Nonlinear Formulation for Flexible Multibody System Applied With Thermal Load

2007 ◽  
Author(s):  
Jinyang Liu ◽  
Hao Lu
Keyword(s):  
Heat Conduction ◽  
Thermal Load ◽  
Multibody System ◽  
Thermal Strain ◽  
Sudden Change ◽  
Dynamic Equations ◽  
Flexible Beam ◽  
Flexible Multibody System ◽  
Beam System ◽  
Flexible Multibody

In this paper, temperature variation and dynamic performance of flexible multibody system applied with thermal load are investigated. Considering thermal strain and geometric nonlinear terms, heat conduction equations and dynamic equations for a flexible beam are derived, and then the system heat conduction equations and dynamic equations of flexible multibody system are assembled, and temperature, kinematic and driving constraint equations are used to obtain Lagrange’s equations of the first kind with Lagrange multipliers. Simulation of a rotating hub-beam system with simply-supported boundary condition is carried out to show the softening effect of the beam with temperature increase. Finally, thermal bending of flexible beam system applied with heat flux at upper surface is investigated. Coupling between rotational motion and transverse deformation as well as sudden change of constraint forces and axial stresses are shown to reveal the characteristics of thermal shock.

Dynamic Analysis of Space Structure Deployment with Transient Thermal Load

2012 ◽  
Vol 479-481 ◽  
pp. 803-807 ◽  
Author(s):  
Jiang Wu ◽  
Zhi Hua Zhao ◽  
Ge Xue Ren
Keyword(s):  
Thermal Load ◽  
Multibody System ◽  
Driving Forces ◽  
Beam Element ◽  
Space Structure ◽  
Dynamic Equations ◽  
Flexible Multibody System ◽  
New Approach ◽  
Flexible Multibody ◽  
Transient Thermal

Thermal load is non-ignorable in the design and analysis of high precision and reliable space deployable structures. A new approach based on flexible multibody system is presented in order to investigate the thermoelastic effect on the deployment of space structure. Dynamic equations of an Euler Bernoulli beam element with transient thermal load are derived in Absolute Nodal Coordinate Formulation. The temperature distribution in the beam section is assumed as linear, which is reasonable for slender beams. The resulting generalized thermoelastic forces can be decomposed into thermal axial force and thermal bending moments, which can cause tension/compression and bending of the beam respectively. The dynamic equations of the beam element are then assembled into a flexible multibody system. Deployment analysis of a space mechanism with transient thermal load is studied with the new approach. Simulation result shows that thermoelasticity could cause static deformation of the final configuration as well as affect the external driving forces.

Impact Dynamics of Flexible Multibody System Based on Continuous Contact Force Method

2015 ◽  
Vol 744-746 ◽  
pp. 1628-1634
Author(s):  
Yue Chen Duan ◽  
Xia Li ◽  
Wei Wei Zhang ◽  
Guo Ning Liu ◽  
Ting Ting Wang
Keyword(s):  
Contact Force ◽  
Multibody System ◽  
Dynamic Equations ◽  
Impact Dynamics ◽  
Flexible Multibody System ◽  
Flexible Coupling ◽  
Continuous Contact ◽  
Force Method ◽  
Flexible Multibody ◽  
The Impact

The impact dynamics of spatial multi-link flexible multibody system is studied based on the continuous contact force method (CCFM). According to the rigid-flexible coupling dynamic theory of flexible multibody system, the rigid-flexible coupling continuous dynamic equations of the system are established by using the recursive Lagrange method. The impact dynamic equations of the system are stylized derived on the use of CCFM basing on the nonlinear spring-damper model. The contact separation criterion is given to achieve the conversion and calculation of the dynamic model for the system at different stages. An impact dynamic simulation example for a two-link planar flexible multibody system is given, as well as the global dynamic response. The results show that the impact dynamic solving method based on CCFM can be used for the global impact dynamics of multi-link flexible multibody systems. The dynamic behavior of the system changes dramatically during the impact process. The large overall motion, the small deformation motion and the impact effect are coupled.

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.

Model reduction of a flexible multibody system with clearance

2015 ◽  
Vol 85 ◽  
pp. 106-115 ◽  
Author(s):  
Dongyang Sun ◽  
Guoping Chen ◽  
Yan Shi ◽  
Tiecheng Wang ◽  
Rujie Sun
Keyword(s):  
Model Reduction ◽  
Multibody System ◽  
Flexible Multibody System ◽  
Flexible Multibody

Multiple Dynamic Response Patterns of Flexible Multibody Systems With Random Uncertain Parameters

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Zhe Wang ◽  
Qiang Tian ◽  
Haiyan Hu
Keyword(s):  
Dynamic Response ◽  
Multibody System ◽  
Uncertain Parameters ◽  
Response Patterns ◽  
Algebraic Equations ◽  
Flexible Multibody System ◽  
Random Parameters ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Flexible Multibody

The mechanisms with uncertain parameters may exhibit multiple dynamic response patterns. As a single surrogate model can hardly describe all the dynamic response patterns of mechanism dynamics, a new computation methodology is proposed to study multiple dynamic response patterns of a flexible multibody system with uncertain random parameters. The flexible multibody system of concern is modeled by using a unified mesh of the absolute nodal coordinate formulation (ANCF). The polynomial chaos (PC) expansion with collocation methods is used to generate the surrogate model for the flexible multibody system with random parameters. Several subsurrogate models are used to describe multiple dynamic response patterns of the system dynamics. By the motivation of the data mining, the Dirichlet process mixture model (DPMM) is used to determine the dynamic response patterns and project the collocation points into different patterns. The uncertain differential algebraic equations (DAEs) for the flexible multibody system are directly transformed into the uncertain nonlinear algebraic equations by using the generalized-alpha algorithm. Then, the PC expansion is further used to transform the uncertain nonlinear algebraic equations into several sets of nonlinear algebraic equations with deterministic collocation points. Finally, two numerical examples are presented to validate the proposed methodology. The first confirms the effectiveness of the proposed methodology, and the second one shows the effectiveness of the proposed computation methodology in multiple dynamic response patterns study of a complicated spatial flexible multibody system with uncertain random parameters.

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