On the dynamics of flexible beams under large overall motions - The plane case. I. (English) Zbl 0607.73057

Simo, J. C.; Vu-Quoc, L.

J. Appl. Mech. 53, 849-854 (1986).

The dynamic response of a flexible beam subject to large overall motions is traditionally formulated relative to a floating frame, sometimes referred to as the shadow beam. This type of formulation leads to equations of motion of the form \(\tilde g(\dot y,y,t)=0\), that are implicit, nonlinear and highly coupled in the inertia terms. An alternative approach is proposed whereby all quantities are referred to the inertial frame. As a result, the inertia term enters linearly in the formulation simply as mass times acceleration. Crucial to this formulation is the use of finite strain rod theories capable of treating finite rotations.

MSC:

74H45	Vibrations in dynamical problems in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)
74B20	Nonlinear elasticity
74K10	Rods (beams, columns, shafts, arches, rings, etc.)

Keywords:

invariant strain measure under superposed rigid body motion; kinetic energy; quadratic uncoupled form; linear and uncoupled inertia operator; nonlinear stiffness operator; dynamic response; flexible beam; large overall motions; inertial frame

Citations:

Zbl 0607.73058