Symbolic formulation of dynamic equations for interconnected flexible bodies: The GEMMES software

2005 ◽  
pp. 17-27
Author(s):  
C. Garnier
Keyword(s):  
Dynamic Equations ◽  
Flexible Bodies

scholarly journals Earthquake dynamic response of large flexible multibody systems

2013 ◽  
Vol 4 (1) ◽  
pp. 131-137 ◽  
Author(s):  
E. V. Zahariev
Keyword(s):  
Flexible Structures ◽  
High Amplitude ◽  
Differential Algebraic Equations ◽  
Dynamic Equations ◽  
Motion Simulation ◽  
Algebraic Equations ◽  
Power Generator ◽  
Flexible Bodies ◽  
Wind Power Generator ◽  
Generalized Newton

Abstract. In the paper dynamics of large flexible structures imposed on earthquakes and high amplitude vibrations is regarded. Precise dynamic equations of flexible systems are the basis for reliable motion simulation and analysis of loading of the design scheme elements. Generalized Newton–Euler dynamic equations for rigid and flexible bodies are applied. The basement compulsory motion realized because of earthquake or wave propagation is presented in the dynamic equations as reonomic constraints. The dynamic equations, algebraic equations and reonomic constraints compile a system of differential algebraic equations which are transformed to a system of ordinary differential equations with respect to the generalized coordinates and the reactions due to the reonomic constraints. Examples of large flexible structures and wind power generator dynamic analysis are presented.

An Efficient Dynamic Formulation for Solving Rigid and Flexible Multibody Systems Based on Semirecursive Method and Implicit Integration

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Francisco Javier Funes ◽  
Javier García de Jalón
Keyword(s):  
Multibody Systems ◽  
Dynamic Equations ◽  
Integration Process ◽  
Implicit Integration ◽  
Flexible Bodies ◽  
Velocity Transformation ◽  
Dynamic Formulation ◽  
Variable Stepsizes ◽  
Tangent Manifold ◽  
Stability Issues

This paper presents a method for solving the dynamic equations of multibody systems containing both rigid and flexible bodies. The proposed method uses independent coordinates and projects the dynamic equations on the constraint tangent manifold by means of a velocity transformation matrix. It can be used with a wide variety of integration formulae, considering both fixed and variable stepsizes. Topological semirecursive methods are used to take advantage of the relatively small number of parameters needed. An in depth implementation analysis is performed in order to evaluate the terms involved in the integration process. Numerical and stability issues are also discussed.

Recognition of Neurons Impulses with the Use of Nonlinear Dynamic Equations

2001 ◽  
Vol 33 (5-8) ◽  
pp. 10
Author(s):  
Tatyana I. Aksenova ◽  
Igor V. Tetko ◽  
Olga K. Chibirova ◽  
Alexandro Villa
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Equations ◽  
Nonlinear Dynamic Equations

scholarly journals Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales

2020 ◽  
Vol 18 (1) ◽  
pp. 353-377 ◽  
Author(s):  
Zhien Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Quaternion Algebra ◽  
Matrix Exponential ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Quaternion Matrix ◽  
Exponential Functions ◽  
Cauchy Matrix ◽  
Adjoint Matrix ◽  
Sufficient And Necessary Condition

Abstract In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex adjoint matrix of a quaternion matrix. Moreover, the Cauchy matrices and Liouville formulas for the quaternion homogeneous and nonhomogeneous impulsive dynamic equations are given and proved. Based on it, the existence, uniqueness, and expressions of their solutions are also obtained, including their scalar and matrix forms. Since the quaternion algebra is noncommutative, many concepts and properties of the non-quaternion impulsive dynamic equations are ineffective, we provide several examples and counterexamples on various time scales to illustrate the effectiveness of our results.

scholarly journals Sufficient conditions for hyperbolicity and consistency of the dynamic equations for fluid-saturated solids

2021 ◽  
Author(s):  
Vladimir A. Osinov
Keyword(s):  
Boundary Value Problem ◽  
Wave Speed ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Systems Of Equations ◽  
Acoustic Tensor ◽  
Ill Posed

AbstractPrevious studies showed that the dynamic equations for a porous fluid-saturated solid may lose hyperbolicity and thus render the boundary-value problem ill-posed while the equations for the same but dry solid remain hyperbolic. This paper presents sufficient conditions for hyperbolicity in both dry and saturated states. Fluid-saturated solids are described by two different systems of equations depending on whether the permeability is zero or nonzero (locally undrained and drained conditions, respectively). The paper also introduces a notion of wave speed consistency between the two systems as a necessary condition which must be satisfied in order for the solution in the locally drained case to tend to the undrained solution as the permeability tends to zero. It is shown that the symmetry and positive definiteness of the acoustic tensor of the skeleton guarantee both hyperbolicity and the wave speed consistency of the equations.

scholarly journals Analysis on Force Transmission Characteristics of Two-Legged Shield Support under Impact Loading

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Qing-liang Zeng ◽  
Zhao-sheng Meng ◽  
Li-rong Wan ◽  
Cheng-long Wang
Keyword(s):  
Structural Design ◽  
Load Transfer ◽  
Impact Load ◽  
Force Transmission ◽  
Full Account ◽  
Flexible Bodies ◽  
Powered Support ◽  
Structural Design Optimization ◽  
Hinge Points ◽  
The Impact

To study the load transfer characteristics of a two-legged shield powered support, a numerical simulation model of the support was established using the multibody dynamics software ADAMS. The model took full account of the hydraulic-elastic deformation characteristics of the support, as a series spring-damper system was used to replace the leg and the equilibrium jack. The canopy, goaf shield, lemniscate bars, and equilibrium jack are equivalent to flexible bodies. The setting force of the leg was provided by the preload of the equivalent spring, the static roof load was simulated using a slope signal, and the impact load was simulated using a step signal. Using the model, the impact and excitation effects of each hinge joint of the support were analyzed under different impact load conditions across the canopy. The results show that the location of the impact load affects the force transmissions of all hinge points of the support. Both the impact effect and the excitation effect are at a minimum when the impact force is located near the leg action line. These results are useful for the adaptive control and structural design optimization of the support.

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