Unraveling the Dynamic Behavior of Ecological Models: Algebraic, Geometric and Numerical Methods of Analysis

2002 ◽  
Vol 7 (3) ◽  
pp. 155-176
Author(s):  
J. V. Greenman
Keyword(s):  
Numerical Methods ◽  
Dynamic Behavior ◽  
Ecological Models ◽  
Methods Of Analysis

Dynamic analysis of a helical gear reduction by experimental and numerical methods

2020 ◽  
Vol 68 (1) ◽  
pp. 48-58
Author(s):  
Chao Liu ◽  
Zongde Fang ◽  
Fang Guo ◽  
Long Xiang ◽  
Yabin Guan ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Numerical Models ◽  
Helical Gear ◽  
Operating Conditions ◽  
Dynamic Responses ◽  
Lumped Mass ◽  
Gear Mesh

Presented in this study is investigation of dynamic behavior of a helical gear reduction by experimental and numerical methods. A closed-loop test rig is designed to measure vibrations of the example system, and the basic principle as well as relevant signal processing method is introduced. A hybrid user-defined element model is established to predict relative vibration acceleration at the gear mesh in a direction normal to contact surfaces. The other two numerical models are also constructed by lumped mass method and contact FEM to compare with the previous model in terms of dynamic responses of the system. First, the experiment data demonstrate that the loaded transmission error calculated by LTCA method is generally acceptable and that the assumption ignoring the tooth backlash is valid under the conditions of large loads. Second, under the common operating conditions, the system vibrations obtained by the experimental and numerical methods primarily occur at the first fourth-order meshing frequencies and that the maximum vibration amplitude, for each method, appears on the fourth-order meshing frequency. Moreover, root-mean-square (RMS) value of the acceleration increases with the increasing loads. Finally, according to the comparison of the simulation results, the variation tendencies of the RMS value along with input rotational speed agree well and that the frequencies where the resonances occur keep coincident generally. With summaries of merit and demerit, application of each numerical method is suggested for dynamic analysis of cylindrical gear system, which aids designers for desirable dynamic behavior of the system and better solutions to engineering problems.

Rattlebacks for Undergraduate Engineers: Modelling Complex Behavior Using Introductory Dynamics and Numerical Methods

2018 ◽  
Author(s):  
Simon Jones ◽  
Kirby Kern
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Reference Frame ◽  
Engineering Students ◽  
Rotary Motion ◽  
Complex Dynamic ◽  
Time Stepping ◽  
Undergraduate Engineering ◽  
Clockwise Direction

Rattlebacks are semi-ellipsoidal tops that have a preferred direction of spin. If spun in, say, the clockwise direction, the rattleback will exhibit stable rotary motion. If spun in the counter-clockwise direction, the rattleback’s rotary motion will transition to a rattling motion, and then reverse its spin resulting in clockwise rotation. This counter-intuitive dynamic behavior has long been a favored subject of study in graduate-level dynamics classes. Previous literature on rattleback dynamics offer insight into a myriad of advanced topics, including three-dimensional motion, sliding and rolling friction models, stability regions, nondimensionalization, etc. However, it is the current authors’ view that focusing on these advanced topics clouds the students’ understanding of the fundamental kinetics of the body. The goal of this paper is to demonstrate that accurately simulating rattleback behavior need not be complicated; undergraduate engineering students can accurately model the behavior using concepts from introductory dynamics and numerical methods. The current paper develops an accurate dynamic model of a rattleback from first principles. All necessary steps are discussed in detail, including computing the mass moment of inertia, choice of reference frame, conservation of momenta equations, and application of kinematic constraints. Basic numerical techniques like Gaussian quadrature, Newton-Raphson root-finding, and Runge-Kutta time-stepping are employed to solve the necessary integrals, nonlinear algebraic equations, and ordinary differential equations. Since not all undergraduate engineering students are familiar with 3D dynamics, a simpler 2D rocking semi-ellipse example is first introduced to develop the transformation matrix between an inertial reference frame and a body-fixed reference frame. This provides the framework to transition seamlessly into 3D dynamics using roll, pitch, and yaw angles, concepts that are widely understood by engineering students. In fact, when written in vector notation, the governing equations for the rocking ellipse and the spin-biased rattleback are shown to be the same, enforcing the concept that 3D dynamics need not be intimidating. The purpose of this paper is to guide a typical undergraduate engineering student through a complex dynamic simulation, and to demonstrate that he or she already has the tools necessary to simulate complex dynamic behavior. Conservation of momenta will account for the dynamics, intimidating integrals and differentials can be tackled numerically, and classic time-stepping approaches make light work of nonlinear differential equations.

scholarly journals Effective numerical methods to model dynamic behavior of springs with torsion

2018 ◽  
Author(s):  
◽  
E. Dilan Fernando
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Method ◽  
Dynamic Behavior ◽  
Numerical Models ◽  
Software Implementation ◽  
Computer Language ◽  
Newtonian Mechanics ◽  
Systems Of Differential Equations ◽  
Kirchhoff Problem

The purpose of this thesis is to find effective algorithms to numerically solve certain systems of differential equations that arise from standard Newtonian mechanics. Numerical models of elastica has already been well studied. In this thesis we concentrate on the Kirchhoff problem. The goal is to create an effective and robust numerical method to model the dynamic behavior of springs that have a prescribed natural curvature. In addition to the mathematics, we also provide the implementation details of the numerical method using the computer language Python 3. We also discuss in detail the various difficulties of such a software implementation and how certain auxiliary computations can make the software more effective and robust.

Correct Numerical Methods of Analysis of Structural Strength and Stability of High-Rise Panel Buildings - Part 1: Theoretical Foundations of Modelling

2016 ◽  
Vol 685 ◽  
pp. 217-220 ◽  
Author(s):  
Alexandr M. Belostosky ◽  
Sergey B. Penkovoy ◽  
Sergey V. Scherbina ◽  
Pavel A. Akimov ◽  
Taymuraz B. Kaytukov
Keyword(s):  
Numerical Methods ◽  
Computational Models ◽  
Structural Strength ◽  
Simulation Software ◽  
High Rise ◽  
Methods Of Analysis ◽  
Software Information ◽  
Theoretical Foundations

The distinctive paper is devoted to development and verification of correct numerical methods for analysis of structural strength and stability of high-rise panel buildings. Particularly the first part of the paper contains brief introduction, description of methods of analysis and simulation software. Information about verification of corresponding computational models is presented as well.

Micro-Modeling Options for Masonry

2016 ◽  
pp. 28-60 ◽  
Author(s):  
Vasilis Sarhosis
Keyword(s):  
Numerical Methods ◽  
Bond Strength ◽  
Mechanical Behavior ◽  
Data Availability ◽  
Masonry Structures ◽  
Initial State ◽  
Computational Approaches ◽  
Methods Of Analysis ◽  
Full Knowledge ◽  
Micro Modeling

In this chapter, a review of the available methods and their challenges to simulate the mechanical behavior of masonry structures are presented. Different micro-modeling computational options are considered and compared with regard to their ability to define the initial state of the structure, realism in simulation, computer efficiency and data availability for their application to model low bond strength masonry structures. It is highlighted that different computational approaches should lead to different results and these will depend on the adequacy of the approach used and the information available. From the results analysis it is also highlighted that a realistic analysis and assessment of existing masonry structures using numerical methods of analysis is not a straight forward task even under full knowledge of current conditions and materials.

Fast Reactor Cores: Seismic Excitation in the Vertical Direction — Numerical Methods

2018 ◽  
Author(s):  
Daniel Broc ◽  
Gianluca Artini ◽  
Jérome Cardolaccia ◽  
Laurent Martin
Keyword(s):  
Numerical Methods ◽  
Dynamic Behavior ◽  
Nonlinear Model ◽  
Fast Reactor ◽  
Vertical Direction ◽  
Seismic Excitation ◽  
Fluid Structure ◽  
The Core ◽  
Fuel Assemblies ◽  
Reactor Cores

In the frame of the GEN IV Forum and of the ASTRID Project, a program is in progress in the CEA (France) for the development and the validation of numerical tools for the simulation of the dynamic mechanical behavior of the Fast Reactor cores, with both experimental and numerical parts. The cores are constituted of Fuel Assemblies (or FA) and Neutronic Shields (or NS) immersed in the primary coolant (sodium), which circulates inside the Fuel Assemblies. The FA and the NS are slender structures, inserted in a grid plate, which may be considered as beams form a mechanical point of view. The dynamic behavior of this system has to be understood, for design and safety studies. This dynamic behavior of the core is strongly influenced by the sodium and by contacts between the beams at the pads level and at the top. The fluid leads to complex interactions between the structures in the whole core. The contacts between the beams limit the relative displacements. Two main movements have been considered so far: global horizontal movements under a seismic excitation, and opening of the core. Physical and numerical methods and tools have been developed to describe and simulate the dynamic behavior. These methods are integrated in CAST3M, general computer code developed at the CEA Saclay. The assemblies are modeled as beams. The impacts at the pads between the assemblies are taken into account by using a nonlinear model. The Fluid Structure Interaction is taken into account by using homogenization methods. This paper is devoted to the improvement of these methods to take into account the vertical component of a seismic excitation. The key points are: - the fluid structure coupling in the vertical direction, - the modification of the description of the impacts to take into account the vertical displacements of the assemblies, - the modification of the boundary condition at the foot of the assembly, in order to take into account the uplift with a nonlinear model.

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