Shooting Method Using Analytical Solutions for a Nonlinear System with Piecewise Linear Characteristics.

Yoshitake, Yutaka; Sueoka, Atsuo; Tamura, So; Kohira, Sachiko; Miyuki, Tatsuhiko

doi:10.1299/kikaic.66.23

Cited by 2 publications

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“…The authors have developed a shooting method (18) to be applicable on a system with discontinuous force such as a frictional force, for example. Moreover they submitted the new shooting method (19) for piecewise linear systems which uses analytical solutions on each of the linear regions instead of numerically integrated solutions. However, the application of the shooting method to the impacting system is difficult and the shooting method for the impacting system has not yet been developed, because it is unknown how instantaneous change of momentum is introduced to an equation of motion and its variational equation.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the authors have proposed a shooting method for impact vibration systems that contain not only discontinuous force but also the discontinuous changes in momentum. This method is developed highly from shooting methods (18), (19) that the author previously developed for systems with discontinuous forces. The equation of motion in the impact vibration system is expressed by an equation with a step function and a delta function, and its variational equation is expressed by an equation with a delta function and its differentiation; therefore, by solving the problem of calculating the process of variation at an instance of impact, application of the shooting method to the impact vibration system becomes possible.…”

Section: Introductionmentioning

confidence: 99%

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Development of Shooting Method for Impact Systems

Yoshitake

Sueoka

Miyuki

et al. 2004

JSME Int. J., Ser. C

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A shooting method is a very powerful numerical method to obtain periodic solutions of nonlinear systems. However, as a variational equation of motion is needed in the shooting method and it is very difficult to obtain it in the impact systems, the shooting method for impact systems has not been developed. In this report, a shooting method for impact systems is presented by solving this problem of variational equation. Namely, the variational equation with the delta function and its differentiation is derived. It is shown that the calculation speed of this method is very fast and complicated periodic solutions are easily obtainable in high accuracy. The stabilities of periodic solutions obtained in the shooting method are in good accordance with those obtained by the analytical method. The discontinuities in the stability of the periodic solutions are shown using characteristic multiplier. Lyapunov exponents are also calculated by applying the integral technique of variational equation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Development of Shooting Method for Impact Systems

Yoshitake

Sueoka

Miyuki

et al. 2004

JSME Int. J., Ser. C

Self Cite

View full text Add to dashboard Cite

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Analysis of responses of semi-active vibration control systems using piezoelectric actuators to harmonic disturbance forces

Nakahara

Fujimoto

2018

Transactions of the JSME (In Japanese)

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A semi-active vibration control technique using piezoelectric actuators with switched inductance shunts has been studied. This technique can be used for not only vibration suppression but also energy harvesting. In order to design semi-active vibration control systems and energy harvesters using this technique efficiently, it is necessary to analyze and understand the effects of design parameters on the performance of these systems. Responses of these systems to harmonic disturbance forces can be used for performance evaluation and previous studies analyze periodic responses of semi-active vibration control systems by assuming sinusoidal displacement responses and using method of harmonic balance. However, this control technique induces rectangular control forces and the displacement responses are distorted. Enhancing the control forces leads to stronger distortion of the responses and the validity of the assumption of the previous studies becomes lost. In order to overcome this problem, the authors have proposed to use shooting method which is a numerical method to calculate periodic solutions of non-linear systems without assuming certain forms of responses. This paper presents periodic responses obtained by shooting method with an improved non-dimensional model and the periodic responses are compared with ones obtained by method of harmonic balance. Furthermore, this paper considers not only the periodic responses but also non-periodic chaotic responses obtained by long term simulations with the non-dimensional model.

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Shooting Method Using Analytical Solutions for a Nonlinear System with Piecewise Linear Characteristics.

Cited by 2 publications

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Development of Shooting Method for Impact Systems

Development of Shooting Method for Impact Systems

Analysis of responses of semi-active vibration control systems using piezoelectric actuators to harmonic disturbance forces

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