TY - JOUR
T1 - HIGHER APPROXIMATE SOLUTIONS OF THE DUFFING EQUATION (PRIMARY RESONANCE IN THE SOFT SPRING SYSTEM).
AU - Tamura, Hideyuki
AU - Kondou, Takahiro
AU - Sueoka, Atsuo
AU - Ueda, Noboru
PY - 1986
Y1 - 1986
N2 - The Duffing system with soft spring is analyzed by using a new algorithm which computes nonlinear steady-state oscillations and their stability with high speed and accuracy, based on the lines of the harmonic balance method. Detailed results of the frequency response of the primary resonance, up to the 9th harmonics, are presented. The following are demonstrated: a new unstable region, an isolated branch, the bifurcation of the non-odd order solutions, subharmonic oscillations (order 1/2 and 1/4), random almost periodic oscillations and superharmonic resonances (order 2 to 7). Some of these are confirmed by numerical simulation.
AB - The Duffing system with soft spring is analyzed by using a new algorithm which computes nonlinear steady-state oscillations and their stability with high speed and accuracy, based on the lines of the harmonic balance method. Detailed results of the frequency response of the primary resonance, up to the 9th harmonics, are presented. The following are demonstrated: a new unstable region, an isolated branch, the bifurcation of the non-odd order solutions, subharmonic oscillations (order 1/2 and 1/4), random almost periodic oscillations and superharmonic resonances (order 2 to 7). Some of these are confirmed by numerical simulation.
UR - http://www.scopus.com/inward/record.url?scp=0022777584&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0022777584&partnerID=8YFLogxK
U2 - 10.1299/jsme1958.29.3075
DO - 10.1299/jsme1958.29.3075
M3 - Article
AN - SCOPUS:0022777584
SN - 0021-3764
VL - 29
SP - 3075
EP - 3082
JO - Bulletin of the JSME
JF - Bulletin of the JSME
IS - 255
ER -