In flexible multibody dynamics nonlinear equations of motion are considered. Nonlinearities are present due to large overall motions of reference frames associated with each flexible body assembled from finite elements and also due to nonlinear springs, dampers, control systems, etc. For linearly elastic bodies a modal superposition (with few modes) for the finite element degrees-of-freedom (often a large number) is often of advantage in order to minimize computer efforts while keeping the analysis results sufficiently accurate. In fact, in some problems where long time simulations of large complex systems (trucks, space platforms, etc.) are of interest the modal truncation may be the only possible way to achieve any results at all in today's computer environments. Modes and finite element data may be extracted from finite element programs and then be used in a nonlinear time integration using a general purpose dynamics simulation program. Although the aim of the work presented here was to develop procedures for such a dynamics program, the statements below have applications also for linear systems. One objective is to show advantages of using an orthogonalization procedure, i. e. how a combination of modes, for example so-called constraint modes and fixed-interface eigenmodes, can be linearly combined into a new set of modes that are orthogonal with respect to the mass and stiffness matrices of a finite element assembly. Another objective is to point out that so-called attachment modes may be linearly combined into constraint modes and as a consequence produce the same orthogonalized modes and eigenvalues. One advantage of orthogonalization is that the resulting diagonal modal mass and stiffness matrix entries will indicate how small time steps one will expect during simulations. Another advantage, of special importance in flexible multibody dynamics, is that one may detect (and reject) possible rigid body modes contained in a set of constraint modes. Furthermore, modes corresponding to high frequencies may be detected and considered to be of no interest for the response. The orthogonalization procedure makes it possible to introduce, for each orthogonalized mode, a modal damping parameter that will reflect the internal damping properties of the finite element body. No assumption of proportional damping for the complete mechanical system is made since discrete nonlinear dampers, etc. also are allowed to exist in the dynamic analysis and design system model.
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