The Skateboard Speed Wobble

2015 ◽  
Author(s):  
Marco Rosatello ◽  
Jean-Luc Dion ◽  
Franck Renaud ◽  
Luigi Garibaldi
Keyword(s):  
Vehicle Dynamics ◽  
Dynamic Instability ◽  
Equations Of Motion ◽  
Stability Study ◽  
Loss Of Control ◽  
Parametric Stability ◽  
Human Control ◽  
Multipliers Method ◽  
The Subject ◽  
Lagrange Formalism

The speed wobble is a phenomenon in nonlinear dynamics that can occur in many vehicles such as bicycles, motorbikes, skateboards and airplanes nose landing gear. The dynamic instability affects the steerable wheels of a vehicle and can lead to the loss of control. While for bikes, motorbikes and airplanes the dynamics and causes of the wobble are well known and the literature fully describes the subject, for the skateboard the literature is very poor and there is no paper which investigates this type of instability. In order to do that, the skateboard equations of motion were obtained through Lagrange formalism and Lagrange multipliers method was used to solve the non-holonomic constraints. A parametric stability study was carried out on the linearized equations of motion and the influence of different skateboard parameters was investigated. The main discovery is that the wobble doesn’t strictly depend on skateboard configuration, but the human control characteristics are predominant in the vehicle dynamics.

Analysis of Flow Induced Vibration Using the Vorticity Transport Equation

1993 ◽  
Vol 115 (3) ◽  
pp. 485-492 ◽  
Author(s):  
Jure Marn ◽  
Ivan Catton
Keyword(s):  
Parametric Analysis ◽  
Dynamic Instability ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Governing Equations ◽  
Flow Induced Vibration ◽  
The Subject ◽  
An Array Of Cylinders ◽  
Vorticity Transport ◽  
Square Array

Crossflow induced vibrations are the subject of this work. The analysis is two dimensional. The governing equations for fluid motion are solved using linearized perturbation theory and coupled with the equations of motion for cylinders to yield the threshold of dynamic instability for an array of cylinders. Parametric analysis is performed to determine the lowest instability threshold for a rotated square array and correlations are developed relating the dominant parameters. The results are compared with theoretical and experimental data for similar arrays and the discrepancies are discussed.

Control Reversal Effects on Swept-Back Wings

1949 ◽  
Vol 1 (1) ◽  
pp. 3-34
Author(s):  
Haydn Templeton
Keyword(s):  
Mathematical Analysis ◽  
Quantitative Estimation ◽  
Dynamic Condition ◽  
Loss Of Control ◽  
General Introduction ◽  
Mathematical Basis ◽  
Control Power ◽  
Physical Picture ◽  
The Subject ◽  
Definition Of

SummaryAileron reversal effects on swept-back wings in general and elevon reversal effects on tailless swept-back wings in particular are discussed on a non-mathematical basis, attention being confined to the orthodox flap type of control. The main purpose of the paper is to convey in the simplest terms possible a clear physical picture of the conditions producing loss of control power, emphasis being naturally laid upon the part played by structural wing distortion. Certain qualitative features relating to the two phenomena are also discussed. As a general introduction to the discussion on aileron reversal effects, the definition of “aileron power” in relation to the actual dynamic condition of rolling is described at some length. For elevon reversal effects on tailless aircraft the effect of wing flexibility on both “elevon power” and on trim in steady symmetric flight is considered. With the descriptive treatment adopted the analysis is of necessity broad and general but is designed to appeal to those not too familiar with the subject. The results of certain calculations on a hypothetical wing, which may be of interest, are included. A mathematical analysis for the quantitative estimation of both aileron and elevon reversal effects is given in the Appendix.

The Role of Modal Coupling on the Non-Linear Response of Cylindrical Shells Subjected to Dynamic Axial Loads

2000 ◽  
Author(s):  
Paulo B. Gonçalves ◽  
Zenón J. G. N. Del Prado
Keyword(s):  
Dynamic Instability ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Parametric Instability ◽  
Compressive Load ◽  
Basins Of Attraction ◽  
Dynamic Component ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Low Dimensional

Abstract This paper discusses the dynamic instability of circular cylindrical shells subjected to time-dependent axial edge loads of the form P(t) = P0+P1(t), where the dynamic component p1(t) is periodic in time and P0 is a uniform compressive load. In the present paper a low dimensional model, which retains the essential non-linear terms, is used to study the non-linear oscillations and instabilities of the shell. For this, Donnell’s shallow shell equations are used together with the Galerkin method to derive a set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. To study the non-linear behavior of the shell, several numerical strategies were used to obtain Poincaré maps, stable and unstable fixed points, bifurcation diagrams and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions: parametric instability and escape from the pre-buckling potential well. The numerical results obtained from this investigation clarify the conditions, which control whether or not instability may occur. This may help in establishing proper design criteria for these shells under dynamic loads, a topic practically unexplored in literature.

Propagation of Nonlinearities in the Inertia Matrix of Tracked Vehicles

1994 ◽  
Author(s):  
J. H. Choi ◽  
A. A. Shabana ◽  
Roger A. Wehage
Keyword(s):  
Numerical Solution ◽  
Vehicle Dynamics ◽  
Equations Of Motion ◽  
Coefficient Matrix ◽  
Influence Coefficient ◽  
Dynamic Force ◽  
Tracked Vehicles ◽  
Revolute Joints ◽  
Inertia Matrix ◽  
Force Coupling

Abstract In this investigation, a procedure is presented for the numerical solution of tracked vehicle dynamics equations of motion. Tracked vehicles can be represented as two kinematically decoupled subsystems. The first is the chassis subsystem which consists of chassis, rollers, idlers, and sprockets. The second is the track subsystem which consists of track links interconnected by revolute joints. While there is dynamic force coupling between these two subsystems, there is no inertia coupling since the kinematic equations of the two subsystems are not coupled. The objective of the procedure developed in this investigation is to take advantage of the fact that in many applications, the shape of the track does not significantly change even though the track links undergo significant configurations changes. In such cases the nonlinearities propagate along the diagonals of a velocity influence coefficient matrix. This matrix is the only source of nonlinearities in the generalized inertia matrix. A permutation matrix is introduced to minimize the number of generalized inertia matrix LU factor evaluations for the track.

Real-Time Multibody Vehicle Dynamics Software for Virtual Handling Tests

2007 ◽  
Author(s):  
Sung-Soo Kim ◽  
Kyoungnam Ha ◽  
Dohyun Kim ◽  
Taeoh Tak ◽  
Seung-Eon Shin
Keyword(s):  
Virtual Reality ◽  
Real Time ◽  
Vehicle Dynamics ◽  
Equations Of Motion ◽  
Synthesis Method ◽  
Hardware In The Loop ◽  
Vehicle Modeling ◽  
Time Dynamics ◽  
Point Data ◽  
Suspension Model

Real-time multibody vehicle dynamics software has been developed for virtual handling tests. The software can be utilized for hardware in the loop simulations and consists of three modules such as a graphical vehicle modeling preprocessor, real time dynamics solver, and virtual reality graphic postprocessor for virtual handling tests. In the graphical vehicle modeling preprocessor, vehicle hard point data for a suspension model are automatically converted into multibody vehicle model. In the real time dynamics solver, efficient subsystem synthesis method is used to create multibody equations of motion a subsystem by a subsystem. In the virtual reality graphic postprocessor, virtual proving ground environment has been also developed by using OpenGL for virtual handling tests. This software is written C and can be converted to the S-function as a plant model in the RT-LAB real time environment for HILS application.

Vibration Control of Conical Shells Using Viscoelastic Materials

1992 ◽  
Vol 206 (3) ◽  
pp. 167-178 ◽  
Author(s):  
K N Khatri
Keyword(s):  
Equations Of Motion ◽  
Geometrical Parameters ◽  
Viscoelastic Materials ◽  
Complex Moduli ◽  
Conical Shells ◽  
Harmonic Vibrations ◽  
End Conditions ◽  
Layered Shells ◽  
The Subject ◽  
Viscoelastic Layers

The vibration and damping analysis of multi-layered conical shells incorporating layers of viscoelastic materials in addition to elastic ones, the former causing dissipation of vibratory energy, is the subject matter of this paper. The analysis given herein uses Hamilton's variational principle for deriving equations of motion of a general multi-layered conical shell. In view of the correspondence principle of linear viscoelasticity which is valid for harmonic vibrations, the solution is obtained by replacing the moduli of viscoelastic layers by complex moduli. An approximate solution for axisymmetric vibrations of multi-layered conical shells with two end conditions—simply supported edges and clamped edges—is obtained by utilizing the Galerkin procedure. The damping effectiveness in terms of the system loss factor for all families of modes of vibrations for three-, five- and seven-layered shells is evaluated and its variation with geometrical parameters is investigated.

Dynamic Stability of a Cantilever Shaft-Disk System

1992 ◽  
Vol 114 (3) ◽  
pp. 326-329 ◽  
Author(s):  
Lien-Wen Chen ◽  
Der-Ming Ku
Keyword(s):  
Dynamic Stability ◽  
Dynamic Instability ◽  
Equations Of Motion ◽  
Beam Theory ◽  
The Finite Element Method ◽  
Disk System ◽  
Stability Behavior ◽  
Gyroscopic Moment ◽  
The Mathematical Model ◽  
Cantilever Shaft

The dynamic stability behavior of a cantilever shaft-disk system subjected to axial periodic forces varying with time is studied by the finite element method. The equations of motion for such a system are formulated using deformation shape functions developed from Timoshenko beam theory. The effects of translational and rotatory inertia, gyroscopic moment, bending and shear deformation are included in the mathematical model. Numerical results show that the effect of the gyroscopic term is to shift the boundaries of the regions of dynamic instability outwardly and, therefore, the sizes of these regions are enlarged as the rotational speed increases.

scholarly journals Stabilizing skateboard speed-wobble with reflex delay

2016 ◽  
Vol 13 (121) ◽  
pp. 20160345 ◽  
Author(s):  
Balazs Varszegi ◽  
Denes Takacs ◽  
Gabor Stepan ◽  
S. John Hogan
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Linear Instability ◽  
Uniform Motion ◽  
Rectilinear Motion ◽  
Neutral Delay ◽  
Human Control ◽  
Control Gain ◽  
Delay Differential ◽  
And Control

A simple mechanical model of the skateboard–skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard–skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity.

scholarly journals A Brief Review of Elasticity and Viscoelasticity for Solids

2011 ◽  
Vol 3 (1) ◽  
pp. 1-51 ◽  
Author(s):  
Harvey Thomas Banks ◽  
Shuhua Hu ◽  
Zackary R. Kenz
Keyword(s):  
Food Industry ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Specific Form ◽  
Stress And Strain ◽  
Viscoelastic Materials ◽  
Mine Detection ◽  
Land Mine ◽  
Land Mine Detection ◽  
The Subject

AbstractThere are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging. Here we provide an overview of the subject for both elastic and viscoelastic materials in order to understand the behavior of these materials. We begin with a brief introduction of some basic terminology and relationships in continuum mechanics, and a review of equations of motion in a continuum in both Lagrangian and Eulerian forms. To complete the set of equations, we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain proposed in the literature for both elastic and viscoelastic materials. In addition, we discuss some applications for these constitutive equations. Finally, we give a computational example describing the motion of soil experiencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion.

On establishing equations of motion of mechanical vibration systems placed on moving bases

2017 ◽  
Vol 45 (3) ◽  
pp. 209-227
Author(s):  
M Gürgöze ◽  
F Terzioğlu
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Mechanical Vibration ◽  
Main Idea ◽  
Vertical Axis ◽  
Constant Angular Velocity ◽  
Vibration System ◽  
Reaction Forces ◽  
The Subject ◽  
Vibrating Systems

The first author has been teaching the postgraduate course, “The Dynamics of Mechanical Systems” in The ITU Faculty of Mechanical Engineering for nearly 20 years. He has observed that students frequently have problems in obtaining the equations of motion of the vibrating systems which were placed on moving bases. Starting from this observation, he has found that the homework stated below, which was given to the students occasionally, was very helpful in learning the subject. The main idea of the homework is the derivation of the equations of motion, with the help of formulating the Lagrange’s equations with respect to a moving set of axis for a vibration system with two degrees of freedom which consists of a horizontal table rotating with a constant angular velocity around a vertical axis. The students were also asked to solve the same problem with a different method of their choice and to determine the reaction forces as well. We want to share this problem with the reader, which we have assessed as very instructive and appropriate from the viewpoint of applicability of different methods.

Sign in / Sign up

Export Citation Format

Share Document