scholarly journals INVESTIGATION OF THE DYNAMICS OF NONLINEAR MECHANICAL SYSTEMS WITH LONG POWER LINES THROUGH DIGITAL MODELING

2019 ◽  
Vol 16 (33) ◽  
pp. 668-680
Author(s):  
L. A. KONDRATENKO ◽  
L. I. MIRONOVA ◽  
V. G. DMITRIEV ◽  
O. V. EGOROVA ◽  
A. O. SHEMIAKOV
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Wave Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Hydraulic Drive ◽  
Operating Conditions ◽  
Dynamic Features ◽  
Good Convergence ◽  
Operating Modes

Many of the mechanisms used in industry contain input and output links connected by long lines of force. Increasing the efficiency and service life of mechanical systems with long lines is of great importance for the country's economy. For a more rational use of these devices, it is important to maintain these operating modes with maximum accuracy, usually including the required speed of the actuator and the voltage in the lines. Such parameters can spontaneously change depending on the operating conditions of the system. In the presence of various influences, similar tasks to determine the marked regimes and parameters indicating the need for their change can be solved only with the help of the corresponding theory and research methods. The article presents the problems and the method of studying two-tier mechanical systems with an infinite number of degrees of freedom on the basis of the equations of momentum and moment of momentum in differential form. Transformations with the use of well-known wave equations are proposed, which made it possible to explicitly take into account the oscillations of the speeds of motion and stresses in the force lines of mechanical systems when describing dynamic processes. The solution of systems of partial differential equations is given using the Laplace transform, which made it possible to obtain general equations of motion and, after some simplifications, proceed to ordinary differential equations that take into account the dynamic features of systems with distributed parameters. The modernized Runge-Kutta method obtained solutions and carried out numerical simulation of transient processes in the hydraulic drive, the results of which have good convergence with full-scale experiments.

scholarly journals CONSTRUCTION OF EQUATIONS OF MOTION OF MULTIBODY SYSTEMS AND COMPUTER MODELING

2018 ◽  
pp. 74-81
Author(s):  
Darina Hroncová
Keyword(s):  
Mathematical Model ◽  
Computer Modeling ◽  
Computer Model ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Ideal Gas ◽  
Material Point ◽  
Operating Conditions ◽  
Contact Friction ◽  
Knowledge Process

Urgency of the research. Computer models mean new quality in the knowledge process. Using a computer model, the properties of the subject under investigation can be tested under different operating conditions. By experimenting with a com-puter model, we learn about the modelled object. We can test different machine variants without having to produce and edit prototypes. Target setting. The development of computer technology has expanded the possibility of solving mathematical models and allowed to gradually automate the calculation of mathematical model equations. It is necessary to insert appropriate inputs of the mathematical model and monitor and evaluate the output results through the computer output device The target was to describe the mathematical apparatus required for mathematical modeling and subsequently to compile a model for computer modeling. Actual scientific researches and issues analysis. When formulating a mathematical model for a computer, the laws and the theory we use are always valid under more or less idealized conditions, and operate with fictitious concepts such as, material point, ideal gas, intangible spring, and the like. However, with these simplifications, we describe a realistic phenomenon where the initial assumptions are only met to a certain extent. In order for the results not to be different from the modeled reality, it is to be assumed that a good computer model arises gradually, by verifying and modifying it, which is one of the advantages of MSC Adams. Uninvestigated parts of general matters defining. The question of building a real manipulator model. Based on the above simulation, it is possible to build a real model. The research objective. Using MSC Adams to simulate multiple body systems and verify its suitability for simulating ma-nipulator and robot models. In various versions of the assembled model we can monitor its behavior under different operating conditions. The statement of basic materials. In computer simulation, MSC Adams-View is used to simulate mechanical systems. It has an interactive environment for automated dynamic analysis of parameterized mechanical systems with an arbitrary struc-ture of rigid and flexible bodies with geometric or force joints, in which act gravity, inertia, experimentally designed contact, friction, aerodynamic, hydrodynamic or electromechanical forces and have integrated control, hydraulic, pneumatic or elec-tromechanical circuits. Conclusions. Working with a mathematical model on a computer opens space for specific synthesis of empirical and ana-lytical method of scientific knowledge. Working with the computer model carries the characteristic features of classical experi-mentation. It represents a qualitatively new way of solving tasks that can not be experimented with on a real object. The result is the equivalence of the computer model and the object being investigated with the features and expressions chosen as essen-tial, with accuracy sufficient to the exact purpose.

Model Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes

1999 ◽  
Author(s):  
E. Pesheck ◽  
C. Pierre ◽  
S. W. Shaw
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Single Equation ◽  
Rotating Beam ◽  
Model Size ◽  
Nonlinear Normal

Abstract Equations of motion are developed for a rotating beam which is constrained to deform in the transverse (flapping) and axial directions. This process results in two coupled nonlinear partial differential equations which govern the attendant dynamics. These equations may be discretized through utilization of the classical normal modes of the nonrotating system in both the transverse and extensional directions. The resultant system may then be diagonalized to linear order and truncated to N nonlinear ordinary differential equations. Several methods are used to determine the model size necessary to ensure accuracy. Once the model size (N degrees of freedom) has been determined, nonlinear normal mode (NNM) theory is applied to reduce the system to a single equation, or a small set of equations, which accurately represent the dynamics of a mode, or set of modes, of interest. Results are presented which detail the convergence of the discretized model and compare its dynamics with those of the NNM-reduced model, as well as other reduced models. The results indicate a considerable improvement over other common reduction techniques, enabling the capture of many salient response features with the simulation of very few degrees of freedom.

Automatic Generation of Equations of Motion of Mechanical Systems

2014 ◽  
Vol 611 ◽  
pp. 40-45
Author(s):  
Darina Hroncová ◽  
Jozef Filas
Keyword(s):  
Computer Simulation ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Automatic Generation ◽  
Lagrange Equations ◽  
Kinematic Chains ◽  
Transformation Matrices

The paper describes an algorithm for automatic compilation of equations of motion. Lagrange equations of the second kind and the transformation matrices of basic movements are used by this algorithm. This approach is useful for computer simulation of open kinematic chains with any number of degrees of freedom as well as any combination of bonds.

Contributions to the Determination of the Equations of Motion for Multidegree of Freedom Systems

1971 ◽  
Vol 93 (1) ◽  
pp. 191-195 ◽  
Author(s):  
Desideriu Maros ◽  
Nicolae Orlandea
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
System Of Differential Equations ◽  
Original Contribution ◽  
Deductive Method ◽  
Method Of Solution ◽  
Further Development ◽  
Three Degrees Of Freedom

This paper is a further development of the kinematic problem presented in our 1967 paper [1] in which we have obtained the transmission functions for different orders of plane systems with many degrees of freedom. This paper establishes the corresponding system of differential equations of motion beginning with these functions. The purpose of this paper is to facilitate computer programming. Our study is based on the work of R. Beyer [2, 3] and is the first original addition to his papers. A second original contribution to Beyer’s theories is the deductive method of solution, from general to particular, which we have, incorporated in our work. Beyer concluded that the cases having two or three degrees of freedom can be considered as particular solutions to the results obtained.

scholarly journals New Aspects Concerning Dynamics of Rigid Solid Body in Plane-Parallel Motion Subjected to Real Constraints. Part One

2019 ◽  
Vol 24 (2) ◽  
pp. 175-180
Author(s):  
Vladimir Dragoş Tătaru ◽  
Mircea Bogdan Tătaru
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Original Method ◽  
Horizontal Force ◽  
Constraint Forces ◽  
Inclined Plane ◽  
Parallel Motion

Abstract The present paper approaches in an original manner the dynamic analysis of a wheel which climbs on an inclined plane under the action of a horizontal force. The wheel rolls and slides in the same time. The two movements, rolling and sliding are considered to be independent of each other. Therefore we are dealing with a solid rigid body with two degrees of freedom. The difficulty of approaching the problem lies in the fact that in the differential equations describing the motion of the solid rigid body are also present the constraint forces and these are unknown. For this reason they must be eliminated from the differential equations of motion. The paper presents as well an original method of the constraint forces elimination.

Dynamic Contribution of Tires in Vehicle Suspension Modeling: An Experimental Approach

2003 ◽  
Author(s):  
Giuseppe Catania ◽  
Alessandro Zanarini
Keyword(s):  
Degrees Of Freedom ◽  
Experimental Approach ◽  
Structural Model ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Vehicle Suspension ◽  
Frequency Range ◽  
Full System ◽  
Linear Complex ◽  
Modal Model

An analytical-experimental approach is followed to obtain the dynamic model of a car vehicle, taking into account the full dynamic contribution due to tires. Linearized and condensed vehicle equations of motion are first introduced. The experimental modal model of a car tire, consisting of limited sets of eigenfrequencies and eigenshapes is then experimentally estimated in the frequency range Δftire=0÷300 Hz, starting from a restricted set of experimental degrees of freedom (d.o.f.). The tire is locally loaded to simulate the displacements due to gravitational loads and road contact occurring in operating conditions. Elastic coupling between the car structural model and the tire modal model is thus obtained; a linear, complex eigenproblem is thus formulated, and eigenfrequencies related to the full system are obtained as well. Results are reported and discussed in detail.

scholarly journals Dynamical analysis of a 2-degrees of freedom spatial pendulum

2018 ◽  
Vol 184 ◽  
pp. 01003 ◽  
Author(s):  
Stelian Alaci ◽  
Florina-Carmen Ciornei ◽  
Sorinel-Toderas Siretean ◽  
Mariana-Catalina Ciornei ◽  
Gabriel Andrei Ţibu
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Dynamical Analysis ◽  
Analysis Software ◽  
Lagrange Equations ◽  
Moments Of Inertia ◽  
Dynamical Simulation ◽  
Principal Moments Of Inertia

A spatial pendulum with the vertical immobile axis and horizontal mobile axis is studied and the differential equations of motion are obtained applying the method of Lagrange equations. The equations of motion were obtained for the general case; the only simplifying hypothesis consists in neglecting the principal moments of inertia about the axes normal to the oscillation axes. The system of nonlinear differential equations was numerically integrated. The correctness of the obtained solutions was corroborated to the dynamical simulation of the motion via dynamical analysis software. The perfect concordance between the two solutions proves the rightness of the equations obtained.

Differential equations of motion of mechanical systems with variable parameters

1974 ◽  
Vol 10 (6) ◽  
pp. 671-674
Author(s):  
V. A. Lazaryan ◽  
L. A. Manashkin ◽  
A. V. Yurchenko
Keyword(s):  
Differential Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Variable Parameters

Hamiltonian formulation for mechanical systems with nonholonomic constraints

2014 ◽  
Vol 11 (03) ◽  
pp. 1450017
Author(s):  
G. F. Torres del Castillo ◽  
O. Sosa-Rodríguez
Keyword(s):  
Finite Number ◽  
Mechanical System ◽  
Infinite Number ◽  
Degrees Of Freedom ◽  
Hamiltonian Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Hamilton Equations

It is shown that for a mechanical system with a finite number of degrees of freedom, subject to nonholonomic constraints, there exists an infinite number of Hamiltonians and symplectic structures such that the equations of motion can be written as the Hamilton equations, with the original constraints incorporated in the Hamiltonian structure.

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