scholarly journals Characteristic Analysis of longitudinal vibration Sucker Rod String With Variable Equivalent Stiffness

2018 ◽  
Vol 153 ◽  
pp. 06009 ◽  
Author(s):  
Jian Lv ◽  
Mingming Xing
Keyword(s):  
Longitudinal Vibration ◽  
Step Function ◽  
Load Force ◽  
System Response ◽  
Equivalent Stiffness ◽  
Function Form ◽  
Characteristic Analysis ◽  
Response Curves ◽  
Sucker Rod ◽  
Force Excitation

Considering the influence of variable equivalent stiffness on system response, the equivalent stiffness is defined as a step function, and a mathematical model of nonlinear longitudinal vibration of sucker rod string (SRS) is built. The dynamic response under displacement and load force excitation is solved by fourth-order Runge-Kutta method with zero initial condition. The results show the steady-state responses under the displacement and load force excitation of different function forms are different. The response curves of both displacement and velocity under the displacement and load force excitation of cosine function form have larger fluctuation than it under the displacement and load force excitation of sine function form. Therefore, the characteristic analysis of SRS plays an important role in understanding the influence of the excitation form and sensitive parameters on steady response.

Second Order Averaging Study of an Autoparametric System

1993 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Dynamical Behavior ◽  
Period Doubling ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Pitchfork Bifurcation ◽  
Second Order ◽  
System Response ◽  
Response Curves ◽  
Vibratory System ◽  
First Order

Abstract The autoparametric vibratory system consisting of a primary spring-mass-dashpot system coupled with a damped simple pendulum serves as an useful example of two degree-of-freedom nonlinear systems that exhibit complex dynamic behavior. It exhibits 1:2 internal resonance and amplitude modulated chaos under harmonic forcing conditions. First-order averaging studies of this system using AUTO and KAOS have yielded useful information about the amplitude dynamics of this system. Response curves of the system indicate saturation and the pitchfork bifurcation sets are found to be symmetric. The period-doubling route to chaotic solutions is observed. However questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid cannot be answered by a first-order study. Some observed dynamical behavior, like saturation, may not persist when higher-order nonlinear effects are taken into account. Second-order averaging of the system, using Mathematica (Maeder, 1991; Wolfram, 1991) is undertaken to address these questions. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. The dynamics of the system is found to be very sensitive to damping, with extremely complicated behavior arising for low values of damping. For large ε second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response.

Calculation of Load and Stroke in Oil-Well Pump Rods

1943 ◽  
Vol 10 (1) ◽  
pp. A1-A12
Author(s):  
B. F. Langer ◽  
E. H. Lamberger
Keyword(s):  
Longitudinal Vibration ◽  
Oil Wells ◽  
Oil Well ◽  
Test Results ◽  
Sucker Rod ◽  
Sucker Rod Pump ◽  
Polished Rod

Abstract The sucker-rod pump as used in oil wells is treated as a problem in the longitudinal vibration of bars. Solutions are obtained for the forces and motions at both ends of the rod string, thus giving formulas for the calculation of polished-rod load and plunger travel. The results of the calculations are compared with test results.

Analysis of Free Nonlinear Vibration Behavior for Curved Embedded Carbon Nanotubes on Elastic Foundation

2010 ◽  
Author(s):  
M. Rezaee ◽  
H. Fekrmandi
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Behavior ◽  
Continuum Mechanics ◽  
Nonlinear Term ◽  
Nonlinear Oscillations ◽  
Equation Of Motion ◽  
System Response ◽  
Response Curves ◽  
Vibration Behavior ◽  
The Continuum

Carbon nanotubes (CNTs) are expected to have significant impact on several emerging nanoelectromechanical (NEMS) applications. Vigorous understanding of the dynamic behavior of CNTs is essential for designing novel nanodevices. Recent literature show an increased utilization of models based on elastic continuum mechanics theories for studying the vibration behavior of CNTs. The importance of the continuum models stems from two points; (i) continuum simulations consume much less computational effort than the molecular dynamics simulations, and (ii) predicting nanostructures behavior through continuum simulation is much cheaper than studying their behavior through experimental verification. In numerous recent papers, CNTs were assumed to behave as perfectly straight beams or straight cylindrical shells. However, images taken by transmission electron microscopes for CNTs show that these tiny structures are not usually straight, but rather have certain degree of curvature or waviness along the nanotubes length. The curved morphology is due to process-induced waviness during manufacturing processes, in addition to mechanical properties such as low bending stiffness and large aspect ratio. In this study the free nonlinear oscillations of wavy embedded multi-wall carbon nanotubes (MWCNTs) are investigated. The problem is formulated on the basis of the continuum mechanics theory and the waviness of the MWCNTs is modeled as a sinusoidal curve. The governing equation of motion is derived by using the Hamilton’s principle. The Galerkin approach was utilized to reduce the equation of motion to a second order nonlinear differential equation which involves a quadratic nonlinear term due to the curved geometry of the beam, and a cubic nonlinear term due to the stretching effect. The system response has been obtained using the incremental harmonic balanced method (IHBM). Using this method, the iterative relations describing the interaction between the amplitude and the frequency for the single-wall nanotube and double-wall nanotube are obtained. Also, the influence of the waviness, elastic medium and van der Waals forces on frequency-response curves is researched. Results present some useful information to analyze CNT’s nonlinear dynamic behavior.

scholarly journals Modelling of Electro-mechanical Servo System Based on the Planetary Roller Screw Mechanism

2020 ◽  
Vol 306 ◽  
pp. 02004
Author(s):  
Jianxin Zhang ◽  
Chuanming Du ◽  
Shangjun Ma ◽  
Geng Liu
Keyword(s):  
Contact Stiffness ◽  
Servo System ◽  
Response Speed ◽  
Load Force ◽  
System Response ◽  
Analysis Model ◽  
Roller Screw ◽  
Fluctuation Amplitude ◽  
Screw Mechanism ◽  
Main Components

Taking the electro-mechanical servo system as the research object, considering the contact stiffness, friction and clearance of the main components in the electro-mechanical servo system, the analysis model of the electro-mechanical servo system based on Planetary roller screw mechanism (PRSM) is established by using AMESim software. The results showed that the response speed of the system slowed down when the friction of PRSM was taken into account. The larger the clearance or the smaller the stiffness, the greater the fluctuation amplitude of the system response. After the controller was adjusted, the steady-state error of the system caused by the load force can be reduced quickly.

Variational Modal Identification of Conservative Nongyroscopic Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 160-171 ◽  
Author(s):  
L. Silverberg ◽  
S. Kang
Keyword(s):  
Longitudinal Vibration ◽  
Modal Identification ◽  
System Response ◽  
Bending Vibration ◽  
Free System ◽  
Dirac Delta ◽  
Vibration Problem ◽  
Identification Method ◽  
Delta Functions ◽  
Admissible Functions

A new modal identification method for Conservative Nongyroscopic Systems is proposed. The modal identification method is formulated as a variational problem in which stationary values of a functional quotient are sought. The computation of the functional quotient is carried out using a set of admissible functions defined over the spatial domain of the system. Measurements of the free system response at discrete points are carried out using any combination of displacements, velocities, and/or accelerations. Three types of admissible functions have been considered—global functions, spatial Dirac-delta functions, and finite element interpolation functions. The variational modal identification method is applied to a pure bending vibration problem, to a pure longitudinal vibration problem, and to a combined bending and longitudinal vibration problem. The effectiveness of the variational modal identification method using different sets of admissible functions is examined.

Intrinsic Localized Modes of Harmonic Oscillations in Pendulum-Arrays Subjected to Horizontal Excitation

2013 ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Keisuke Nishimura
Keyword(s):  
Theoretical Analysis ◽  
Frequency Response ◽  
Excitation Frequency ◽  
System Response ◽  
Stable Steady State ◽  
Frequency Range ◽  
Localized Modes ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Intrinsic Localized Modes

The behavior of intrinsic localized modes (ILMs) is investigated for an array with N pendula which are connected with each other by weak, linear springs when the array is subjected to horizontal, sinusoidal excitation. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves are presented for N = 2 and 3 and compared with the results of the numerical simulations. Patterns of oscillations are classified according to the stable steady-state solutions of the response curves, and the patterns in which ILMs appear are discussed in detail. The influence of the connecting springs of the pendula on the appearance of ILMs is examined. Increasing the values of the connecting spring constants may affect the excitation frequency range of ILMs and cause Hopf bifurcation to occur, followed by amplitude modulated motions (AMMs) including chaotic vibrations. The influence of the imperfections of the pendula on the system response is also investigated. Bifurcation sets are calculated to examine the influence of the system parameters on the excitation frequency range of ILMs and determine the threshold value for the connecting spring constant after which ILMs do not appear. Experiments were conducted for N = 2, and the data were compared with the theoretical results in order to confirm the validity of the theoretical analysis.

OTEC Plant Response and Control Analysis

1982 ◽  
Vol 104 (3) ◽  
pp. 208-215 ◽  
Author(s):  
W. L. Owens
Keyword(s):  
Nonlinear Differential Equations ◽  
System Response ◽  
Small Scale ◽  
Control Analysis ◽  
Plant Design ◽  
Operational Control ◽  
Response Curves ◽  
Control Schemes ◽  
Mass Flow Rates ◽  
And Control

An analysis is presented which allows prediction of closed-cycle OTEC power plant system response and control. Two basic operational control schemes are presented, which are primarily related to the type of seawater pumps employed. Variable flow seawater pumps allow optimization of the OTEC thermal-cycle state points for maximization of net generated power. Constant flow pumps are cheaper and simpler, but do not allow direct control over the evaporator and condenser operating temperatures. A system of nonlinear differential equations representing the basic elements of a constant seawater flow OTEC plant with turbine bypass flow control has been formulated for computer solution. Typical normalized response curves are presented for pressures, temperatures, mass flow rates, and generator speed for a small-scale, 50-kW OTEC plant design.

Vibration Control of Horizontally Excited Structures Utilizing Internal Resonance of Liquid Sloshing in Nearly Square Tanks

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Passive Control ◽  
Harmonic Excitation ◽  
Liquid Sloshing ◽  
Maximum Efficiency ◽  
System Response ◽  
Response Curves ◽  
System Parameters ◽  
Theoretical Results

Passive control of vibrations in an elastic structure subjected to horizontal, harmonic excitation by utilizing a nearly square liquid tank is investigated. When the natural frequency ratio 1:1:1 is satisfied among the natural frequencies of the structure and the two predominant sloshing modes (1,0) and (0,1), the performance of a nearly square tank as a tuned liquid damper (TLD) is expected to be superior to rectangular TLDs due to internal resonance. In the theoretical analysis, Galerkin's method is used to determine the modal equations of motion for liquid sloshing considering the nonlinearity of sloshing. Then, van der Pol's method is used to obtain the expressions for the frequency response curves for the structure and sloshing modes. Frequency response curves and bifurcation set diagrams are shown to investigate the influences of the aspect ratio of the tank cross section and the tank installation angle on the system response. From the theoretical results, the optimal values of the system parameters can be determined in order to achieve maximum efficiency of vibration suppression for the structure. Hopf bifurcations occur and amplitude modulated motions (AMMs) may appear depending on the values of the system parameters. Experiments were also conducted, and the theoretical results agreed well with the experimental data.

Investigation of the nonlinear phenomena of a Langevin ultrasonic transducer caused by high applied voltage

2021 ◽  
pp. 095440622110093 ◽  
Author(s):  
Shibo Zhang ◽  
Yang Li ◽  
Sisi Li ◽  
Yongbo Wu ◽  
Jiang Zeng
Keyword(s):  
Nonlinear Model ◽  
Longitudinal Vibration ◽  
Ultrasonic Transducer ◽  
Linear Functions ◽  
Vibration Velocity ◽  
System Response ◽  
Nonlinear Phenomena ◽  
Amplitude Curve ◽  
Nonlinear Phenomenon ◽  
Physical Point

In the field of power ultrasound, Langevin ultrasonic transducers (LUTs) usually operate at a large displacements output power by applying high voltages. However, empirically, a LUT exhibits nonlinearities such as amplitude jumping and peak hysteresis for high voltages in actual operations. The nonlinearities would reduce the efficiency and output accuracy of an LUT. In this research, the burst-mode method was used to measure the longitudinal vibration velocity of the LUT, which gradually decreased with time after the excitation voltage was turned off. The equivalent mechanical losses and equivalent spring constants were determined using the velocity attenuation rate and resonant frequency and they were found to be the linear functions of velocity, helping to develop a novel nonlinear model. This model contained two quadratic nonlinear terms based on the linear model. Furthermore, the developed nonlinear model was analyzed using the Lagrangian method as well as the multiscale method, which confirmed that the model was effective in describing the nonlinear behavior. It was also found that the frequency-amplitude curve bent when the nonlinear term was taken into account, which resembled the nonlinear phenomenon tested experimentally. From a physical point of view, this bending was meaningful because it led to the formation of multi-valued response regions with jumping phenomena. Additionally, according to the obtained results, the maximum value of the system response was independent of the degree of nonlinearity of the system.

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