142 真直はりおよび曲がりはりに対する低次元非線形方程式の導出

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This paper presents a procedure to derive reduced-order nonlinear equations using the projection onto the sub-space which includes a solutions of whole-space equations in approximation. Nonlinear finite element(FE) equations are derived by the principle of virtual work taking into account geometrical nonlinearity. Reduced-order equations are derived by the projection onto the space defined by vectors that are obtained by solving static nonlinear FE equations on which equivalent inertia force is acting and by decomposing the solution vectors of the static equations. Reduced-order equations for straight beam and curved beam are derived, and numerical results about the fundamental natural frequency show good agreement with those obtained by applying a numerical integration directly to the equations in the whole space.
2006-08-06