Nonlinear Truck Ride Analysis

1974 ◽  
Vol 96 (2) ◽  
pp. 597-602 ◽  
Author(s):  
G. R. Potts ◽  
H. S. Walker
Keyword(s):  
Numerical Integration ◽  
Nonlinear Equations ◽  
Digital Computer ◽  
Dry Friction ◽  
Shock Absorber ◽  
Equations Of Motion ◽  
Deflection Curve ◽  
Force Velocity ◽  
Nonlinear Equations Of Motion ◽  
Dry Friction Damping

The nonlinear vibratory motions of a three-axle semitrailer truck were investigated via the use of a digital computer. The nonlinear equations of motion are presented and a method of numerical integration is discussed. The analysis allows any shape of suspension force-deflection curve (including wheel hop, suspension stops, and dry friction damping) and a similar liberality of shock absorber force-velocity characteristics. An experimental vibration study, performed on a model truck, is described and the results compare favorably with the calculated results of the numerical integration.

Low-Speed Controllability of Ships in Wind

1968 ◽  
Vol 12 (03) ◽  
pp. 181-200
Author(s):  
H. Eda
Keyword(s):  
Mathematical Model ◽  
Nonlinear Equations ◽  
Digital Computer ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Equilibrium Conditions ◽  
Region Of Stability ◽  
Nonlinear Equations Of Motion ◽  
Hydrodynamic Data ◽  
Relative Wind

Aerodynamic and hydrodynamic data for the Manner-class vessel, gathered in earlier experiments, were used to formulate a mathematical model representing the dynamic behavior of ships in wind. A digital computer was used to solve the eigenvalues of the system. Perturbation equations were linearized, with respect to equilibrium conditions, from nonlinear equations of motion. In addition, ship trajectory in certain wind conditions was examined by means of numerical solutions of the nonlinear equations of motion. Results indicate that the ship in bow wind tends, even without an autopilot system, to maintain its original course-with perturbation in yaw inducing yaw oscillations, the convergence of which depends upon the magnitude of relative wind velocity. It is shown that beam wind creates greater difficulties, although the use of an adequate autopilot increases the region of stability in wind of certain velocities (except in some conditions of relatively strong beam wind). An increase in rudder size is shown to improve controllability in wind significantly. Computations with and without the assumption of constant longitudinal speed indicate that the effect of surge motion on yaw and sway responses in wind is important, especially in beam wind.

Blade Vibration Suppression Using Friction Elements in Shrouding

2011 ◽  
Author(s):  
Michal Hajzˇman ◽  
Miroslav Byrtus ◽  
Vladimi´r Zeman
Keyword(s):  
Numerical Integration ◽  
Nonlinear Equations ◽  
Harmonic Balance ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Blade Vibration ◽  
Friction Element ◽  
Nonlinear Equations Of Motion

The problem of two blades with a friction element is studied in order to analyze the effects of the friction on the undesirable vibration suppression. The simplified contact model between friction planes of the blade shrouding and the friction element is derived to be a fast computational tool comparing with a time-consuming finite element solution. The harmonic balance method is suitable for the linearization of originally nonlinear equations of motion under certain assumptions given on the excitation of the system and on its dynamic response. On the other hand the nonlinear equations of motion can be solved directly by their numerical integration, which is more time-consuming but it is not limited by given assumptions. The comparison of results of the harmonic balance method and of the numerical integration of motion equations is given in the paper.

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