakly nonlinear systems through the resonance as a control or excitation parameter varies slowly across points of instabilities corresponding to the appearance of bifurcations. The method is applied to obtain non-stationary resonance curves of transition across points of instabilities during the passage through primary resonance of harmonically excited oscillators of Duffing type.

Analysis of shape memory alloy vibrator using harmonic balance method

2020 ◽  
Vol 126 (7) ◽  
Author(s):  
Haoyuan Du ◽  
Xuan He ◽  
Linxiang Wang ◽  
Roderick Melnik
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method
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