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

Model Order Reduction of Complex Airframes Using Component Mode Synthesis for Dynamic Aeroelasticity Load Analysis

Airframe structural optimization at different design stages results in new mass and stiffness distributions which modify the critical design loads envelop. Determination of aircraft critical loads is an extensive analysis procedure which involves simulating the aircraft at thousands of load cases as defmed in the certification requirements. It is computationally prohibitive to use a GFEM （Global Finite Element Model） for the load analysis, hence reduced order structural models are required which closely represent the dynamic characteristics of the GFEM. This paper presents the implementation of CMS （Component Mode Synthesis） method for the generation of high fidelity ROM （Reduced Order Model） of complex airframes. Here, sub-structuring technique is used to divide the complex higher order airframe dynamical system into a set of subsystems. Each subsystem is reduced to fewer degrees of freedom using matrix projection onto a carefully chosen reduced order basis subspace. The reduced structural matrices are assembled for all the subsystems through interface coupling and the dynamic response of the total system is solved. The CMS method is employed to develop the ROM of a Bombardier Aerospace business jet which is coupled with aerodynamic model for dynamic aeroelasticity loads analysis under gust turbulence. Another set of dynamic aeroelastic loads is also generated employing a stick model of same aircraft. Stick model is the reduced order modelling methodology commonly used in the aerospace industry based on stiffness generation by unitary loading application. The extracted aeroelastic loads from both models are compared against those generated employing the GFEM. Critical loads modal participation factors and modal characteristics of the different ROMs are investigated and compared against those of the GFEM. Results obtained show that the ROM generated using Craig Bampton CMS reduction process has a superior dynamic characteristics compared to the stick model.

Generalized Odd-Even Mode Theory and Mode Synthesis Antenna Design Approach

In this article,studies on the multimode excitation problem of waveguides and antennas,the balance/unbalance mech-anism and the balanced feeding techniques in dipole antenna systems are first briefly historically reviewed.In this context,general-ized odd-even mode theory is advanced to quantitatively and approximately describe the mutual coupling effect between a feed line and an antenna.As is mathematically deduced and demonstrated,the modal parity mismatch between the feed line and the antenna should ultimately dominate the unbalance phenomenon in antenna systems.Thus,an elegant,closed-form formula is derived to ap-proximately calculate the“unbalance degree”of a straight dipole off-center fed by a symmetric twin-wire line.Design approaches for the simplest,linear,1-D multimode resonant antennas are introduced.Moreover,the“falling tone excitation”law gauged based on prototype dipoles is revealed and used to develop a mode synthesis design approach for microstrip patch antennas(MPAs)and 2-D sectorial electric dipole antennas.Design examples with distinctive radiation performance are presented and discussed.Finally,possible development trends of multimode resonant antennas are prospected.

High-speed tracked vehicle model order reduction for static and dynamic simulations

In this paper, a model order reduction strategy is adopted for the static and dynamic behaviour simulation of a high-speed tracked vehicle. The total number of degree of freedom of the structure is condensed through a selection of interface degrees of freedom and significant global mode shapes, for an approximated description of vehicle dynamic behaviour. The methodology is implemented in a customised open-source software to reduce the computational efforts. The modelled tracked vehicle includes the sprung mass, the unsprung masses, connected by means of torsional bars, and all the track assemblies, composing the track chain. The proposed research activity presents a comprehensive investigation of the influence of the track chain, combined with longitudinal vehicle speed, on statics and vehicle dynamics, focusing on vertical dynamics. The vehicle response has been investigated both in frequency and time domain. In this last case road-wheel displacements are assumed as inputs for the model, under different working conditions, hence considering several road profiles with different amplitudes and characteristic excitation frequencies. Simulation results have proven a high fidelity in model order reduction approach and a significant contribution of the track chain in the global dynamic behaviour of the tracked vehicle.

Study on LQR control algorithm using superelement model

The conventional linear quadratic regulator(LQR) control algorithm is one of the most popular active control algorithms.One important issue for LQR control algorithm is the reduction of structure's degrees of freedom(DOF). In this work, an LQR control algorithm with superelement model is intended to solve this issue leading to the fact that LQR control algorithm can be used in large finite element(FE) model for structure. In proposed model, the Craig-Bampton(C-B) method, which is one of the component mode syntheses(CMS), is used to establish superelement modeling to reduce structure's DOF and applied to LQR control algorithm to calculate Kalman gain matrix and obtain control forces. And then, the control forces are applied to original structure to simulate the responses of structure by vibration control. And some examples are given. The results show the computational efficiency of proposed model using synthesized models is higher than that of the classical method of LQR control when the DOF of structure is large. And the accuracy of proposed model is well. Meanwhile, the results show that the proposed control has more effects of vibration absorption on the ground structures than underground structures.

Experimental and simulation studies on similitude design method for shock responses of beam-plate coupled structure

The similitude theory helps to understand the physical behaviors of large structures through scaled models. Several papers have studied the similitude of shock issues. However, the dynamic similitude for shock responses of coupled structures is rarely incorporated in open studies. In this paper, scaling laws are derived for the shock responses and spectra of coupled structures. In the presented scaling laws, the geometric distortion and energy loss are considered. The ability of the proposed scaling laws is demonstrated in the simulation and experimental cases. In both cases, the similitude prediction for the prototype's time-domain waveform and spectrum is conducted with the scaled model and scaling laws. The simulation and experimental cases indicate that the predicted shock responses and spectra agree well with those of the prototype, which verifies the proposed scaling laws for predicting shock responses.

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.

Application of Power Series on Vibration Analyses

Power series is extensively used for engineering studies. To raise the synthesis efficiency and computation accuracy of vibration mode synthesis (MS), the choosing of power series as the component mode-function is studied in this paper, and emphasis is laid on its effect upon the system computation accuracy when using the mode synthesis method for a high speed compound rotating elastic system.

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.

Nonlinear aeroelastic analysis of a twin-tail boom UAV with rudder freeplay nonlinearities

The issue of nonlinear structural freeplays in aircraft has always been a significant con-cern.This study investigates the aeroelastic characteristics of a twin-tail boom Unmanned Aerial Vehicle(UAV)with simultaneous freeplay nonlinearity in its left and right rudders.A comprehen-sive Limit Cycle Oscillation(LCO)solution route is proposed for complex aircraft with multiple freeplays,which can consider both accuracy and effciency.For the first time,this study reveals the unique LCO characteristics exhibited by twin-tail boom UAVs with rudder freeplays and pro-vides simulations and explanations of interesting phenomena observed during actual flight.The governing equations are established using the free-interface component mode synthesis method,and the LCOs of the system are mainly solved through the improved time-domain numerical con-tinuation method and frequency-domain numerical continuation method.Furthermore,the study investigates the influence of the left and right rudder freeplay size ratio on the LCO characteristics.The results demonstrate that the twin-tail boom UAV exhibits two stable LCO types:close and dif-fering left and right rudder amplitudes.The proposed method successfully describes the complete LCO behaviors of the system.Overall,this study makes significant contributions to our understand-ing of the aeroelastic behavior of twin-tail boom UAVs with rudder freeplays.

Modeling, measurement and simulation of the disturbance torque generated via solar array drive assembly

The disturbance torque generated via solar array drive assembly(SADA) can significantly degrade the key performance of satellite.The discussed SADA is composed of a two-phase hybrid stepping motor and a set of two-stage straight gear reducer. Firstly, the vibration equation of the two-phase hybrid stepping motor is established via simplifying and linearizing the electromagnetic torque.Secondly, based on the vibration equation established, the disturbance torque model of SADA is created via force analysis and force system simplification. Thirdly, for precisely ground measuring the disturbance torque aroused by SADA, a measurement system,including a strain micro-vibrations measurement platform(SMMP) and a set of gravity unloading device(GUD), is designed.Fourthly, the proposed disturbance torque model is validated by measuring and simulating the disturbance torque produced via SADA driving rigid load through GUD. The results indicate that, the proposed disturbance torque model holds the ability to describe the disturbance torque caused by SADA with high precision. Finally, the disturbance torque emitted by SADA driving a flexible load, designed to simulate solar array, is modeled and simulated via using fixed-interface mode synthesis method(FIMSM). All the conclusions drawn from this article do have a meaningful help for studying the disturbance torque produced by SADA driving solar array on orbit.

Identification of nonlinear multi-degree-of freedom structures based on Hilbert transformation

The modeling method and identified method adapted to multi-degree-of-freedom structures with strucrural nonlinearities are established.The component mode synthesis method is used to establish the nonlinear governing equations by extending the connected relationships.Based on the modeling method,the Hilbert transform method is applied to identify the nonlinear stiffness of multi-degree-of-freedom structures.Nonlinear analysis and identification of a typical folding wing configuration with three freeplay hinges are investigated.The nonlinear governing equation is established based on present methods and the computing results of different stiffness are checked by finite element programming.In order to illustrate the influence of the nonlinearities,the frequency response characteristics of the structure are analyzed and Hilbert transform is performed.The Hilbert transform identification method is utilized to identify the nonlinear stiffness of nonlinear hinges in the time domain and several parametric studies are performed.In addition,the comparison of response is made to illustrate the feasibility of the methods.The results show that the extending component mode synthesis method in the present work can be used to establish the governing equation with structural nonlinearities.Based on the modeling method,the Hilbert transform identified method can be extended to multi-degree-of-freedom structures accurately.