Effect of initial imperfection on the connection forces in the spatial analysis of flexible mechanical systems

In both the augmented and recursive formulation of the dynamic equations of flexible mechanical systems, the inertia, constraints, and applied forces must be properly defined. In this approach the system is kinematically driven using specified trajectories, and the objective is to determine the driving forces and torques. In flexible body dynamics, however, a force that acts at a point on the deformable body is equipollent to a system, defined at another point, that consists of the same force, a moment that depends on the relative deformation between the two points, and a set of generalized forces associated with the elastic coordinates. Furthermore, a moment in flexible body dynamics is no longer a free vector. It is defined by the location of its line of action as well as its magnitude and direction. The actual and generalized constraint forces represent equipollent systems of forces. Both systems in flexible body dynamics are functions of the deformation. In this investigation, a procedure is developed for the determination of the actual system of constraint forces in spatial flexible mechanical systems. The mathematical formulation of some mechanical joints that are often encountered in the analysis of constrained flexible mechanical systems is discussed. The effect of the elastic deformation on the actual reaction forces is also examined numerically using the spatial flexible multibody RSSR (Revolute-Spherical-Spherical-Revolute) mechanism that consists of a set of interconnected rigid and elastic bodies. The procedure described in this investigation can also be used to determine the joint torques in kinematically driven spatial elastic mechanism and manipulator systems.; The effect of the initial curvature and the rotary inertia on the actual joint forces is also examined in this investigation. Nonlinear terms that represent the coupling between the rotary inertia and the initial curvature of plates are identified and their dependence on the finite rotation of the plate is demonstrated. The effect of the rotary inertia on the kinematic relationships as well as the centrifugal and Coriolis force components is examined. The nonlinear dynamic differential equations of motion of the initially curved plate are formulated using the principle of virtual work in dynamics. It is demonstrated in this investigation that the use of the mode shapes of flat plates in the analysis of initially curved plates can lead to erroneous results. It is also shown that the effect of the kinematic coupling as the result of including the effect of the rotary inertia is not as significant as the effect of the kinematic coupling as the result of considering the effect of the initial curvature.