Contact-impact formulation for multi-body systems using component mode synthesis

The efficiency and accuracy are two most concerned issues in the modeling and simulation of multi-body systems involving contact and impact. This paper proposed a formulation based on the component mode synthesis method for planar contact problems of flexible multi-body systems. A flexible body is divided into two parts： a contact zone and an un-contact zone. For the un-contact zone, by using the fixed-interface substructure method as reference, a few low-order modal coordinates are used to replace the nodal coordinates of the nodes, and meanwhile, the nodal coordinates of the local impact region are kept unchanged, therefore the total degrees of freedom （DOFs） are greatly cut down and the computational cost of the simulation is significantly reduced. By using additional constraint method, the impact constraint equations and kinematic constraint equations are derived, and the Lagrange equations of the first kind of flexible multi-body system are obtained. The impact of an elastic beam with a fixed half disk is simulated to verify the efficiency and accuracy of this method.

PRECISELY COMPENSATED EFFICIENT COMPONENT MODE SYNTHESIS METHOD

Based on the improved mode superposition method proposed by Z. D. Ma and I.Hagiwara, a precisely compensated efficient mode synthesis method is developed. The calculationprocedure is discussed in detail and the truncation error is also analyzed. By comparison, it isshown that this method has a higher accuracy and a less calculation time than the general used ones.

THE FREE-INTERFACE METHOD OF COMPONENT MODE SYNTHESIS FOR SYSTEMS WITH VISCOUS DAMPING

This paper presents a new free-interface method of component mode synthesis for linear systems with arbitrary viscous damping. The left and right projection matrices described by state-variable vectors are first introduced for components with rigid-body freedom. The operator function of projection matrices for state displacement and state force is proved, and then the state residual flexibility matrix and the state residual inertia-relief attachment mode are defined and employed. The results of three examples demonstrate that the method proposed in this paper leads to very accurate system eigenvalues and high mode-synthesis efficiency

An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.

Experimental and numerical flutter analysis of a folding fin with multiple asymmetric free-plays

Experimental folding fin models with an adjustable free-play are tested in a wind tunnel.The fin structure is modeled using the free-interface component mode synthesis method,and its free-play is modeled as four independent nonlinear springs with asymmetric stiffness.A nonplanar unsteady vortex-lattice method considering compressibility is employed to address nonlinear deformation and high subsonic flow.Surface spline interpolation is improved through projection and partition.The aeroelastic characteristics of folding fins with different free-play magnitudes,initial conditions and elastic-axis positions are analyzed using an established time-marching method because of its relatively small computation scale and high precision.The results show good consistency among the presented method,the wind tunnel test and the harmonic balance method.There is a negative correlation between the critical speed of divergent motion and the ratio of the initial condition to the free-play magnitude.If either the free-play magnitude or the initial condition is extreme(tiny or vast),the system nonlinearity degenerates to linearity.Generally,the flutter prevention design of a linear model can be applied to a nonlinear model,such as moving the elastic-axis position aftward.The presented fin configuration exhibits an unstable limit cycle oscillation because the orders of coupled flutter modes do not change with variations in equivalent linear stiffness.