著者
津田 吉広 田村 英之 末岡 淳男 松岡 寛憲
出版者
一般社団法人日本機械学会
雑誌
日本機械学會論文集. C編 (ISSN:03875024)
巻号頁・発行日
vol.60, no.578, pp.3300-3307, 1994-10-25

The characteristic which the Duffing oscillator with a softening spring property under harmonically stimulating force presents in the main resonant region has been investigated numerically. With regard to the structure which the system exhibits in this region, there exists another branch which appears due to bifurcation from the resonant branch at a certain frequency, in addition to the resonant and nonresonant branches. It has been clarified that many kinds of periodic solutions exist in the region between this new branch and the resonant one. Furthermore, besides the traditional harmonic solutions, i. e., resonant and nonresonant solutions, it has been shown that another harmonic solution appears, although it is unstable. This unstable solution enables us to reasonably explain the constitution of attractors in this resonant region. Chaotic phenomena, which appear due to period doubling bifurcation also exist.
著者
田村 英之 松崎 健一郎 岡部 匡
出版者
一般社団法人日本機械学会
雑誌
日本機械学會論文集. C編 (ISSN:03875024)
巻号頁・発行日
vol.60, no.579, pp.3719-3726, 1994-11-25

In the previous paper, the general theory of exact solutions in a family of Duffing oscillators including hard, soft and snap-through spring systems was studied. In particular the paper discussed the hard spring system in detail, and a listing of the numeration program was included. As a continued report, the soft spring system is dealt with here in detail. All the free vibrations in a family of Duffing oscillators are solved exactly and formally in terms of a family of Jacobian elliptic functions ; however, their precise numeration is a very important task. The present study is devoted to discussing excellent algorithms/programs. A FORTRAN program with the precision of REAL * 16 is presented, which ensures an accuracy with relative error of less than 10^<-30>. The listing of the program and numerical results of the dynamics of the Duffing oscillator with the soft spring system are demonstrated.