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A new partitioned staggered scheme for flexible multibody interactions with strong inertial effects. (English) Zbl 1439.70011
Summary: In generic flexible multibody interaction problems, the differences in the mass, damping and stiffness of the bodies can be very large. Of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure. In this work, a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems. The equation of motion of body with larger inertia is integrated by implicit Newmark method, whereas the smaller inertia is solved using a robust self-starting explicit integration procedure. The coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity, which plays a key role in the stability and accuracy of the simulations. A wide range of mass ($$10^{-6}$$–$$10^{-1}$$), damping and stiffness ($$10^{-3}$$–$$10^3$$) ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme. The closed-form expressions for the coupling parameter have been constructed for both matching and non-matching time stepping through the Godunov-Ryabenkii normal mode analysis. The stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system. The time step of the heavier body significantly influences the stability more than the lighter body. To maintain the staggering error minimal, an optimal range of the coupling parameter is identified. The error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods. The partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems. As a potential application of this scheme, flexible multibody problems in the field of offshore engineering, viz., wave energy converter and floater-mooring systems are presented and validated with experimental measurements.
##### MSC:
 70E55 Dynamics of multibody systems 65L05 Numerical methods for initial value problems 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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