Formulation of a Basic Building Block Model for Interaction of High Speed Vehicles on Flexible Structures

1989 ◽  
Vol 56 (2) ◽  
pp. 451-458 ◽  
Author(s):  
L. Vu-Quoc ◽  
M. Olsson
Keyword(s):  
Nonlinear Equations ◽  
Building Block ◽  
High Speed ◽  
Traditional Approach ◽  
Equations Of Motion ◽  
A Priori ◽  
Flexible Structures ◽  
Structural Deformation ◽  
Block Model ◽  
Nonlinear Equations Of Motion

In traditional analyses of vehicle/structure interaction, especially when there are constraints between vehicle masses and the structure, vehicle nominal motion is prescribed a priori, and therefore unaffected by the structure flexibility. In this paper, a concept of nominal motion is defined, and a methodology is proposed in which the above restriction is removed, allowing the vehicle nominal motion to become unknown, and encompassing the traditional approach as a particular case. General nonlinear equations of motion of a building block model, applicable to both wheel-on-rail and magnetically levitated vehicles, are derived. These equations are simplified to a set of mildly nonlinear equations upon introducing additional assumptions — essentially on small structural deformation. An example is given to illustrate the present formulation.

High-Speed Vehicle Models Based on a New Concept of Vehicle/Structure Interaction Component: Part I—Formulation

1993 ◽  
Vol 115 (1) ◽  
pp. 140-147 ◽  
Author(s):  
L. Vu-Quoc ◽  
M. Olsson
Keyword(s):  
Nonlinear Equations ◽  
Building Block ◽  
High Speed ◽  
Equations Of Motion ◽  
Interaction Model ◽  
Component Part ◽  
Structure Interaction ◽  
Vehicle Structure ◽  
Interaction Component ◽  
High Speed Vehicle

High-speed vehicle/structure models constructed based on a new formulation of dynamic interaction between high-speed vehicles and flexible guideways are presented. A basic vehicle/structure interaction model forms a basic building block of complex vehicle/structure models in which lumped-parameter sub-components of the vehicle component (e.g., suspended masses with springs and dashpots) are assembled onto the basic vehicle/structure interaction component. A vertical and an inclined vehicle models are formulated. These vehicle models can serve as yet more advanced building-block models in the hierarchical construction of complex vehicle/structure models. The inclined vehicle model can be used to study the effects of braking of high-speed vehicles of flexible guideways. Fully nonlinear equations of motion of both models are given. Upon introducing approximations to the nonlinear kinematics, mildly nonlinear equations with an unusual mathematical structure are consistently derived. These equations are appropriate for use under realistic working conditions of the system, and are particularly amenable for numerical treatment using a recently proposed class of predictor/corrector algorithms.

Direct Linearization of Continuous and Hybrid Dynamical Systems

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Julie J. Parish ◽  
John E. Hurtado ◽  
Andrew J. Sinclair
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Equations ◽  
Equilibrium Configuration ◽  
Equations Of Motion ◽  
Hybrid Dynamical Systems ◽  
Linearized Equations ◽  
Direct Linearization ◽  
Taylor Series Expansions ◽  
Nonlinear Equations Of Motion ◽  
And Control

Nonlinear equations of motion are often linearized, especially for stability analysis and control design applications. Traditionally, the full nonlinear equations are formed and then linearized about the desired equilibrium configuration using methods such as Taylor series expansions. However, it has been shown that the quadratic form of the Lagrangian function can be used to directly linearize the equations of motion for discrete dynamical systems. This procedure is extended to directly generate linearized equations of motion for both continuous and hybrid dynamical systems. The results presented require only velocity-level kinematics to form the Lagrangian and find equilibrium configuration(s) for the system. A set of selected partial derivatives of the Lagrangian are then computed and used to directly construct the linearized equations of motion about the equilibrium configuration of interest, without first generating the entire nonlinear equations of motion. Given an equilibrium configuration of interest, the directly constructed linearized equations of motion allow one to bypass first forming the full nonlinear governing equations for the system. Examples are presented to illustrate the method for both continuous and hybrid systems.

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