Lateral Dynamics and Stability of Two Full Vehicles in Tandem

1998 ◽  
Vol 120 (1) ◽  
pp. 50-56 ◽  
Author(s):  
N. A. El-Esnawy ◽  
J. F. Wilson
Keyword(s):  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Mean Square ◽  
Critical System ◽  
Lateral Dynamics ◽  
System Parameters ◽  
Vehicle System ◽  
Articulated Vehicle ◽  
The Stability ◽  
Oscillatory Instabilities

The lateral dynamics and stability of two full vehicles in tandem are investigated. The nonlinear differential equations of motion of this four-axle articulated vehicle system are presented in matrix form and then linearized. The critical forward velocity of the steady state for oversteering conditions is derived in a closed form, and the criteria for understeer, neutral steer, or oversteer are given. Uncertainty of the critical forward velocity and its sensitivity to errors in the system parameters are evaluated using the root mean square method. Conditions for nonoscillatory and oscillatory instabilities of the linearized vehicle system are given. Effects of the critical system parameters (mainly the mass distribution) on the stability are investigated.

Stability of the High-Speed Journal Bearing Under Steady Load: 1—The Incompressible Film

1962 ◽  
Vol 84 (3) ◽  
pp. 351-357 ◽  
Author(s):  
M. M. Reddi ◽  
P. R. Trumpler
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Orbital Motion ◽  
Hydrodynamic Force ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Static Equilibrium ◽  
The Stability ◽  
External Loads ◽  
Steady Load

The phenomenon of oil-film whirl in bearings subjected to steady external loads is analyzed. The journal, assumed to be a particle mass, is subjected to the action of two forces; namely, the external load acting on the bearing and the hydrodynamic force developed in the fluid film. The resulting equations of motion for a full-film bearing and a 180-deg partial-film bearing are developed as pairs of second-order nonlinear differential equations. In evaluating the hydrodynamic force, the contribution of the shear stress on the journal surface is found to be negligible for the full-film bearing, whereas for the partial-film bearing it is found to be significant at small attitude values. The equations of motion are linearized and the coefficients of the resulting characteristic equations are studied for the stability of the static-equilibrium positions. The full-film bearing is found to have no stable static-equilibrium position, whereas the 180-deg partial-film bearing is found to have stable static-equilibrium positions under certain parametric conditions. The equations of motion for the full-film bearing are integrated numerically on a digital computer. The results show that the journal center, depending on the parametric conditions, acquired either an orbital motion or a dynamical path of increasing attitude terminating in bearing failure.

scholarly journals Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers

Machines ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 58 ◽  
Author(s):  
Bissembayev ◽  
Jomartov ◽  
Tuleshov ◽  
Dikambay
Keyword(s):  
Solid Body ◽  
Quantitative Methods ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Horizontal Displacement ◽  
Oscillatory Process ◽  
Highly Nonlinear ◽  
Cumulative Curve ◽  
The Stability ◽  
Oscillating Motion

This article considers the oscillation of a solid body on kinematic foundations, the main elements of which are rolling bearers bounded by high-order surfaces of rotation at horizontal displacement of the foundation. Equations of motion of the vibro-protected body have been obtained. It is ascertained that the obtained equations of motion are highly nonlinear differential equations. Stationary and transitional modes of the oscillatory process of the system have been investigated. It is determined that several stationary regimes of the oscillatory process exist. Equations of motion have been investigated also by quantitative methods. In this paper the cumulative curves in the phase plane are plotted, a qualitative analysis for singular points and a study of them for stability are performed. In the Hayashi plane a cumulative curve of a body protected against vibration forms a closed path which does not tend to the stability of a singular point. This means that the vibration amplitude of a body protected against vibration does not remain constant in a steady state, but changes periodically.

scholarly journals Mixed forced, parametric, and self-oscillations with nonideal energy source and lagging forces

2021 ◽  
Vol 29 (5) ◽  
pp. 739-750
Author(s):  
Alishir Alifov ◽  
Keyword(s):  
Energy Source ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Point Of View ◽  
Ease Of Use ◽  
Direct Linearization ◽  
Plane Change ◽  
The Stability ◽  
The Right

The purpose of this study is to determine the effect of retarded forces in elasticity and damping on the dynamics of mixed forced, parametric, and self-oscillations in a system with limited excitation. A mechanical frictional self-oscillating system driven by a limited-power engine was used as a model. Methods. In this work, to solve the nonlinear differential equations of motion of the system under consideration, the method of direct linearization is used, which differs from the known methods of nonlinear mechanics in ease of use and very low labor and time costs. This is especially important from the point of view of calculations when designing real devices. Results. The characteristic of the friction force that causes self-oscillations, represented by a general polynomial function, is linearized using the method of direct linearization of nonlinearities. Using the same method, solutions of the differential equations of motion of the system are constructed, equations are obtained for determining the nonstationary values of the amplitude, phase of oscillations and the speed of the energy source. Stationary motions are considered, as well as their stability by means of the Routh–Hurwitz criteria. Performed calculations obtained information about the effect of delays on the dynamics of the system. Conclusion. Calculations have shown that delays shift the amplitude curves to the right and left, up and down on the amplitude–frequency plane, change their shape, and affect the stability of motion.

On the Stability of PD Control for a Two-Link Rigid-Flexible Manipulator

1994 ◽  
Vol 116 (2) ◽  
pp. 208-215 ◽  
Author(s):  
Ahmet S. Yigit
Keyword(s):  
Controller Design ◽  
Equations Of Motion ◽  
Flexible Manipulator ◽  
Simulation Studies ◽  
Parameter Uncertainties ◽  
Pd Control ◽  
System Parameters ◽  
Flexible System ◽  
The Stability

Controller design for a rigid-flexible two-link manipulator is considered. Robustness of independent joint PD control is investigated. It has been shown that the stability of independent joint PD control does not depend explicitly on the system parameters. No discretization or linearization of the equations of motion is required to assure the stability. Simulation studies also show that independent joint PD control gives reasonably good results for the flexible system, and is robust to parameter uncertainties.

On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation

2018 ◽  
Vol 25 (5) ◽  
pp. 1058-1079 ◽  
Author(s):  
N. K. A. Attari ◽  
F. R. Rofooei ◽  
Z. Waezi
Keyword(s):  
Differential Equations ◽  
Perturbation Analysis ◽  
Multiple Scales ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Structural Response ◽  
Single Mode ◽  
Excitation Amplitude ◽  
Combined System ◽  
The Stability

The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode response with respect to the excitation amplitude. The saturation phenomenon is observed in the decoupled modes of the system; however, the structural mode and the first anti-symmetric mode of liquid are a combination of the saturated mode and another mode whose scale factor is crucial for the structural response. The results of perturbation analysis are in good agreement with results obtained from numerical methods.

On the Stability of Porous Journal Bearings

1974 ◽  
Vol 96 (2) ◽  
pp. 585-590 ◽  
Author(s):  
T. F. Conry ◽  
C. Cusano
Keyword(s):  
Differential Equations ◽  
Design Variable ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Motion Stability ◽  
Region Of Stability ◽  
Regions Of Stability ◽  
Static Eccentricity ◽  
The Stability

This investigation deals with the stability characteristics of lubricated porous journal bearings. Using the short-bearing approximation and a fully cavitated film, the regions of stability are determined by simulation of the nonlinear differential equations of motion. Stability curves are presented for values of the design variable Φ from 0.0001 to 0.02. As Φ increases, the area of the region of stability decreases. For values of Φ greater than 0.001, the value of the dimensionless speed tends to decrease with increasing static eccentricity ratios at the threshold of stability.

Dynamic Characteristics for a Planar Two-Link Flexible Multibody System Including the Gravity Effects

1992 ◽  
Author(s):  
G. J. Wiens ◽  
H. Tsai
Keyword(s):  
Eigenvalue Problems ◽  
Multibody System ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Field Method ◽  
Space Applications ◽  
Flexible Multibody ◽  
Gravity Effects ◽  
The Stability

Abstract This paper addresses modeling issues that arise in the formulation of the equations of motion for the flexible multibody mechanical systems intended for space applications and designed according to ground test results. A planar multibody system consisting of two flexible links interconnected by two revolute joints and a payload at its free end is proposed for the investigations. In addition to the gravity and transverse deflections (most common two conditions adopted for the research in this field), the foreshortening effects, the axial deflections and the work done by the system’s own weight on the elastic deflections are also taken into consideration. Since the slender link assumption is made, the Euler-Bernoulli Beam theory is considered sufficient and satisfactory for describing the behavior of the deformed link components. The Lagrangian formulation in conjunction with assumed displacement field method is then implemented to develop the equations of motion for the system. After achieving the analytical model for the system, a linearization about various system configurations transforms the fully coupled nonlinear differential equations into standard eigenvalue problems. In doing so, the roles played by gravity, foreshortening and system’s own weight (‘weight-load’) on the dynamic behavior of the system undergoing ground testing are examined. For analysis, the fundamental frequency of the system is chosen as a measurement index. Finally, parametric studies focusing on the mass properties of payload, lower and upper links, and actuators are undertaken to address the stability problems. Results indicate that the ‘weight-load’ exhibits interesting effects on the ‘foreshortening and stability’, hence, merits further investigation.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

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