1986 Volume 29 Issue 248 Pages 525-532
An improved algorithm is proposed to obtain numerically a highly approximated steady-state solution for a nonlinear system with an arbitrary number of degrees of freedom. The so-called harmonic balance method is employed to compute the solution and the final Jacobian matrix obtained in the process of successive approximation is used to examine the stability of the solution. The theory is presented concisely by making use of the complex Fourier series. As a numerical example, the Duffing equation with hard spring is treated. The detained analytical results of the primary resonance are presented and the occurrence of the superharmonic resonances of order 2 to 9 is confirmed. Four regions in which the superharmonic resonances of even order bifurcate (that is, the unstable regions of the odd order harmonic solution) are indicated in terms of three parameters of the system.
JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing
JSME International Journal Series B Fluids and Thermal Engineering
JSME International Journal Series A Solid Mechanics and Material Engineering
JSME international journal. Ser. C, Dynamics, control, robotics, design and manufacturing
JSME international journal. Ser. 3, Vibration, control engineering, engineering for industry
JSME international journal. Ser. A, Mechanics and material engineering
JSME international journal. Ser. 1, Solid mechanics, strength of materials