In this paper, an explicit formulation of the shooting scheme for computation of multiple periodic attractors of a harmonically excited oscillator which is asymmetric with both stiffness and viscous damping piecewise linearities is derived. The numerical simulation by the shooting method is compared with that by the incremental harmonic balance method (IHB method), which shows that the shooting method is in many respects distinctively advantageous over the incremental harmonic balance method. | Vietnam Journal of Mechanics, VAST, Vol. 34, No. 3 (2012), pp. 157 – 167 CALCULATION OF NONLINEAR VIBRATIONS OF PIECEWISE-LINEAR SYSTEMS USING THE SHOOTING METHOD Nguyen Van Khang, Hoang Manh Cuong, Nguyen Thai Minh Tuan Hanoi University of Science and Technology, Vietnam Abstract. In this paper, an explicit formulation of the shooting scheme for computation of multiple periodic attractors of a harmonically excited oscillator which is asymmetric with both stiffness and viscous damping piecewise linearities is derived. The numerical simulation by the shooting method is compared with that by the incremental harmonic balance method (IHB method), which shows that the shooting method is in many respects distinctively advantageous over the incremental harmonic balance method. Key words: Nonlinear vibration, shooting method, numerical simulation, piecewise linear system, Floquet stability. 1. INTRODUCTION One of the most important objectives of the nonlinear dynamics is to determine the periods of the periodic orbits of the strongly nonlinear dynamic systems, since it is related to many important problems such as bifurcation, stability, chaos and so on. There are many ways to determine periodic orbits and periods of a nonlinear dynamic system. Those methods generally can be classified into categories, namely, frequency domain methods and time domain methods. In the frequency-domain formulation, the method of harmonic balance and generalized versions of this method are commonly used. In the time-domain formulation, finite-difference schemes, shooting techniques, and Poincare map methods are also widely used [1-5]. In recent years, much attention has been paid to the system with piecewise-linearity. The considered oscillator is a typical nonlinear system that is widely used in engineering systems. The determination of the periodic vibrations of piecewise-linear systems using the incremental harmonic balance method has been studied by a number of papers [6-10]. In the .
