二次曲線ばね系自由振動の厳密解とその数値化プログラム

概要

論文の詳細を見る
A classical nonlinear oscillator possesses a spring function expressed in terms of the 2nd-or the 3rd-order polynomial, viz. , the so-called Helmholtz or Duffing systems. The latter, a symmetrical system, has been studied extensively since Duffing proposed the mathematical models ; however, the former, an asymmetrical system, is less well known than the latter. The exact solution of their free oscillation seems to be at the same stage of development, in that an expression in terms of the Jacobian elliptic functions, i. e. , sn, cn or dn for the Duffing system, exists already, whereas sn^2 or cn^2 have only recently been found for the Helmholtz system. This paper summarizes existing numeration algorithms and proposes a program for exact solutions of the free oscillation in the Helmholtz system. This solution successufully verifies the accuracy of a numerical or an approximate scheme applicable to solve a nonlinear problem which may essentially have no exact solution.
一般社団法人日本機械学会の論文
1993-10-25