1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.

Dynamics of multibody systems

In this paper, a review of past and recent developments in the dynamics of flexible multibody systems is presented. The objective is to review some of the basic approaches used in the computer aided kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. Among the formulations reviewed in this paper are the floating frame of reference formulation, the finite element incremental methods, large rotation vector formulations, the finite segment method, and the linear theory of elastodynamics. Linearization of the flexible multibody equations that results from the use of the incremental finite element formulations is discussed. Because of space limitations, it is impossible to list all the contributions made in this important area. The reader, however, can find more references by consulting the list of articles and books cited at the end of the paper. Furthermore, the numerical procedures used for solving the differential and algebraic equations of flexible multibody systems are not discussed in this paper since these procedures are similar to the techniques used in rigid body dynamics. More details about these numerical procedures as well as the roots and perspectives of multibody system dynamics are discussed in a companion review by Schiehlen [79]. Future research areas in flexible multibody dynamics are identified as establishing the relationship between different formulations, contact and impact dynamics, control-structure interaction, use of modal identification and experimental methods in flexible multibody simulations, application of flexible multibody techniques to computer graphics, numerical issues, and large deformation problem. Establishing the relationship between different flexible multibody formulations is an important issue since there is a need to clearly define the assumptions and approximations underlying each formulation. This will allow us to establish guidelines and criteria that define the limitations of each approach used in flexible multibody dynamics. This task can now be accomplished by using the “absolute nodal coordinate formulation” which was recently introduced for the large deformation analysis of flexible multibody systems.

Flexible Multibody Dynamics: Review of Past and Recent Developments

Chatter Stability of Metal Cutting and Grinding

Literature survey of contact dynamics modelling

https://repositorium.sdum.uminho.pt/bitstream/1822/19623/1/6.7.32%202012.pdf

Compliant contact force models in multibody dynamics : evolution of the Hertz contact theory

Stability analysis of an axially accelerating string

Transverse Vibration of an Axially Accelerating String

The dynamic-response of a rotating shaft subject to a moving load

A nonlinear model is developed which describes the rotational response of automotive serpentine belt drive systems. Serpentine drives utilize a single {long) belt to drive all engine accessories from the crankshaft. An equilibrium analysis leads to a closed-form procedure for determining steady-state tensions in each belt span. The equations of motion are linearized about the equilibrium state and rotational mode vibration characteristics are determined from the eigenvalue problem governing free response. Numerical solutions of the nonlinear equations of motion indicate that, under certain engine operating conditions, the dynamic tension fluctuations may be sufficient to cause the belt to slip on particular accessory pulleys. Experimental measurements of dynamic response are in good agreement with theoretical results and confirm theoretical predictions of system vibration, tension fluctuations, and slip. 1 Introduction The trend in automotive accessory drives has been to replace multiple V-belt drives with a single flat belt drive to power all the accessories. Such systems are termed "serpentine" belt drives and include a spring loaded tensioner, as well as multiple accessory pulleys (see Fig. 1). These systems can exhibit com­plex dynamic behavior, including rotational vibrations of the pulleys with the belt spans serving as coupling springs, and transverse belt vibrations in the various spans. The transverse vibrations of translating belts [1, 2] belongs to the broad cat­egory of systems referred to as axially moving materials. Other examples of axially moving materials include chain drives [3, 4], band saws [5, 6, 7], V-belts [8], moving threadlines [9], translating cables [10], etc. The recent literature on axially moving materials is reviewed in [11]. Several recent studies have focused on serpentine belt drive systems (see Fig. 1). Gasper etal. [12] and Hawker [13] consider longitudinal deflection of the belt and rotational vibrations of the pulleys in the analysis of free and forced response. These studies, however, do not consider the effect of the tensioner on either the equilibrium state (steady-state tensions) or the dynamic response. The influence of the tensioner on longi­tudinal belt deflection is examined by Barker et al. [14] who focus on transient response due to drive pulley acceleration. Beikmann et al. [15] develop a prototypical model (two pulleys with a tensioner) to calculate the steady-state tensions and the tensioner position as functions of steady operating conditions. Ulsoy et al. [16] consider the coupling between the transverse

Rotational Response and Slip Prediction of Serpentine Belt Drive

A nonlinear model is developed which describes the rotational response of automotive serpentine belt drive systems. Serpentine drives utilize a single {long) belt to drive all engine accessories from the crankshaft. An equilibrium analysis leads to a closedform procedure for determining steady-state tensions in each belt span. The equations of motion are linearized about the equilibrium state and rotational mode vibration characteristics are determined from the eigenvalue problem governing free response. Numerical solutions of the nonlinear equations of motion indicate that, under certain engine operating conditions, the dynamic tension fluctuations may be sufficient to cause the belt to slip on particular accessory pulleys. Experimental measurements of dynamic response are in good agreement with theoretical results and confirm theoretical predictions of system vibration, tension fluctuations, and slip.

A. G. Ulsoy

Papers

Stability analysis of an axially accelerating string

Transverse Vibration of an Axially Accelerating String

The dynamic-response of a rotating shaft subject to a moving load

Rotational Response and Slip Prediction of Serpentine Belt Drive

Rotational response and slip prediction of serpentine belt drive systems