scholarly journals Integration of Nonlinear Models of Flexible Body Deformation in Multibody System Dynamics

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Martin Schulze ◽  
Stefan Dietz ◽  
Bernhard Burgermeister ◽  
Andrey Tuganov ◽  
Holger Lang ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Multibody System ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
Flexible Structures ◽  
General Purpose ◽  
Cosserat Rod ◽  
Rod Model ◽  
Flexible Deformation ◽  
Run Up

Current challenges in industrial multibody system simulation are often beyond the classical range of application of existing industrial simulation tools. The present paper describes an extension of a recursive order-n multibody system (MBS) formulation to nonlinear models of flexible deformation that are of particular interest in the dynamical simulation of wind turbines. The floating frame of reference representation of flexible bodies is generalized to nonlinear structural models by a straightforward transformation of the equations of motion (EoM). The approach is discussed in detail for the integration of a recently developed discrete Cosserat rod model representing beamlike flexible structures into a general purpose MBS software package. For an efficient static and dynamic simulation, the solvers of the MBS software are adapted to the resulting class of MBS models that are characterized by a large number of degrees of freedom, stiffness, and high frequency components. As a practical example, the run-up of a simplified three-bladed wind turbine is studied where the dynamic deformations of the three blades are calculated by the Cosserat rod model.

Periodic Steady State Response and Fatigue Analysis of a Nonlinear City Bus Model

2009 ◽  
Author(s):  
George Valsamos ◽  
Christos Theodosiou ◽  
Sotirios Natsiavas
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
High Stress ◽  
Direct Determination ◽  
Accurate Information ◽  
Steady State Response ◽  
State Response ◽  
Periodic Steady State

Dynamic response related to fatigue prediction of an urban bus is investigated. First, a quite complete model subjected to road excitation is employed in order to extract sufficiently reliable and accurate information in a fast way. The bus model is set up by applying the finite element method, resulting to an excessive number of degrees of freedom. In addition, the bus suspension units involve nonlinear characterstics. A step towards alleviating this difficulty is the application of an appropriate coordinate transformation, causing a drastic reduction in the dimension of the final set of the equations of motion. This allows the application of a systematic numerical methodology leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. Next, typical results were obtained for excitation resulting from selected urban road profiles. These profiles have either a known form or known statistical properties, expressed by an appropriate spatial power spectral density function. In all cases examined, the emphasis was put on investigating ride response. The main attention was focused on identifying areas of the bus suspension and frame subsystems where high stress levels are developed. This information is based on the idea of a nonlinear transfer function and provides the basis for applying suitable criteria in order to perform analyses leading to prediction of fatigue failure.

Constrained Multibody Dynamics With Python: From Symbolic Equation Generation to Publication

2013 ◽  
Author(s):  
Gilbert Gede ◽  
Dale L. Peterson ◽  
Angadh S. Nanjangud ◽  
Jason K. Moore ◽  
Mont Hubbard
Keyword(s):  
Open Source ◽  
Undergraduate Students ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Academic Research ◽  
General Purpose ◽  
Engineering Software ◽  
Symbolic Equations Of Motion ◽  
High Level

Symbolic equations of motion (EOMs) for multibody systems are desirable for simulation, stability analyses, control system design, and parameter studies. Despite this, the majority of engineering software designed to analyze multibody systems are numeric in nature (or present a purely numeric user interface). To our knowledge, none of the existing software packages are 1) fully symbolic, 2) open source, and 3) implemented in a popular, general, purpose high level programming language. In response, we extended SymPy (an existing computer algebra system implemented in Python) with functionality for derivation of symbolic EOMs for constrained multibody systems with many degrees of freedom. We present the design and implementation of the software and cover the basic usage and workflow for solving and analyzing problems. The intended audience is the academic research community, graduate and advanced undergraduate students, and those in industry analyzing multibody systems. We demonstrate the software by deriving the EOMs of a N-link pendulum, show its capabilities for LATEX output, and how it integrates with other Python scientific libraries — allowing for numerical simulation, publication quality plotting, animation, and online notebooks designed for sharing results. This software fills a unique role in dynamics and is attractive to academics and industry because of its BSD open source license which permits open source or commercial use of the code.

scholarly journals MICE-PES: An Algorithm for Accurate Conformational Analysis and its Implementation to Natural Products

2021 ◽  
Author(s):  
◽  
Muhammad Ali Hashmi
Keyword(s):  
Conformational Analysis ◽  
Degrees Of Freedom ◽  
Force Fields ◽  
Flexible Structures ◽  
Chemical Properties ◽  
General Purpose ◽  
Field Methods ◽  
Relative Configuration ◽  
Incremental Construction

<p>Secondary metabolites from natural sources have revolutionized the modern drug industry by acting as lead compounds. Many commercial drugs have evolved originally from natural molecules before being synthesized in the laboratory for commercialization. Because of the importance of natural molecules, it is crucial to determine their structural properties carefully as it is essential for their synthesis and studying their pharmacological behaviour. Many natural molecules have flexible structures and can adopt many different conformations in solution at room temperature. Hence, the determination of their relative configuration is a challenging task with the available experimental techniques. For structural analysis of natural molecules and to study their properties, all conformers which might be responsible for their chemical properties have to be considered.  Theoretical chemistry has been very helpful in absolute structure determination of complex and conformationally flexible natural molecules by calculating their theoretical nuclear magnetic resonance, ultraviolet, infra red, and circular dichroism spectra etc. There are a number of software tools that offer conformational analysis by utilizing different molecular mechanics approaches. They produce a large number of possible conformers and are not general purpose, thus compromising accuracy. Apart from that, different force fields available for conformational analysis and minimization have been designed for specific molecular classes and do not produce good results beyond their scope.  In the past, there have been reports about a “build-up procedure” for predicting the low energy conformations of peptides by optimising smaller fragments of the molecule under study and then joining them while minimizing their energies using force fields. Later on, this method was extended to predict the structure of DNA from sequences. This method used force field methods and did not gain much popularity due to its various limitations.  Here, MICE-PES (Method for the Incremental Construction and Exploration of the Potential Energy Surface) is presented, an algorithm which performs a conformational analysis using high level quantum chemical calculations by building the molecule incrementally from its smallest possible analogue whose conformational degrees of freedom are very well separated than the rest of the molecule. MICE-PES has been validated through studies on known biomolecule 3-epi-xestoaminol whose absolute configuration has been determined already by experimental and theoretical methods. MICE-PES has also been used to assign the relative configuration of a natural product (meroterphenol C) whose configuration could not be established experimentally. Overall, the development of MICE-PES will be very helpful in solving problems in the study of conformationally flexible systems, in all aspects of organic chemistry.</p>

Multibody Dynamics of a Floating Wind Turbine Considering the Flexibility Between Nacelle and Tower

2018 ◽  
Vol 18 (06) ◽  
pp. 1850085 ◽  
Author(s):  
Vahid Jahangiri ◽  
Mir Mohammad Ettefagh
Keyword(s):  
Wind Turbine ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Equations Of Motion ◽  
System Response ◽  
Floating Wind Turbine ◽  
Conservation Of Momentum ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
6 Degrees Of Freedom

Stability and dynamic modeling of the floating wind turbine (FWT) is a crucial challenge in designing of the type of structures. In this paper, the tension leg platform (TLP) type FWT is modeled as a multibody system considering the flexibility between the nacelle and tower. The flexibility of the FWT is modeled as a torsional spring and damper. It has 6 degrees of freedom (DOFs) related to the large-amplitude translation and rotation of the tower and 4 DOFs related to the relative rotation between the rotor-nacelle assembly and the tower. First, the nonlinear equations of motion are derived by the theory of momentum cloud based on the conservation of momentum. Then, the equations of motion are solved and the system is simulated in MATLAB. Moreover, the effect of flexibility between the nacelle and tower is investigated via the dynamic response. The stability of the system in three different environmental conditions is studied. Finally, the spring and damping coefficients for the system response to get near to instability are determined, by which the critical region is defined. The simulation results demonstrate the importance of the flexibility between the nacelle and tower on the overall behavior of the system and its stability.

Recursive formulation for the analytical or numerical application of the Gibbs-Appell method to the dynamics of robots

Robotica ◽  
1989 ◽  
Vol 7 (4) ◽  
pp. 343-347 ◽  
Author(s):  
K. Desoyer ◽  
P. Lugner
Keyword(s):  
Degrees Of Freedom ◽  
Multibody System ◽  
Equations Of Motion ◽  
Industrial Robots ◽  
Jacobi Matrices ◽  
Gibbs Function ◽  
Numerical Application ◽  
Kinetic Effects ◽  
Derivatives Of ◽  
Fast Rotating

SUMMARYTo derive the equations of motion for a multibody system using the Gibbs-Appell calculus – the partial derivatives of the Gibbs function G = 1/2 ∫ a2 dm with respect to the generalized accelerations equal the generalized forces-shows special advantages. Describing the kinematics with Jacobi matrices and local terms, these equations can be written in such a way that the partial derivations need not be performed explicitly. Kinetic effects of fast rotating driving devices attached to the moving links can be included in a similar way. Though an analytical formulation of the equations of motion is especially desirable with respect to its application for industrial robots, such a formulation becomes too extended and susceptible to errors for systems with more than 3 or 4 bodies. Therefore an approach is developed for tree structured robots with rotational or translational joints for calculating the Jacobi matrices and the local terms without employing any differentiation process. So it is possible to use the Gibbs-Appell method numerically in a recursive way e.g. for calculating the torques of the actuators of a robot with 6 or more degrees of freedom for a given motion.

Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review

2007 ◽  
Vol 463 (2084) ◽  
pp. 1955-1982 ◽  
Author(s):  
J.P Meijaard ◽  
Jim M Papadopoulos ◽  
Andy Ruina ◽  
A.L Schwab
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Point Contact ◽  
Ground Level ◽  
Conservative System ◽  
Rear Wheel ◽  
General Purpose ◽  
Dynamic Programs ◽  
Dynamics Simulations

We present canonical linearized equations of motion for the Whipple bicycle model consisting of four rigid laterally symmetric ideally hinged parts: two wheels, a frame and a front assembly. The wheels are also axisymmetric and make ideal knife-edge rolling point contact with the ground level. The mass distribution and geometry are otherwise arbitrary. This conservative non-holonomic system has a seven-dimensional accessible configuration space and three velocity degrees of freedom parametrized by rates of frame lean, steer angle and rear wheel rotation. We construct the terms in the governing equations methodically for easy implementation. The equations are suitable for e.g. the study of bicycle self-stability. We derived these equations by hand in two ways and also checked them against two nonlinear dynamics simulations. In the century-old literature, several sets of equations fully agree with those here and several do not. Two benchmarks provide test cases for checking alternative formulations of the equations of motion or alternative numerical solutions. Further, the results here can also serve as a check for general purpose dynamic programs. For the benchmark bicycles, we accurately calculate the eigenvalues (the roots of the characteristic equation) and the speeds at which bicycle lean and steer are self-stable, confirming the century-old result that this conservative system can have asymptotic stability.

EQUATIONS OF MOTION OF COMPLEX MULTIBODY SYSTEMS USING KINEMATICAL DIFFERENTIALS

1989 ◽  
Vol 13 (4) ◽  
pp. 113-121 ◽  
Author(s):  
M. HILLER ◽  
A. KECSKEMETHY
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Nonholonomic Systems ◽  
Automatic Generation ◽  
Minimal Order ◽  
Closed Form Solutions ◽  
Constraint Equations

In complex multibody systems the motion of the bodies may depend on only a few degrees of freedom. For these systems, the equations of motion of minimal order, although more difficult to obtain, give a very efficient formulation. The present paper describes an approach for the automatic generation of these equations, which avoids the use of LAGRANGE-multipliers. By a particular concept, designated “kinematical differentials”, the problem of determining the partial derivatives required to state the equations of motion is reduced to a simple re-evaluation of the kinematics. These cover the solution of the global position, velocity and acceleration problems, i.e. the motion of all bodies is determined for given generalized (independent) coordinates. For their formulation and solution, the multibody system is mapped to a network of nonlinear transformation elements which are connected by linear equations. Each transformation element, designated “kinematical transformer”, corresponds to an independent multibody loop. This mapping of the constraint equations makes it possible to find closed-form solutions to the kinematics for a wide variety of technical applications, and (via kinematical differentials) leads also to an efficient formulation of the dynamics. The equations are derived for holonomic, scleronomic systems, but can also be extended to general nonholonomic systems.

scholarly journals MICE-PES: An Algorithm for Accurate Conformational Analysis and its Implementation to Natural Products

2021 ◽  
Author(s):  
◽  
Muhammad Ali Hashmi
Keyword(s):  
Conformational Analysis ◽  
Degrees Of Freedom ◽  
Force Fields ◽  
Flexible Structures ◽  
Chemical Properties ◽  
General Purpose ◽  
Field Methods ◽  
Relative Configuration ◽  
Incremental Construction

<p>Secondary metabolites from natural sources have revolutionized the modern drug industry by acting as lead compounds. Many commercial drugs have evolved originally from natural molecules before being synthesized in the laboratory for commercialization. Because of the importance of natural molecules, it is crucial to determine their structural properties carefully as it is essential for their synthesis and studying their pharmacological behaviour. Many natural molecules have flexible structures and can adopt many different conformations in solution at room temperature. Hence, the determination of their relative configuration is a challenging task with the available experimental techniques. For structural analysis of natural molecules and to study their properties, all conformers which might be responsible for their chemical properties have to be considered.  Theoretical chemistry has been very helpful in absolute structure determination of complex and conformationally flexible natural molecules by calculating their theoretical nuclear magnetic resonance, ultraviolet, infra red, and circular dichroism spectra etc. There are a number of software tools that offer conformational analysis by utilizing different molecular mechanics approaches. They produce a large number of possible conformers and are not general purpose, thus compromising accuracy. Apart from that, different force fields available for conformational analysis and minimization have been designed for specific molecular classes and do not produce good results beyond their scope.  In the past, there have been reports about a “build-up procedure” for predicting the low energy conformations of peptides by optimising smaller fragments of the molecule under study and then joining them while minimizing their energies using force fields. Later on, this method was extended to predict the structure of DNA from sequences. This method used force field methods and did not gain much popularity due to its various limitations.  Here, MICE-PES (Method for the Incremental Construction and Exploration of the Potential Energy Surface) is presented, an algorithm which performs a conformational analysis using high level quantum chemical calculations by building the molecule incrementally from its smallest possible analogue whose conformational degrees of freedom are very well separated than the rest of the molecule. MICE-PES has been validated through studies on known biomolecule 3-epi-xestoaminol whose absolute configuration has been determined already by experimental and theoretical methods. MICE-PES has also been used to assign the relative configuration of a natural product (meroterphenol C) whose configuration could not be established experimentally. Overall, the development of MICE-PES will be very helpful in solving problems in the study of conformationally flexible systems, in all aspects of organic chemistry.</p>

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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