Dynamics Of Flexible Multibody Systems Research Articles

Non-smooth numerical solution for Coulomb friction, rolling and spinning resistance of spheres applied to flexible multibody system dynamics

Non-smooth numerical solution for Coulomb friction, rolling and spinning resistance of spheres applied to flexible multibody system dynamics

A new sandwich beam model with layer-to-layer boundary modified displacements based on higher-order absolute nodal coordinate formulation

The absolute nodal coordinate formulation (ANCF) is one of the efficient modeling methods to solve the dynamics of flexible multibody systems. Zig-zag theory can accurately calculate the stress variation in the sandwich structure with only a few unknown variables, thus providing a good balance between computational efficiency and computational accuracy. Combining ANCF and zig-zag theory, this paper proposes a new sandwich beam model, called HANCF-ZZ, by introducing layer-to-layer boundary modified displacements in a high-order ANCF beam model. The capability of HANCF-ZZ for static deformation analysis and free vibration analysis is verified by comparing experimental, analytical, and numerical results in other literature. The results show that the HANCF-ZZ corrects the global stiffness overestimated by the equivalent single-layer theory, eliminates the locking problem of the low-order ANCF, and captures the nonlinear bifurcation phenomenon in large deformation problems under large loads. The HANCF-ZZ is not only an efficient numerical method for zig-zag theory but also enriches the ANCF element types to enable its application to the dynamics analysis of soft core sandwich beams.

Dynamic analysis of a deep-towed seismic system based on a flexible multi-body dynamics frame

A deep-towed seismic system is an effective tool for exploring minerals in strata. Because the exploration accuracy is closely related to the towing depth and array cable shape, a computational framework based on the flexible multi-body dynamics system is proposed to analyze the dynamic characteristics of the deep-towed seismic system caused by the mothership motion and sea current. The towing cable and seismic array cable are modeled using the absolute nodal coordinate formulation (ANCF), and several classical towing cases are designed to systematically analyze the influences of the mothership motion and current. The results indicate that the axial motion of the mothership along the towing cable is approximately rigidly transmitted, and the phase difference is related to the curvature distribution of the towing cable. In addition, currents parallel to the towing speed significantly change the towing depth. These dynamic characteristics can inform the design of array cable arrangements and control algorithms.

A unified framework for corotational flexible multibody system dynamics formulations.

Corotational formulations play an important role for flexible multibody dynamics systems, because they reflect the nature of many technical systems undergoing arbitrarily large rigid body motions but small deformations within each body. This paper defines flexible multibody dynamics and corotational formulations in this context. Furthermore, the «ingredients» and workflow of a flexible multibody dynamics simulation are briefly addressed for the reader less familiar with the topic. This part also points to major review papers and textbooks in the field, and embeds the unified formulations in the literature. The paper's main part presents state-of-the-art corotational flexible multibody dynamics formulations in a systematic and unified way. In this formulation part, the standard integral-based floating frame of reference formulation with modal reduction and with the conventionally employed lumped mass approximation is presented, and its drawbacks highlighted. Then, the so-called nodal-based, i.e., space-wise discretized, equations of motion are presented for several up-to-date nodal-displacement-based formulations within a unified framework. This approach clearly shows the equivalence of the presented formulations, and highlights the fact that the formulations differ only in the choice of degrees of freedom. Moreover, this contribution also intends to reduce the information and complexity within the scientific literature, since this unified framework allows the derivation of these formulations with significantly less effort..

A nonsmooth method for spatial frictional contact dynamics of flexible multibody systems with large deformation

AbstractA nonsmooth contact dynamics computation methodology for spatial frictional contact dynamics of flexible multibody systems with large deformation is presented. The contact and friction conditions between contact bodies are formulated as a cone complementary problem (CCP). Based on the mortar discretization method, nonsmooth frictional contact formulations for surface‐to‐surface and beam‐to‐beam contact problems are derived. These formulations can be used to study a wide range of contact problems between three‐dimensional bodies, thin plates and beams. The nonsmooth multibody dynamics equations are solved by using the generalized‐ method. The CCP is solved by using the accelerated projected gradient descend (APGD) algorithm in each Newton's iteration. Finally, six numerical examples are provided to validate the proposed computation methodology.

An implicit asynchronous variational integrator for flexible multibody dynamics

To accurately capture the dynamic responses of flexible multibody systems with complex geometric shapes or with contact and collision problems, extremely fine meshes have to be used. However, most previous algorithms for simulating these systems adopt a single integration time step size. A way to improve computation efficiency is to use different integration time steps for different elements with different sizes. In this study, a novel implicit AVI (asynchronous variational integrator) is originally proposed to study dynamics of complex flexible multibody systems. The proposed integrator allows different integration time step sizes for different elements with different mesh sizes. The multipoint constraint method is utilized to glue non-matching elements. To establish the system’s discrete Euler–Lagrange equations (DELs) , the diagonal-scaling method is used to construct the lumped mass matrix of elements. Finally, seven numerical examples are presented to comprehensively validate accuracy and efficiency of the proposed integrator. Numerical results indicate that the proposed AVI is capable of accurately capturing the dynamic response of flexible multibody systems and preserving systems’ energy and momentum. Compared with the generalized-α algorithm with a single time step size, the proposed AVI can significantly improve the computation efficiency for the dynamic simulation of complex flexible multibody systems with clearance joints.

Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function

Abstract Deployable antennas, as the core content of national defense technology research at this stage, have the advantages of large flexibility and light weight in practical applications, so this type of antenna can also be called a rigid-flexible hybrid structure. According to the theoretical analysis of the dynamics of flexible multi-body systems, it can be seen that effective control of unfolding antennas is a basic requirement for practical applications. Due to the instability of the specific numerical solution of the static Lagrangian function, it is difficult to completely meet the constraint equation, which is also the main factor affecting the steady development of flexible multibody dynamics. Therefore, in-depth discussion of the numerical calculation method of the static Lagrangian function, obtaining efficient and stable numerical methods from it, and providing effective information for the process control of the deployment of the antenna, is the focus of scientific research scholars at this stage. Based on the understanding of the flexible multi-body dynamics modeling method, this paper systematically analyzes the calculation method of the differential equations, and combines the direct modification method of the constraint violation of the augmentation method to propose the simulation calculation of the model. The final results prove that the dynamics of flexible multi-body systems have a positive effect on the application analysis of deployable antennas.

Detection of critical mode-shapes in flexible multibody system dynamics: The case study of a racing motorcycle

In multibody system models, body flexibility is introduced when the structure compliance is not negligible for an accurate description of the system behaviour. Flexible multibody systems provide a more detailed description of system kinematics and dynamics, introducing the effects of the body dynamics deformations.The influence of component higher frequency harmonics is often undesired during system working conditions. Therefore, in the design of a flexible multibody system the components and assembly modal properties are optimised to avoid resonances in the operating condition frequency ranges. However, in the system optimisation phase or when the system is upgraded to a new release, the least modifications would be ideally performed to optimise the system for its working conditions. In this context, there are no straightforward methods available to recognise which component mode-shapes require structural optimisation to avoid undesired dynamics behaviours.Based on an assembly-to-components modal approach, this paper proposes a method to detect the component mode-shapes responsible for undesired dynamics in the assembled multibody systems; the method is suitable for both numerical model or experimental applications. The inputs to the detection method are the components, sub-structures and assembly mode-shapes, together with the main frequencies exciting the system in operating conditions, to which operative deformations are associated. The procedure reveals the critical components and their mode-shapes requiring modifications.The detection method is conceived especially for systems requiring fast and continuous optimisation, e.g. high-performance racing vehicles, which are at least annually upgraded, or new improved releases of industrial complex machines. Firstly, the proposed method is numerically applied to the flexible multibody model of a slider–crank mechanism, detecting high-frequency vibrations in the piston stroke. Then, it is applied to a race motorcycle chassis frame to detect the critical component mode-shapes in realistic working conditions. Independent application of the procedure to numerical and experimental data of the motorcycle chassis pinpoints the same component mode-shapes as critical, on which optimisation efforts would be required.

Continuum damage dynamics of a large-scale flexible multibody system comprised of composite beams

Herein, a continuum damage dynamic model of a large-scale flexible multibody system comprising composite beams is proposed based on the framework of the absolute nodal coordinate formulation. To accurately model the continuum damage dynamics of a multibody system, the Hashin criterion is adopted to describe damage initiation during dynamics. A type of nonlinear evolution law is used to characterize the value of material damage. Furthermore, a material stiffness degradation rule is introduced to describe the process of structural damage. A formulation for the damage element elastic force and its Jacobian are derived based on the second Piola–Kirchhoff stress tensor. Two dynamic numerical examples, including a deployment dynamic analysis of the spatial beam structural unit, are conducted to verify the availability and applicability of the proposed model.

Interface reduction in flexible multibody systems using the Floating Frame of Reference Formulation

The influence of interface reduction on the dynamics of flexible multibody systems has not been well investigated and the conventional multipoint constraints still suffer when applied to multibody systems. Here, we propose a novel approach to derive rigid and interpolation multipoint constraints exploiting the role of the reference conditions, used in the Floating Frame of Reference Formulation to cancel rigid body modes from the elastic field. Since the connection of the reference conditions to the multipoint constraints seems to be limited to the free-surface case, the proposed formulation combines the interface reduction problem to create a novel Component Mode Synthesis method able to work with any reference condition. Two case studies are presented to show the differences between models with different combinations of reference conditions and multipoint constraints.

Semi-analytical sensitivity analysis approach for fully coupled optimization of flexible multibody systems

Flexible multibody systems have high geometric nonlinearity, which makes it very difficult to solve the dynamic response optimization problem. If mathematical programming tools are used, two main optimization methods are weakly coupled methods and fully coupled methods. The latter must consider the full dynamics of the system. When the objective function and constraint function are related to velocity vector or multicomponent-based constraints are involved in the optimization problem, only fully coupled optimization methods can be used. In this case, dynamic sensitivity analysis is necessary, but the solution is relatively difficult. In this paper, a semi-analytical sensitivity analysis approach for fully coupled optimization of flexible multibody systems is proposed. This approach combines the advantages of finite difference method and analytic method, and solves the bottleneck problem of the sensitivity calculation for fully coupled optimization methods. The formulas of the semi-analytical sensitivity analysis approach at the system and element levels are given. And the correctness and effectiveness are verified by two numerical examples. The results show that fully coupled optimization of flexible multibody system dynamics has good engineering application value.

Research on self-propelled performance of multi-body system of wave-driven robot

wave-driven robot is a flexible multi-body dynamic system driven by ocean waves. Self-propelled performance is an important index of wave-driven robot, which includes propulsion performance, resistance performance and rapidity of wave-driven robot, as well as its ability to capture and utilize ocean wave energy. However, the wave-driven robot belongs to flexible multi-body structure, whose dynamic model is more complex compared with conventional ocean vehicle, and the motion of wave-driven robot is completely driven by waves. It is difficult to predict its dynamic response and kinematic performance. In this paper, a numerical method is developed to solve the self-propelled process of wave-driven robot by coupling flexible multi-body dynamics and computational fluid dynamics. Firstly, the flexible multi-body dynamic model of the whole wave-driven robot is established. Secondly, the numerical flow field which can simulate regular waves is established. Finally, the dynamic model is combined with the numerical flow field, and the self-propelled process of the wave-driven robot is simulated by overlapping grid under typical wave parameters, and the propulsion performance, resistance performance and rapidity of wave-driven robot are analysed in depth. Through the test in water pool, it is found that the prediction accuracy of the velocity of float can reach 92.52%.

A condensed algorithm for adaptive component mode synthesis of viscoelastic flexible multibody dynamics

AbstractA condensed algorithm for adaptive component mode synthesis is proposed to compute the dynamics of viscoelastic flexible multibody systems efficiently and accurately. As studied, the continuous use of modes derived from the initial configuration will lead to poor convergence when dealing with geometric nonlinearity caused by large deformations and overall rotations. The modal reduction at a series of quasi‐static equilibrium configurations should be updated accordingly. According to the loss rate of system energy in the updating process of modal bases, an adaptive mode selection is proposed to reserve the optimal modal bases with their modal number automatically so as to achieve a high‐accuracy simulation. In the proposed condensed iteration algorithm, the order of reduced dynamic equations in the Newton‐Raphson is far less than the number of the unknowns to be discrete in generalized‐α scheme. Using an analytical mapping between the two parts of unknowns, the new algorithm solves a small part of the unknowns iteratively and solves the others noniteratively. Therefore, the saving of time cost comes not only from the proposed adaptive component mode synthesis, but also from the proposed condensed iteration algorithm. The modal bases of subsystems are updated by a series of frame‐like quasi‐static equilibrium configurations independently, in conjunction with the Craig‐Bampton method. Thus, the challenges in the model reduced of extensive ranges of stiffness and damping are removed via the successively updated modal bases. Finally, three numerical tests are made to illuminate the high accuracy and efficiency of the new algorithm proposed.

Geometrically exact planar Euler-Bernoulli beam and time integration procedure for multibody dynamics

A new formulation of geometrically exact planar Euler-Bernoulli beam in multi-body dynamics is proposed. For many applications, the use of the Euler-Bernoulli model is sufficient and has the advantage of being a nodal displacement-only formulation avoiding the integration of rotational degrees of freedom. In this paper, an energy momentum method is proposed for the nonlinear in-plane dynamics of flexible multi-body systems, including the effects of revolute joints with or without torsional springs. Large rotational angles of the joints are accurately calculated. Several numerical examples demonstrate the accuracy and the capabilities of the new formulation.

On the use of component mode synthesis methods for the model reduction of flexible multibody systems within the floating frame of reference formulation

This paper is focused on the application of the fundamental model reduction techniques used in structural dynamics to flexible multibody systems. In particular, an effective computational approach is developed and tested in this work for adapting the conventional structural model condensation strategies to the dynamics of flexible multibody systems. Thereby, the synthesis methods considered in this work can be readily implemented in the principal computational framework used for modeling flexible multibody systems subjected to large reference displacements and small deformations, namely the Finite Element (FE) Floating Frame of Reference Formulation (FFRF). Three component mode synthesis methods are of interest for this study: the Guyan-Iron condensation method, the well-known modal truncation technique, and the Craig-Bampton synthesis approach. Employing the computational approach proposed in this paper, it is demonstrated by means of numerical experiments that the three fundamental reduction methods considered in this investigation lead to correct numerical results when used for obtaining condensed mechanical models of flexible multibody systems based on the FE-FFRF. In the case of flexible multibody systems, the computational approach developed in this paper consists of two fundamentally distinct steps. First, the reference conditions are formulated in the FE-FFRF in a way consistent with the geometric properties of the mechanical joints that connects the bodies of the flexible multibody system under consideration. This is a key step that allows the analyst to model multibody systems in complex geometric configurations. Subsequently, a reduction technique is selected and used for reducing the dimensionality of the problem at hand. It is remarked that the reference conditions assumed in the first step of the proposed computational procedure modify all the component modes resulting from the application of the reduction strategy chosen in the second step of the computational algorithm and may or may not delete some of these. In the second step of the computational approach mentioned before, the conventional model reduction techniques can be effectively used leading to consistent numerical results. In this work, three numerical examples are employed for demonstrating the effectiveness of the computational procedure developed in the paper. More importantly, considerations on the choice of either isostatic or hyperstatic reference conditions associated with a particular choice of component modes are discussed in detail throughout the manuscript. The numerical simulations demonstrate that these choices can have a significant influence also on the efficiency of the integration schemes.

Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

The dynamics of flexible multibody systems (FMBSs) is governed by ordinary differential equations or differential-algebraic equations, depending on the modeling approach chosen. In both the cases, the resulting models are highly nonlinear. Thus, they are not directly suitable for the application of the modal analysis and the development of modal models, which are very useful for several advanced engineering techniques (e.g., motion planning, control, and stability analysis of flexible multibody systems). To define and solve an eigenvalue problem for FMBSs, the system dynamics has to be linearized about a selected configuration. However, as modal parameters vary nonlinearly with the system configuration, they should be recomputed for each change of the operating point. This procedure is computationally demanding. Additionally, it does not provide any numerical or analytical correlation between the eigenpairs computed in the different operating points. This paper discusses a parametric modal analysis approach for FMBSs, which allows to derive an analytical polynomial expression for the eigenpairs as function of the system configuration, by solving a single eigenvalue problem and using only matrix operations. The availability of a similar modal model, which explicitly depends on the system configuration, can be very helpful for, e.g., model-based motion planning and control strategies towards to zero residual vibration employing the system modal characteristics. Moreover, it allows for an easy sensitivity analysis of modal characteristics to parameter uncertainties. After the theoretical development, the method is applied and validated on a flexible multibody system, specifically using the Equivalent Rigid Link System dynamic formulation. Finally, numerical results are presented and discussed.

Computational simulation and free flight validation of body vibration of flapping-wing MAV in forward flight

FWMAVs (Flapping Wing Micro Air Vehicles) turn to be a flexible multi-body dynamic (FMBD) system when the inertia and flexibility of flapping wing are considered. The vibration caused by interaction of unsteady aerodynamics, structural dynamics and multi-body dynamics makes the analysis of aerodynamic and acquisition of equilibrium become full of challenge. In this study, a method coupled three-dimensional CFD (Computational Fluid Dynamics) and CSD (Computational Structural Dynamics) considering FMBD (flexible multi-body dynamics) between flexible wings and body is developed. And a trim algorithm is developed to satisfy three aspects of conditions including convergence of structural deformation and periodic condition of body's vibration in longitudinal direction and conditions of equilibrium. The computational results show that the trim conditions when body's vibration is taken into account are different from that when body's vibration is ignored. The vibration of body mainly increases the aerodynamic drag while having a little effect on lift. When the flight is trimmed, the corresponding flapping frequency increases and angle of attack decreases. In order to validate the method of simulation, the free flight data including the time course of oscillated plunging acceleration and pitch angle is collected based on the steady flight ability of “DOVE” FWMAV. Through comparison, though there is slight discrepancy between computational results and free flight data, it proves that CFD/FMBD method provides a sufficiently good accuracy for the simulation of body vibration of FWMAVs. Based on the proposed and validated model, the influence of various take-off mass on the vibration of body is studied and it indicates that a proper mass ratio between wing to body can suppress the maximum acceleration of vibration to protect the precise sensors and equipment.

Theoretical modeling and numerical solution methods for flexible multibody system dynamics

Flexible multibody system dynamics (MSD) is one of the hot spots and difficulties in modern mechanics. It provides a powerful theoretical tool and technical support for dynamic performance evaluation and optimization design of a large number of complex systems in many engineering fields, such as machinery, aviation, aerospace, weapon, robot and biological engineering. How to find an efficient accurate dynamics modeling method and its stable reliable numerical solving algorithm are the two core problems of flexible MSD. In this paper, the research status of modeling methods of flexible MSD in recent years is summarized first, including the selection of reference frames, the flexible body’s kinematics descriptions, the deductions of dynamics equation, the model reduction techniques and the modeling methods of the contact/collision, uncertainty and multi-field coupling problems. Then, numerical solution technologies and their latest developments of flexible MSD are discussed in detail. Finally, the future research directions of modeling and numerical computation of flexible MSD are briefly prospected.

Multibody dynamic modelling of a direct wind turbine drive train

Wind turbines normally have a long operational lifetime and experience a wide range of operating conditions. A representative set of these conditions is considered as part of a design process, as codified in standards. However, operational experience shows that failures occur more frequently than expected, the costlier of these including failures in the main bearings and gearbox. As modern turbines are equipped with sophisticated online systems, an important task is to evaluate the drive train dynamics from online measurement data. In particular, internal forces leading to fatigue can only be determined indirectly from other locations’ sensors. In this contribution, a direct wind turbine drive train is modelled using the floating frame of reference formulation for a flexible multibody dynamics system. The purpose is to evaluate drive train response based on blade root forces and bedplate motions. The dynamic response is evaluated in terms of main shaft deformation and main bearing forces under different wind conditions. The model was found to correspond well to a commercial wind turbine system simulation software (ViDyn).

Flexible Multibody System Dynamics by Means of a Spectral Based Meshless Approach

Flexible Multibody System Dynamics by Means of a Spectral Based Meshless Approach