scholarly journals A Simplified Flexible Multibody Dynamics for a Main Landing Gear with Flexible Leaf Spring

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhi-Peng Xue ◽  
Ming Li ◽  
Yan-Hui Li ◽  
Hong-Guang Jia
Keyword(s):  
Linear Theory ◽  
Mass Matrix ◽  
Flexible Multibody Dynamics ◽  
Landing Gear ◽  
Leaf Spring ◽  
Dynamics Of Multibody Systems ◽  
Small Uav ◽  
Flexible Multibody ◽  
Flexible Part ◽  
Spring Type

The dynamics of multibody systems with deformable components has been a subject of interest in many different fields such as machine design and aerospace. Traditional rigid-flexible systems often take a lot of computer resources to get accurate results. Accuracy and efficiency of computation have been the focus of this research in satisfying the coupling of rigid body and flex body. The method is based on modal analysis and linear theory of elastodynamics: reduced modal datum was used to describe the elastic deformation which was a linear approximate of the flexible part. Then rigid-flexible multibody system was built and the highly nonlinearity of the mass matrix caused by the limited rotation of the deformation part was approximated using the linear theory of elastodynamics. The above methods were used to establish the drop system of the leaf spring type landing gear of a small UAV. Comparisons of the drop test and simulation were applied. Results show that the errors caused by the linear approximation are acceptable, and the simulation process is fast and stable.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

Energy-Momentum Conserving Time Integration of Modally Reduced Flexible Multibody Systems

2013 ◽  
Author(s):  
Alexander Humer ◽  
Johannes Gerstmayr
Keyword(s):  
Angular Momentum ◽  
Multibody Systems ◽  
Mass Matrix ◽  
Time Integration ◽  
Flexible Multibody Dynamics ◽  
Integration Scheme ◽  
Integration Schemes ◽  
Flexible Multibody ◽  
Floating Frame ◽  
Energy And Momentum

Many conventional time integration schemes frequently adopted in flexible multibody dynamics fail to retain the fundamental conservation laws of energy and momentum of the continuous time domain. Lack of conservation, however, in particular of angular momentum, may give rise to unexpected, unphysical results. To avoid such problems, a scheme for the consistent integration of modally reduced multibody systems subjected to holonomic constraints is developed in the present paper. As opposed to the conventional approach, in which the floating frame of reference formulation is combined with component mode synthesis for approximating the flexible deformation, an alternative, recently proposed formulation based on absolute coordinates is adopted in the analysis. Owing to the linear relationship between the generalized coordinates and the absolute displacement, the inertia terms in the equations of motion attain a very simple structure. The mass matrix remains independent of the current state of deformation and the velocity dependent term known from the floating frame approach vanishes due to the absence of relative coordinates. These advantageous properties facilitate the construction of an energy and momentum consistent integration scheme. By the mid-point rule, algorithmic conservation of both linear and angular momentum is achieved. In order to consistently integrate the total energy of the system, the discrete derivative needs to be adopted when evaluating the strain energy gradient and the derivative of the algebraic constraint equations.

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