A mathematical model for structural analysis of dynamical systems

2005 ◽  
pp. 56-66
Author(s):  
Kazuo Murota
Keyword(s):  
Mathematical Model ◽  
Structural Analysis ◽  
Dynamical Systems

scholarly journals Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

1973 ◽  
Vol 95 (2) ◽  
pp. 525-532 ◽  
Author(s):  
M. Huang ◽  
A. H. Soni
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Piston Cylinder ◽  
General Constraints ◽  
Analysis And Synthesis ◽  
Linear And Nonlinear

Using graph theory and Polya’s theory of counting, the present paper performs structural synthesis and analysis of planar and three-dimensional kinematic chains. The Section 2 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of planar kinematic chains with kinematic elements such as revolute pairs, cam pairs, springs, belt-pulley, piston-cylinder, and gears. The theory developed is applied to enumerate eight-link kinematic chains with these kinematic elements. The Section 3 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of multi-loop spatial kinematic chains with higher and lower kinematic pairs. The theory developed is applied to enumerate all possible two-loop kinematic chains with or without general constraints.

Characterization and Mathematical Modelling of Geometric Effects on Piezoelectric Actuators

2019 ◽  
Vol 201 (1) ◽  
pp. 201-217
Author(s):  
Hareem Jawaid ◽  
Waqar Ahmed Qureshi ◽  
Riffat Asim Pasha ◽  
Rizwan Ahmed Malik
Keyword(s):  
Mathematical Model ◽  
Structural Analysis ◽  
Mathematical Modelling ◽  
Piezoelectric Actuator ◽  
Piezoelectric Actuators ◽  
Numerical Results ◽  
Hydraulic Valves ◽  
Geometric Effects

This paper focuses on the characterization and static structural analysis of piezoelectric actuator to investigate the sequential increasing effect of piezoelectric patches. The effect on the tip deflection is observed analytically, numerically and experimentally. By varying the quantity and the geometry of piezoelectric patches/beams, the actuation effect is analyzed. A mathematical model has been developed for the unequal lengths of patches and beam. The analysis is carried out numerically to examine the tip deflection under various parameters. The results are analyzed and verified experimentally. The results are found to be in accordance with the analytical and numerical results. This permits the desired configuration of an actuator in applications like hydraulic valves for actuating and controlling the flow of liquid as per need.

The Conceptual Design of a Perfusion Reactor Using a Complexity Measure

2008 ◽  
Author(s):  
Andreas Bischof ◽  
Jorge Angeles ◽  
Lucienne Blessing
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Dynamical Systems ◽  
Simple Model ◽  
Conceptual Design ◽  
Living Cells ◽  
Complexity Measure ◽  
Ceramic Foam ◽  
Cell Life ◽  
The Subject

The conceptual design of a perfusion reactor is the subject of this paper. The main objective of the reactor is the provision of nutrients to living cells grown in a porous medium fabricated of a given ceramic foam. In order to increase reactor throughput, the nutrients should be provided in a minimum time, without affecting the cell life. Various layouts of identical ceramic-foam pieces hosting the cells are proposed, the purpose being to select the variant with the highest likelihood of optimum performance, in the absence of a detailed mathematical model. A simple model is proposed, drawn from the discipline of hydraulic dynamical systems, which leads to a flow-complexity measure. The variant with the lowest complexity is then selected, for which a possible embodiment is proposed.

scholarly journals Mathematical problems of reliability assurance the building constructions

2019 ◽  
Vol 97 ◽  
pp. 03031 ◽  
Author(s):  
Victor Orlov ◽  
Oleg Kovalchuk
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Structural Analysis ◽  
Singular Point ◽  
General Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Nonlinear Differential Equations ◽  
Structural Failure ◽  
Mathematical Problems

The paper deals with a mathematical model of console type based on the nonlinear differential equation having a mobile feature of the General solution (or a mobile singular point). The presence of mobile singular points indicates affiliation of this type of equations to the class of intractable in the general case in of quadratures. This fact, taking into account the interpretation of mobile singular point as the coordinate of structural failure, actualizes the development of an analytical approximate method for solving nonlinear differential equations. Taking into account these features for of structural analysis increases the authenticity of results and reliability of construction.

scholarly journals The Verhulst-Like Equations: Integrable OΔE and ODE with Chaotic Behavior

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1446 ◽  
Author(s):  
Igor Andrianov ◽  
Galina Starushenko ◽  
Sergey Kvitka ◽  
Lelya Khajiyeva
Keyword(s):  
Mathematical Model ◽  
Dynamical Systems ◽  
Difference Equations ◽  
Chaotic Behavior ◽  
Logistic Equation ◽  
Deterministic System ◽  
Characteristic Parameters ◽  
Chaotic Dynamical Systems ◽  
The Mathematical Model ◽  
Continualization Procedure

In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O Δ E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is a classic example of a simple system with very complicated (chaotic) behavior. In our paper we present examples of deterministic discretization and chaotic continualization. Continualization procedure is based on Padé approximants. To correctly characterize the dynamics of obtained ODE we measured such characteristic parameters of chaotic dynamical systems as the Lyapunov exponents and the Lyapunov dimensions. Discretization and continualization lead to a change in the symmetry of the mathematical model (i.e., group properties of the original ODE and O Δ E). This aspect of the problem is the aim of further research.

scholarly journals Importance of Modeling and Simulation of Materials in Research

2018 ◽  
Vol 1 (1) ◽  
pp. 1-2
Keyword(s):  
Mathematical Model ◽  
Dynamical Systems ◽  
Modeling And Simulation ◽  
System Modeling ◽  
Experimental Results ◽  
Experimental Setup ◽  
Complex Dynamical Systems ◽  
Inputs And Outputs

All researchers have experience with various complicated phenomena and processes in materials and have contact with understanding of different complex dynamical systems. Consequently, one has to predict and optimize the system under study and compare the output results to its experimental setup. The experimental setup is done to confirm and spread out information about the system; however still, many researchers are not familiar with the results arising from the experimental setup or fabrications processes. To obtain valid experimental results, it is necessary to pay carful attentions to the tools, devices and the applied techniques for measuring and observations detectors. This experimentations and fabrications process cover all area from forming and characterizations of nanostructures to macrostructures. In system characterizations, it is common to apply system modeling to predict and represent the system by a mathematical model that is accomplishable due to the relations between the inputs and outputs defined by formulas.

scholarly journals An Algorithm for Crawling Robot Climbing or Descending Stair Flights

2020 ◽  
Vol 24 (3) ◽  
pp. 21-34
Author(s):  
L. Yu. Vorochaeva ◽  
S. I. Savin ◽  
A. V. Mal'chikov
Keyword(s):  
Mathematical Model ◽  
Structural Analysis ◽  
Contact Interaction ◽  
Vertical Plane ◽  
Point Of View ◽  
Simulation Experiments ◽  
Sequential Movements ◽  
Base Points ◽  
Reverse Sequence ◽  
Step Algorithm

Purpose of research. The aim of this work is to develop an algorithm for sequential movements of a three-section crawling robot, which enables the device overcoming flights of stairs by crawling on each step or descending each step in the reverse sequence of stages. A special feature of the robot is the combination of three types of movement: snake-, worm - and caterpillar-like, which makes the device more maneuverable and expands its functionality. Methods. To develop a mathematical model of the movement of crawling robot sections at each stage of the algorithm and description of its contact interaction with the surface, the method of dynamics of multi-mass systems is used; methods of kinematic and structural analysis of the robot mechanism are used to form constraints that restrict the movement of the sections. Results. The article presents the results of simulation experiments of a robot crawling on a step of a flight of stairs and descending it, confirming the adequacy of the proposed movement algorithm. Positions of base points at the moments of the beginning and completion of the stages, section lengths and their turning angles in the vertical plane correspond to the values of these variables specified in the algorithm in the form of applied links and laid down conditions for the completion of stages. Conclusion. The article describes a detailed step-by-step algorithm for robot crawling on a step of a stairs flight and descending it; it is shown that crawling and descending are opposite operations from the point of view of sequence of stages implementing. The advantage of this algorithm is the versatility of its stages for moving the robot up and downstairs. In addition, the algorithm stages are designed in such a way that the robot does not roll over.

Stress Analysis of Underground Arch Structure

2011 ◽  
Vol 243-249 ◽  
pp. 938-941
Author(s):  
Bin He ◽  
Jun Long Lu
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Structural Analysis ◽  
Finite Element Model ◽  
Mathematical Models ◽  
Stress Analysis ◽  
Element Model ◽  
Arch Structure ◽  
The Impact ◽  
Actual Stress

To research the safety of an underground defense project and the impact to other buildings, applying basic mechanics principles, established two types of mathematical model for arch about the project, and analyzed stress in different directions of ground arch structure. The data shows that the results were very different in different mathematical models, and mathematical models should be considered as close to actual stress situation in structural analysis. In the structural analysis involved soil, spatial finite element model is more accurate and reasonable than truss finite element model.

Sign in / Sign up

Export Citation Format

Share Document