This paper presents the geometric stiffening effects and the complete nonlinear interaction between elastic and rigid body motion in the study of constrained multibody dynamics. A recursive formulation (or direct path approach) of the equations of motion based on Kane’s equations, finite element method and modal analysis techniques is presented. An extended matrix formulation of the partial angular velocities and partial velocities for flexible (elastic) bodies is also developed and forms the basis for our analysis. Closed loops and kinematical constraints (specified motions) are allowed and their corresponding Jacobian matrices are fully developed. The constraint equations are appended onto the governing equations of motion by representing them in a minimum dimension form using an innovative method called the Pseudo-Uptriangular Decomposition method. Examples are presented to illustrate the method and procedures proposed.
Nonlinear Modeling of Flexible Multibody Systems Dynamics Subjected to Variable Constraints
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Ider, S. K., and Amirouche, F. M. L. (June 1, 1989). "Nonlinear Modeling of Flexible Multibody Systems Dynamics Subjected to Variable Constraints." ASME. J. Appl. Mech. June 1989; 56(2): 444–450. https://doi.org/10.1115/1.3176103
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