The Vibrations of the Engine with Neo-Hookean Suspension

2013 ◽  
Vol 430 ◽  
pp. 53-59 ◽  
Author(s):  
Nicolae Doru Stanescu ◽  
Dinel Popa
Keyword(s):  
Degrees Of Freedom ◽  
Stable Equilibrium ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Harmonic Force ◽  
Small Oscillations ◽  
Excited System ◽  
Beat Phenomenon ◽  
Three Degrees Of Freedom

Our paper realizes a study of the vibrations of an engine excited by a harmonic force and sustained by four identical neo-Hookean springs of negligible masses. The considered model is one with three degrees of freedom (one translation and two rotations) and we obtain for it the equations of motion. Using these equations, we determine for the unexcited system the equilibrium positions and their stability. We also study the small oscillations about the stable equilibrium positions and we find the fundamental eigenpulsations of the system. For the case of the excited system we perform a numerical study considering the situation when the pulsation of the excitation is far away from the eigenpulsations and the situation when the pulsation of the excitation is closed to one eigenpulsation, highlighting the beat phenomenon.

Evaluation of 3-D Computational Model of Oscillating Water Column Converter with Constructal Design with Three Degrees of Freedom and Limited Chimney Height

2021 ◽  
Vol 407 ◽  
pp. 128-137
Author(s):  
Vinícius Bloss ◽  
Camila Fernandes Cardozo ◽  
Flávia Schwarz Franceschini Zinani ◽  
Luiz Alberto Oliveira Rocha
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Mechanical Energy ◽  
Ocean Waves ◽  
Response Surfaces ◽  
Oscillating Water Column ◽  
Promising Source ◽  
Three Degrees Of Freedom

Theoretically, ocean waves contain enough mechanical energy to supply the entire world’s demand and, as of late, are seen as a promising source of renewable energy. To this end, several different technologies of Wave Energy Converters (WEC) have been developed such as Oscillating Water Column (OWC) devices. OWCs are characterized by a chamber in which water oscillates inside and out in a movement similar to that of a piston. This movement directs air to a chimney where a turbine is attached to convert mechanical energy. The analysis conducted was based on the Constructive Design Method, in which a numerical study was carried out to obtain the geometric configuration that maximized the conversion of wave energy into mechanical energy. Three degrees of freedom were used: the ratio of height to length of the hydropneumatic chamber (H1/L), the ratio of the height of the chimney to its diameter (H2/d) and the ratio of the width of the hydropneumatic chamber to the width of the wave tank (W/Z). A Design of Experiments (DoE) technique coupled with Central Composite Design (CCD) allowed the simulation of different combinations of degrees of freedom. This allowed the construction of Response Surfaces and correlations for the efficiency of the system depending on the degrees of freedom (width and height of the chamber), as well as the optimization of the system based on the Response Surfaces.

Small oscillations of systems with several degrees of freedom

2020 ◽  
pp. 29-40
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Free Oscillations ◽  
Small Oscillations ◽  
Symmetry Properties ◽  
Gyroscopic Forces ◽  
Simple Molecules ◽  
Simple Systems ◽  
Three Degrees Of Freedom

This chapter addresses the free and forced oscillations of simple systems (with two or three degrees of freedom), the free oscillations of systems with the degenerate frequencies, and the eigen-oscillations of the electromechanical systems. This chapter also studies the oscillations of more complex systems using orthogonality of eigenoscillations and the symmetry properties of the system, the free oscillations of an anisotropic charged oscillator moving in a uniform constant magnetic field, and the perturbation theory adapted for the small oscillations. Finally, the chapter addresses oscillations of systems in which gyroscopic forces act and the eigen-oscillations of the simple molecules.

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 Decomposition of the Equations of Motion in the Analysis of Dynamics of a 3-DOF Nonideal System

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Roman Starosta ◽  
Grażyna Sypniewska-Kamińska
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Dynamical Behaviour ◽  
Engineering Systems ◽  
System Operation ◽  
Unbalanced Rotor ◽  
Nonideal System ◽  
Analysis Of Dynamics ◽  
Three Degrees Of Freedom

The dynamic response of a nonlinear system with three degrees of freedom, which is excited by nonideal excitation, is investigated. In the considered system the role of a nonideal source is played by a direct current motor, where the central axis of the rotor is not coincident with the axis of rotation. This translation generates a torque whose magnitude depends on the angular velocity. During the system operation a general coordinate assigned to the nonideal source grows rapidly as a result of rotation. We propose the decomposition of the equations of motion in such a way to extract the solution which is directly related to the rotation of an unbalanced rotor. The remaining part of the solution describes pure oscillation depending on the dynamical behaviour of the whole system. The decomposed equations are solved numerically. The influence of selected system parameters on the rotor vibration is examined. The presented approach can be applied to separate vibration and rotation of motions in many other engineering systems.

Near-Integrability and Recurrence in FPU-Cells

2016 ◽  
Vol 26 (14) ◽  
pp. 1650230 ◽  
Author(s):  
Ferdinand Verhulst
Keyword(s):  
Hamiltonian Systems ◽  
Building Block ◽  
Degrees Of Freedom ◽  
Stable Equilibrium ◽  
Chain Recurrence ◽  
Low Dimension ◽  
A Cell ◽  
Linearized System ◽  
A Chain ◽  
Three Degrees Of Freedom

In a neighborhood of stable equilibrium, we consider the dynamics for at least three degrees-of-freedom (dof) Hamiltonian systems (2 dof systems are not ergodic in this case). A complication is that the recurrence properties depend strongly on the resonances of the corresponding linearized system and on quasi-trapping. In contrast to the classical FPU-chain, the inhomogeneous FPU-chain shows nearly all the principal resonances. Using this fact, we construct a periodic FPU-chain of low dimension, called a FPU-cell. Such a cell can be used as a building block for a chain of FPU-cells, called a cell-chain. Recurrence phenomena depend strongly on the physical assumptions producing specific Hamiltonians; we demonstrate this for the [Formula: see text] resonance, both general and for the FPU case; this resonance shows dynamics on different timescales. In addition we will study the relations and recurrence differences between several FPU-cells and a few cell-chains in the case of the classical near-integrable FPU-cell and of chaotic cells in [Formula: see text] resonance.

Modeling and Validation of a Roll Simulator for Recreational Off-Highway Vehicles

2011 ◽  
Author(s):  
Scott B. Zagorski ◽  
Dennis A. Guenther ◽  
Gary J. Heydinger ◽  
Anmol S. Sidhu ◽  
Dale A. Andreatta
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Excellent Correlation ◽  
Motor Systems ◽  
Non Linear ◽  
Entrapped Air ◽  
Three Degrees Of Freedom

A model of a roll simulator for recreational off-highway vehicles (ROV) is presented. Models of each sub-system are described including the equations of motion, the braking, hydraulic and roll motor systems. Derivation of the equations of motion, obtained using Lagrange’s energy equation, demonstrates that they have three degrees-of-freedom (two dynamic, one static) and are coupled and highly non-linear. Results from the hydraulic sub-system illustrated that the amount of entrapped air in the system can significantly influence the response. Comparisons of the model with experimental data from the actual roll simulator showed close agreement. The greatest difference was with motor pressure. The acceleration levels and roll motions for both the model and experimental data showed excellent correlation.

Dynamic Characteristics of an In-Contact Headslider Considering Meniscus Force: Part 1—Formulation and Application to the Disk With Sinusoidal Undulation

1999 ◽  
Vol 122 (3) ◽  
pp. 633-638 ◽  
Author(s):  
Takahisa Kato ◽  
Souta Watanabe ◽  
Hiroshige Matsuoka
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Disk Surface ◽  
Disk Interface ◽  
Meniscus Force ◽  
Calculation Results ◽  
Three Degrees Of Freedom

The authors present a three-degrees-of-freedom (3-DOF) model of an in-contact headslider/disk interface (HDI) system by which the dynamic characteristics of the in-contact headslider-suspension assembly can be obtained. Four regimes with respect to the interface of headslider and disk surface are shown to take the meniscus force of lubricant on the disk surface into account. The equations of motion of the in-contact headslider considering the meniscus force at each regime and the calculation results for the disk with sinusoidal undulation are described. [S0742-4787(00)01802-6]

scholarly journals Effect of Pulse Shape and Duration on Dynamic Response of a Forging System

2019 ◽  
Vol 13 (4) ◽  
pp. 226-232
Author(s):  
Arkadiusz Trąbka
Keyword(s):  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time History ◽  
Pulse Load ◽  
Negative Effects ◽  
Maximum Displacement ◽  
Soil Settlement ◽  
History Of ◽  
Three Degrees Of Freedom

Abstract Forging hammers are machines whose operation causes negative effects both at the place of their foundation (the soil settlement) and in their surroundings (e.g., vibrations propagating to the other devices, noise, etc.). Knowledge of the parameters characterizing the time history of the force that arises as a result of impact of a ram on a shaped material is of fundamental importance for the correct analysis of both the structure of the hammer and its impact on the surroundings. In the paper, the effect of the shape and duration of a pulse load on the dynamic response of a hammer-foundation forging system was assessed. An analytical method of description of the forces that arise as a result of impact of the ram on the forged material, using different forms of pulses was presented. The forces defined in this way as loads in a mathematical model of three degrees of freedom forging system were used. The equations of motion derived from d’Alembert’s principle were solved numerically in the Matlab program. The analyses for eight forms of the pulse loads with the same pulse sizes but different durations were performed. The results in the graphs were presented. It was found, among other things, that a greater impact on the maximum displacement, velocity and acceleration of each component of the hammer-foundation system as well as on the maximum forces transmitted to the soil has the duration of a pulse than its shape.

Small oscillations of systems with several degrees of freedom

2020 ◽  
pp. 191-244
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Free Oscillations ◽  
Small Oscillations ◽  
Symmetry Properties ◽  
Gyroscopic Forces ◽  
Simple Molecules ◽  
Simple Systems ◽  
Three Degrees Of Freedom

This chapter addresses the free and forced oscillations of simple systems (with two or three degrees of freedom), the free oscillations of systems with the degenerate frequencies, and the eigen-oscillations of the electromechanical systems. This chapter also studies the oscillations of more complex systems using orthogonality of eigenoscillations and the symmetry properties of the system, the free oscillations of an anisotropic charged oscillator moving in a uniform constant magnetic field, and the perturbation theory adapted for the small oscillations. Finally, the chapter addresses oscillations of systems in which gyroscopic forces act and the eigen-oscillations of the simple molecules.

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