TY - JOUR

T1 - Higher Approximate Solutions of the Duffing Equation (Odd Order Superharmonic Resonances in the Hard Spring System)

AU - Tamura, Hideyuki

AU - Kondou, Takahiro

AU - Sueoka, Atsuo

PY - 1985

Y1 - 1985

N2 - In the previous paper, an algorithm was presented to obtain the periodic solutions and stability of nonlinear multi-degree-of-freedom systems with high speed and high accuracy, based on the harmonic balance method and the infinitesimal stability criterion. A revised algorithm is presented to give only odd order solutions which are composed of odd order harmonics only, and so reduces the dimensions of the amplitude vector and Jacobian matrix to about one-half of the previous one. The Duffing system with hard spring is analysed by this algorithm and the detailed frequency responses are computed for odd order superharmonic resonances (order 3, 5, 7, 9), which are the odd order solutions. The results are shown for each resonance region in terms of (a) maximum amplitudes and norms, (b) superharmonic amplitudes, (c) fundamental amplitudes, and (d) fundamental and superharmonic phase angles. Some of these are comfirmed by numerical simulation.

AB - In the previous paper, an algorithm was presented to obtain the periodic solutions and stability of nonlinear multi-degree-of-freedom systems with high speed and high accuracy, based on the harmonic balance method and the infinitesimal stability criterion. A revised algorithm is presented to give only odd order solutions which are composed of odd order harmonics only, and so reduces the dimensions of the amplitude vector and Jacobian matrix to about one-half of the previous one. The Duffing system with hard spring is analysed by this algorithm and the detailed frequency responses are computed for odd order superharmonic resonances (order 3, 5, 7, 9), which are the odd order solutions. The results are shown for each resonance region in terms of (a) maximum amplitudes and norms, (b) superharmonic amplitudes, (c) fundamental amplitudes, and (d) fundamental and superharmonic phase angles. Some of these are comfirmed by numerical simulation.

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U2 - 10.1299/kikaic.51.1738

DO - 10.1299/kikaic.51.1738

M3 - Article

AN - SCOPUS:0022097248

VL - 51

SP - 1738

EP - 1747

JO - Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C

JF - Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C

SN - 0387-5024

IS - 467

ER -