Abstract
In this paper we use the method of derivative expansion of multiple scales of singular perturbations, and we have solve the forced vibration equation of a particle attached to a nonlinear spring under the influence of slight viscous damping. The problem is of the fourth order nonlinearity. The four cases discussed are: the soft excitation of non-resonance, the hard excitation of non-resonance, the soft excitation of resonance, the hard excitation of resonance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chien Wei-zang, Theory of Singular Perturbations and Applied in Mechanics, Scientific publishing house (1981). (in Chinese)
Chien Wei-zang, Theory of Singular Perturbations, “Applied methemetics and mechanics” editorial department (1980, 10). (in Chinese)
Din Yi-fei, Analysis of subharmonic resonance of the Duffing equation, The collection of treatises of the metting of nonlinear mechanics of China, Vol. 4 (1982). (in Chinese)
Shaker, B. S., Nonlinear oscillations of single-degree of freedom systems, Int. Cong, on Recent Advances in Structure Dynamics (1980), U. of Southampton, Vol. 2 (1980), 569–578.
Feng Den-tai, Applied Nonlinear Vibration Mechanics, The railway publishing house of China (1982, 7). (in Chinese)
Gu Wu-mao and Nan Yun-ren, Introduction to Nonlinear Vibration, Shanghai scientific and technical publishing house (1962). (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by Li Li and Dai Shi-qiang.
Rights and permissions
About this article
Cite this article
Xin-zhi, W., Tong-xin, Z. A kind of nonlinear oscillations of single degree of non-autonomy system. Applied Mathematics and Mechanics 6, 707–716 (1985). https://doi.org/10.1007/BF03250492
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03250492