scholarly journals Dynamic Analysis of Rotating Pendulum by Hamiltonian Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Nadeem Alam Khan ◽  
Fatima Riaz
Keyword(s):  
Dynamic Analysis ◽  
Numerical Simulations ◽  
Natural Frequency ◽  
Governing Equation ◽  
Conservative System ◽  
Hamiltonian Approach ◽  
Series Approximation ◽  
Suggested Technique ◽  
Approximate Frequency ◽  
Relationship Of

A conservative system always admits Hamiltonian invariant, which is kept unchanged during oscillation. This property is used to obtain the approximate frequency-amplitude relationship of the governing equation with sinusoidal nonlinearity. Here, we applied Hamiltonian approach to obtain natural frequency of the nonlinear rotating pendulum. The problem has been solved without series approximation and other restrictive assumptions. Numerical simulations are then conducted to prove the efficiency of the suggested technique.

scholarly journals Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Muhammad Jamil ◽  
Asmat Ara
Keyword(s):  
Approximate Solution ◽  
Nonlinear Oscillator ◽  
High Accuracy ◽  
Force Term ◽  
Hamiltonian Approach ◽  
New Approach ◽  
Suggested Technique ◽  
Multiple Parameter ◽  
Approximate Frequency ◽  
Relationship Of

We applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). We employed this method for higher-order approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. Many numerical results are given to prove the efficiency of the suggested technique.

Modal interactions in a rotating flexible disc

2008 ◽  
Vol 223 (4) ◽  
pp. 851-857 ◽  
Author(s):  
Yong-Chen Pei ◽  
Qing-Chang Tan
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequency ◽  
Centrifugal Force ◽  
Governing Equation ◽  
Stiffness Matrix ◽  
Modal Interaction ◽  
Modal Interactions ◽  
Rotating Disc ◽  
Rotating Speed ◽  
Dynamic Investigation

This article presents a dynamic investigation on the modal interactions in a rotating flexible disc. The governing equation of the rotating flexible disc is modelled by both considering the disc as a von Kármán plate and including the initial transverse runout of the disc. When the equation is discretized by Galerkin's method, non-diagonal elements of the stiffness matrix induced by the centrifugal force of the rotating disc, which represent the modal interactions, remain. Effects of the modal interactions on natural frequency and total deflection of the disc are investigated. The investigation shows that neglecting the modal interactions should cause evident error in the dynamic analysis of rotating flexible discs. The modal interaction results in the initial transverse runout of a given mode not only affects the deflection of the mode itself but also causes the deflection of other modes with different numbers of nodal circles and becomes stronger with an increase in the disc rotating speed and the number of nodal circles.

Numerical Study for Global Detection of Cracks Embedded in Beams

1999 ◽  
Author(s):  
S. A. Lipsey ◽  
Y. W. Kwon
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Natural Frequency ◽  
Mode Shape ◽  
Numerical Study ◽  
Element Model ◽  
Mode Shapes ◽  
Linear Effect ◽  
Modes Of Vibration ◽  
Damage Simulation

Abstract Damage reduces the flexural stiffness of a structure, thereby altering its dynamic response, specifically the natural frequency, damping values, and the mode shapes associated with each natural frequency. Considerable effort has been put into obtaining a correlation between the changes in these parameters and the location and amount of the damage in beam structures. Most numerical research employed elements with reduced beam dimensions or material properties such as modulus of elasticity to simulate damage in the beam. This approach to damage simulation neglects the non-linear effect that a crack has on the different modes of vibration and their corresponding natural frequencies. In this paper, finite element modeling techniques are utilized to directly represent an embedded crack. The results of the dynamic analysis are then compared to the results of the dynamic analysis of the reduced modulus finite element model. Different modal parameters including both mode shape displacement and mode shape curvature are investigated to determine the most sensitive indicator of damage and its location.

Vibration of Bending-Torsion Coupled Resonance in a Rotor

2013 ◽  
Author(s):  
Hiroyuki Fujiwara ◽  
Tadashi Tsuji ◽  
Osami Matsushita
Keyword(s):  
Numerical Simulations ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Rotational Speed ◽  
Coupling Effect ◽  
The Other ◽  
Resonance Phenomenon ◽  
Horizontal Direction ◽  
Bending Vibration ◽  
Rotor Systems

In certain rotor systems, bending-torsion coupled resonance occurs when the rotational speed Ω (= 2π Ωrps) is equal to the sum/difference of the bending natural frequency ωb (= 2π fb) and torsional natural frequency ωθ(= 2πfθ). This coupling effect is due to an unbalance in the rotor. In order to clarify this phenomenon, an equation was derived for the motion of the bending-torsion coupled 2 DOF system, and this coupled resonance was verified by numerical simulations. In stability analyses of an undamped model, unstable rotational speed ranges were found to exist at about Ωrps = fb + fθ. The conditions for stability were also derived from an analysis of a damped model. In rotational simulations, bending-torsion coupled resonance vibration was found to occur at Ωrps = fb − fθ and fb + fθ. In addition, confirmation of this resonance phenomenon was shown by an experiment. When the rotor was excited in the horizontal direction at bending natural frequency, large torsional vibration appeared. On the other hand, when the rotor was excited by torsion at torsional natural frequency, large bending vibration appeared. Therefore, bending-torsion coupled resonance was confirmed.

Switched Model and Dynamic Analysis of a Hydroturbine Governing System in the Process of Load Rejection Transient

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Huanhuan Li ◽  
Diyi Chen ◽  
Feifei Wang ◽  
Hao Zhang
Keyword(s):  
Mathematical Model ◽  
Dynamic Analysis ◽  
Numerical Simulations ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Hydropower Station ◽  
Transfer Coefficients ◽  
Operational Conditions ◽  
Governing System ◽  
Hammer Impact

In this paper, we pay attention to studying the switched model of the hydroturbine governing system (HTGS) by introducing the concept of the switching of operational conditions. More specifically, utilizing the data of an existent hydropower station in China, we propose six nonlinear dynamic transfer coefficients of the hydroturbine, which can better describe the dynamic characteristics of the HTGS in the process of load rejection transient. Moreover, the elastic water hammer-impact of the penstock system and the nonlinearity of the generator for the process of load rejection transient are considered. Based on the combination of the different regulation modes of the governor and the corresponding running conditions of the hydroelectric generating unit, a novel nonlinear dynamic switched mathematical model of the HTGS is finally established. Meanwhile, the nonlinear dynamic behaviors of the governing system are exhaustively investigated using numerical simulations. These methods and analytical results will provide some theory bases for running a hydropower station.

Infinitely Variable Transmission of Racheting Drive Type Based on One-Way Clutches

2004 ◽  
Vol 126 (4) ◽  
pp. 673-682 ◽  
Author(s):  
F. G. Benitez ◽  
J. M. Madrigal ◽  
J. M. del Castillo
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Numerical Simulations ◽  
Mechanical Efficiency ◽  
Testing Equipment ◽  
Epicyclic Gear ◽  
The Family ◽  
Variable Transmission ◽  
Infinitely Variable Transmission ◽  
Oscillatory Character

An infinitely variable transmission (IVT), based on the use of one-way action clutches, belonging to the family of ratcheting drives is described. The mechanical foundations and numerical simulations carried out along this research envisage a plausible approach to its use as gear-box in general mechanical industry and its prospective use in automobiles and self-propelled vehicles. The system includes one-way clutches—free wheels or overrunning clutches—and two epicyclic gear systems. The output velocity, with oscillatory character, common to the ratcheting drives systems, presents a period similar to that produced by alternative combustion motors, making this transmission compatible with automobile applications. The variation of the transmission is linear in all the working range. The kinematics operating principles behind this IVT is described followed by a numerical simulation of the dynamic analysis. A prototype has been constructed and tested to assess its mechanical efficiency for different reduction ratios. The efficiency values predicted by theory agree with those experimentally obtained on a bench-rig testing equipment.

Natural Frequencies of Plate Systems using the Edge Effect Method

1967 ◽  
Vol 9 (4) ◽  
pp. 318-324 ◽  
Author(s):  
S. M. Dickinson ◽  
G. B. Warburton
Keyword(s):  
Natural Frequency ◽  
Edge Effect ◽  
Series Solution ◽  
Natural Frequencies ◽  
Rectangular Plates ◽  
Form Part ◽  
Approximate Frequency ◽  
Flexural Vibrations ◽  
Effect Method ◽  
Partial Success

In this paper the Bolotin edge effect method is used to consider the free flexural vibrations of systems built up from rectangular plates. The constituent plates of the systems are considered either to lie in the same plane and form part of a plate continuous over line supports or to lie in planes at right angles to each other, as in box constructions. The application of the edge effect method to single-and multi-plate systems is described and the approximate frequency equations for two two-plate systems are given. The first 10 natural frequency parameters for these two systems for particular side ratios are compared with those obtained using a series solution and agreement is shown to be good. A few frequency parameters for a closed box computed using the edge effect method and the series solution are also compared. The range of plate systems to which the edge effect method may be applied with complete success and the range to which it may be applied with only partial success are indicated. The sources of errors in the edge effect solutions are indicated.

Using the Characteristic Equation to Estimate the Initial Values for Numerical Forecasts

2016 ◽  
Vol 20 (7) ◽  
pp. 1147-1151
Author(s):  
Eiichi Matsunaga ◽  
◽  
Tomomasa Ohkubo
Keyword(s):  
Wave Equation ◽  
High Resolution ◽  
Numerical Simulations ◽  
Shallow Water ◽  
Characteristic Equation ◽  
Governing Equation ◽  
Water Wave ◽  
Accurate Estimation ◽  
Initial Value ◽  
Shallow Water Wave

Japan is an island nation that experiences frequent earthquakes. When an earthquake occurs, it is important to forecast its resultant tsunami: its size, location, time of arrival, etc. These forecasts are made using numerical simulations. The initial conditions are very important for numerical simulations, but the small number of tide stations makes it difficult to make highly precise forecasts. The distance between stations is normally several tens of km, and this lowers the precision of the initial data afforded by them. It is therefore common to use data interpolated from the sparse observation data at timet=0. Even so, high-resolution interpolation cannot be expected since the original data is of poor quality. In addition, the interpolated values may not be physically valid because the governing equation may not have been considered when the data were interpolated. We therefore propose a new method of estimating the initial value by using a characteristic equation. In this method, we replace the spatial resolution with time resolution. This results in a high-resolution initial value because the same place is measured more than once. In addition, the characteristic equation is based on the governing equation. Therefore, in this method, an accurate estimation of initial value is considered to be possible. In this paper, we show two applications of this approach, one for a dimensional shallow water wave equation and one for Euler’s equation. The shallow water wave equation is for the tsunami, and the Euler equation is the governing equation of the numerical weather forecast.

Dynamic Analysis and Parameter Identification of a Single Mass Elastomeric Isolation System Using a Maxwell-Voigt Model

2006 ◽  
Vol 128 (6) ◽  
pp. 713-721 ◽  
Author(s):  
Jie Zhang ◽  
Christopher M. Richards
Keyword(s):  
Parameter Identification ◽  
Dynamic Analysis ◽  
Frequency Response ◽  
Natural Frequency ◽  
Damping Ratio ◽  
Response Spectra ◽  
Isolation System ◽  
Single Mass ◽  
Voigt Model ◽  
Stiffness And Damping

Dynamic analysis and parameter identification of a single mass elastomeric isolation system represented by a Maxwell-Voigt model is examined. Influences that the stiffness and damping values of the Maxwell element have on natural frequency, damping ratio, and frequency response are uncovered and three unique categories of Maxwell-type elements are defined. It is also shown that Voigt and Maxwell-Voigt models with equivalent natural frequencies and damping ratios can have considerably different frequency response spectra. Lastly, a parameter identification method is developed for identifying Maxwell-Voigt models from frequency response spectra. The method is based on constant natural frequency and damping ratio curves generated from modal analysis of potential Maxwell-Voigt models.

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