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We investigate various methods of analyzing systems with moving boundaries, using as an example a flexible rod sliding in an ideal frictionless sleeve in the field of gravity. Special attention is paid to the configurational force acting on the rod at the sleeve opening and thus determining the rod's dynamics. The non-material kinematic description used in simulations is based on the re-parametrization of the Lagrangian arc length coordinate. The variational formulation uses the energy expressions written for the entire rod, comprising the free segment and the one inside the sleeve. A novel finite element scheme is efficient for highly flexible rods, which may undergo complete ejection. A simplified two degrees of freedom model, which accelerates simulations, shows a good agreement as the bending stiffness increases. An analytical study using Hamiltonian mechanics exploits the separation of variables into fast oscillations and slow axial motion. The adiabatic invariant approach leads to approximate closed-form solutions for the slow dynamics and yields the maximum injection depth of the rod into the sleeve. • Dynamics of a flexible rod with moving domain boundaries is investigated. • Non-material finite element scheme is applicable to large vibrations leading to full ejection. • The role of the configurational force is studied numerically and analytically. • Simplified two degrees of freedom model allows for rapid time integration. • Closed-form solutions are obtained using the theory of adiabatic invariants for Hamiltonian systems. [ABSTRACT FROM AUTHOR]

Subject of the present work is the stability control of beam-type structures under a compressive force. Main scope of this article is to increase the critical buckling load by means of active feedback control. The compressive force is applied with the help of a cable which is fixed at the tip of the free end and passes through a point at the fixation of the beam. The structural displacement of the column is controlled by a constant gain feedback algorithm, with strain sensors used as input and piezoelectric actuators. A consistent theoretical formulation of this nonconservative system based on the Bernoulli–Euler beam theory is presented. The formulation takes into account the complete mechatronic system, including the influence of the controller with discrete strain measurements as well as distributed piezoelectric patches. The analytical results are compared to numerical simulations. The influence of the controller on the buckling load, the appearance of flutter instability and the limits of the controller’s operation range are highlighted.

Modeling the interaction of fluids with moving, flexible structures is a major and still very challenging subject in the field of multi-physics problems. In this work, an efficient computational approach based on the coupling of modally reduced flexible multibody systems with fluids modeled by means of smoothed particle hydrodynamics is outlined.

In industrial practice, the floating frame of reference formulation (FFRF)—often combined with the component mode synthesis (CMS) in order to reduce the number of flexible degrees-of-freedom—is the common approach to describe arbitrarily shaped bodies in flexible multibody systems. Owed to the relative formulation of the flexible deformation with respect to the reference frame, the equations of motion show state-dependent nonconstant inertia terms. Such relative description, however, comes along with considerable numerical costs, since both the mass matrix and gyroscopic forces, i.e., the quadratic velocity vector, need to be evaluated in every integration step. The state dependency of the inertia terms can be avoided by employing an alternative formulation based on the mode shapes as in the classical CMS approach. In this approach, which is referred to as generalized component mode synthesis (GCMS), the total (absolute) displacements are approximated directly. Consequently, the mass matrix is constant, no quadratic velocity vector appears, and the stiffness matrix is a corotated but otherwise constant matrix. In order to represent the same flexible deformation as in the classical FFRF-based CMS, however, a comparatively large number of degrees-of-freedom is required. The approach described in the present paper makes use of the fact that a majority of components in technical systems are constrained to motions showing large rotations only about a single spatially fixed axis. For this reason, the GCMS is adapted for multibody systems that are subjected to small flexible deformations and undergo a rigid body motion showing large translations, large rotations about one axis, but small rotations otherwise. Thereby, the number of shape functions representing the flexible deformation is reduced, which further increases numerical efficiency compared to the original GCMS formulation for arbitrary rotations.