Study on the Mixed Method of Transfer Matrix Method and Finite Element Method for Vibration of Multibody System

The mixed method of Transfer Matrix Method for Multibody System (MSTMM) and Finite Element Method (FEM) is introduced in this paper. The transfer matrix and transfer equation of multi-rigid-body subsystem are deduced by MSTMM. The mass matrix and stiffness matrix of flexible subsystem are calculated by FEM and then its dynamics equation is established. The connection point relations among subsystems are deduced and the overall transfer matrix and transfer equation of multi-rigid-flexible system are established. The vibration characteristics of the system are obtained by solving the system frequency equation. The computational results of two numerical examples show that the proposed method have good agreements with MSTMM and FEM. Multi-rigid-flexible-body system with multi-end beam can be solved by proposed method, which extends the application field of MSTMM and provides a theoretical basis for calculating complex systems with multi input end flexible bodies of arbitrary shape.

Vehicle-Terrain Interaction Simulation With Parallelized Multiscale Moving Soil Patch Model

Although many physics-based off-road mobility simulation models are proposed and utilized for vehicle performance evaluation as well as for understanding of tire-soil interaction problems, full vehicle simulation on deformable terrain requires addressing the computational complexity associated with the large dimensional physics-based terrain dynamics models for practical use. This paper, therefore, presents a hierarchical multiscale tire-soil interaction model that is fully integrated into parallelized off-road mobility simulation framework. In particular, a co-simulation procedure is developed for full vehicle simulation with multiscale terrain dynamics models by exploiting the moving soil patch technique. To this end, a detailed off-road vehicle simulation model is divided into five subsystems: a multibody vehicle subsystem and four tire-soil subsystems composed of nonlinear FE tires and multiscale moving soil patches. The tire-soil subsystems are interfaced with the vehicle subsystem by MPI through force-displacement coupling. It is demonstrated that the proposed framework allows for alleviating computational intensity of a full vehicle simulation that involves complex hierarchical multiscale terrain dynamics models by effectively distributing computational loads with co-simulation techniques.

Multi-Pulse Chaotic Dynamics of Eccentric Rotating Composite Laminated Circular Cylindrical Shell by Using the Extended Melnikov Method

The researches of global bifurcations and chaotic dynamics for high-dimensional nonlinear systems are extremely challenging. In this paper, we study the multi-pulse orbits and chaotic dynamics of an eccentric rotating composite laminated circular cylindrical shell. The four-dimensional averaged equations are obtained by directly using the multiple scales method under the case of the 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. The system is transformed to the averaged equations. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on the normal form obtained, the extended Melnikov method is utilized to analyze the multi-pulse global homoclinic bifurcations and chaotic dynamics for the eccentric rotating composite laminated circular cylindrical shell. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the eccentric rotating composite laminated circular cylindrical shell are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the eccentric rotating composite laminated circular cylindrical shell.

Effect of Rubber Material Properties on Steady-State Flat Belt Response

Belt-drives are used to transmit power between rotational machine elements in many mechanical systems such as industrial machines, home appliances, and internal combustion engines. The belt cross-section typically consists of axially stiff tension cords (made of steel or polyester strands) embedded in a rubber matrix. The rubber matrix provides the friction interface between the belt and the pulleys through which mechanical torque is transmitted. In this paper, the effect of the rubber’s Young’s modulus and Poisson’s ratio on the steady-state belt normal, tangential and axial stresses, average belt slip, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of a flat belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s cords are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as rigid bodies with a cylindrical contact surface. The equations of motion are integrated using a time-accurate explicit solution procedure.

Comparison of Surface Tension Models in Smoothed Particles Hydrodynamics Method

We compare two surface tension models to solve two-phase fluid interaction problems in the context of the mesh-free Smoothed Particles Hydrodynamics (SPH) method. The Continuum Surface Force (CSF) model (later extended to Continuum Surface Stress, CSS), originally derived from grid-based numerical methods, requires an accurate estimation of the interface curvature to express the surface tension. Unlike CSF, the Inter-Particle Force (IPF) model is more robust in this regard as it draws on a molecular dynamics foundation by considering how the pairwise interaction forces between particles within a cutoff distance act in relation to producing the surface tension. Herein, we rely on second-order consistent gradient and Laplacian operators to improve the accuracy of SPH formulations as well as on a particle shifting technique to “disorder” particles from non-differentiable interface geometries. A 3D liquid droplet deformation test is used to compare CSF and IPF in terms of their pressure field and kinetic energy dissipation accuracy.

Characterization of the Damping Coefficient in the Continuous Contact Model

This article presents an analytical formula to characterize the damping coefficient in a continuous force model of the direct central impact. The contact force element consists of a linear damper which is in a parallel connection to a spring with Hertz force-deformation characteristic. Unlike the existing models in which the separation condition is assumed to be at the time at which both zero penetration (deformation) and zero force occur, in this study, zero contact force is considered as the separation condition. To ensure that the continuous contact model obtains the desired restitution, an optimization process is performed to find the damping coefficient. The numerical investigations show that the damping coefficient can be analytically expressed as a function of system’s parameters such as the effective mass, penetration speed just before the impact, Hertz spring constant, and the coefficient of restitution.

Investigating the Nonlinear Dynamics of Human Balance Using Topological Data Analysis

Understanding the mechanisms behind human balance has been a subject of interest as various postural instabilities have been linked to neuromuscular diseases (Parkinson’s, multiple sclerosis, and concussion). This paper presents a classification method for an individual’s postural stability and estimation of their neuromuscular feedback control parameters. The method uses a generated topological mapping between a subjects experimental data and a data set consisting of time series realizations generated using an inverted pendulum mathematical model of upright balance. The performance of the method is quantified using a time series realizations with known stability and neuromuscular control parameters. The method was found to have an overall sensitivity of 85.1% and a specificity of 91.9%. Furthermore, the method was most accurate when identifying limit cycle oscillations with a sensitivity of 91.1% and a specificity of 97.6%. Such a method has the capability of classifying an individual’s stability and revealing possible neuromuscular impairment related to balance control, ultimately providing useful information to clinicians for diagnostic and rehabilitation purposes.

Effect of Structural Nonlinearity on a Piecewise Linear Aeroelastic System

Aeroelasticity is the study of the interaction of aerodynamic, elastic and inertia forces. When flexible structures, such as an airfoil, undergo wind excitation, divergence or flutter instability may arise. We study the dynamics of a two-degree-of-freedom (pitch and plunge) aeroelastic system with cubic structural nonlinearities. The aerodynamic forces are modeled as a piecewise linear function of the effective angle of attack. Stability and bifurcations of equilibria are analyzed. The effect of the structural nonlinearity is investigated. We find border collision, rapid, Hopf, saddle-node and pitchfork bifurcations. Bifurcation diagrams of the system were calculated utilizing MatCont and Mathematica.

The Effect of Gravity and Rotor Configuration on Dry Friction Whip and Safe Rotor/Stator Clearance

A mathematical model is developed for a real rotor/stator system with high degrees-of-freedoms, multiple disks, flexible bearing supports and couplings. The safe clearance level for coasting up of the rotor is calculated for a general high degree-of-freedom rotor/stator system. The harmful phenomena of dry friction whip, which is generally observable for simple 2 degree-of-freedom Jeffcott rotors in the absence of gravity only, can be proved to exist (in real rotor/stator systems) even in the presence of gravity for a wide range of clearance levels. In case of Jeffcott rotors, by fixing the clearance and increasing the rotor spin frequency, the response of the system follows the pattern: No rub - Forward Annular Rub (FAR) - Partial Forward Whirl (PFW) - Partial Backward Whirl (PBW) - dry whip (WHIP). In case of a real rotor/stator system, at certain frequencies, the system directly jumps to dry whip. The simulated results show a rich variety of system dynamics including FAR, PFW and WHIP in case of vertical rotors where the effect of gravity is neglected. For horizontal rotors, under the effect of gravity, the system response contains multi-harmonics, chaotic responses and multi-period vibrations. Based on these responses, a robust fault diagnosis strategy can be designed to identify the rubbing action in rotating machinery.

Vibration Characteristics Analysis of Multibody Systems With Random Parameters Based on MSTMM

Dynamics characteristics of linear multibidy systems are governed by the eigenfrequencies and the eigenvectors. The study of probabilistic characterization of the eigensolutions is now an important research topic in the field of multibody systems with random parameters. In this paper, by combining transfer matrix method for multibody system (MSTMM) and perturbation approach, a new method named as perturbation MSTMM is presented for random eigenvalue problems of multibody systems. This method has the advantages of, such as low memory storage requirement, high computational efficiency and high computational stability, etc., for dynamic design of multibody systems with random parameters. By using the proposed method, the rapid computation of random eigenvalue problems of general systems with random parameters can be realized, and the problem of repeated eigenvalues can be solved simply and conveniently. Formulations of the proposed method as well as some numerical examples are given to validate the proposed method. The simulation results of the eigenfrequencies are validated by experiment results. All the numerical applications show the merits and efficacy of the proposed method.