Abstract
Modeling and analysis of complex dynamical systems can be effectively performed using multibody system (MBS) simulation software. Many modern MBS packages are able to efficiently and reliably handle rigid and flexible bodies, often offering a wide choice of different formulations. Despite many advances in modeling of flexible systems, the most widely used formulation remains the well-established floating frame of reference formulation (FFRF). Although FFRF usually allows inclusion of only small elastic deformations, this assumption is adequate for many industrial applications. In addition, FFRF is computationally efficient if implemented with appropriate model order reduction techniques and effective handling of system inertia terms by utilization of so-called inertia shape integrals. However, derivation of the system of equations of motion for FFRF bodies is a complex and often error-prone task. The main goal of this paper is to provide a reliable, detailed, universal and clear set of inertia terms within the FFRF. The paper concentrates on detailed derivation of the inertia forces with focus on accurate determination and exploitation of the inertia shape integrals. Two standard methods are employed, namely the Lagrangian and Virtual Work approaches. Additionally, the introduced derivations are executed without selection of specific rotational parameters. Direct application of Euler parameters and Euler angles is presented. It is found that the derived expressions are well suited for direct implementation and simplify derivation of force components.
Highlights
Multibody system dynamics analysis is a numerical simulation tool used to construct and solve equations of motion for complex dynamic systems
Deformation in multibody system dynamics can be defined with a number of different methods, of which the floating frame reference formulation (FFRF) is the approach most commonly used in industrial applications
The main objective of this paper is to present a detailed derivation of the inertial forces for complex dynamic systems based on the floating frame of reference formulation
Summary
Multibody system dynamics analysis is a numerical simulation tool used to construct and solve equations of motion for complex dynamic systems. FFRF can be applied to any arbitrary structural shape or type Such an approach can, only be conveniently used for small elastic deformations, and large body reference motions must be described by translations and rotations of the reference coordinate system itself. Choice of the system coordinates In the current paper, q (t), where t is time, denotes a vector of generalized body coordinates that consists of the translational and rotational coordinates of the floating reference frame and the elastic coordinates. In this approach, the position vector r P (q) of an arbitrary point P of the flexible body can be expressed as: rP = R+Au = R + A u 0 + uf = R + A (u 0 + S p) .
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