円板の振動に対する変分法の一応用

概要

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The direct application of the calculus of variations to minimize the Lagrange's function leads to the partial differential equation called Euler's equation and the natural boundary conditions.　Instead of following such procedure mentioned above, Ritz's method consists of assuming the deflection as a linear series of ”admissible” functions and adjusting the coefficients in the series so as to minimize the Lagrangian.　We adopt the functions, in place of admissible functions, that satisfy the Euler's equation in the domain of the plate surface and the constraint boundary conditions at the boundary, and then determine the coefficients by means of minimizing the Lagrangian so as to satisfy the natural boundary conditions.　In the present problem, the series is an infinite Fourier one. If a finite series of the functions is adopted, the series with the adjusted coefficients satisties approximately the natural boundary conditions.
山形大学の論文
1967-01-20