Nonlinear Stability of a Fluid-Conveying Cantilevered Pipe With End Mass in Case of Horizontal Excitation at the Upper End

2010 ◽  
Author(s):  
Hiroaki Furuya ◽  
Kiyotaka Yamashita ◽  
Hiroshi Yabuno
Keyword(s):  
Limit Cycle ◽  
Excitation Frequency ◽  
Internal Flow ◽  
Frequency Component ◽  
Single Frequency ◽  
Dynamic Features ◽  
Cycle Frequency ◽  
Excited Vibration ◽  
Cantilevered Pipe ◽  
The Stability

Nonplanar vibrations of a cantilevered pipe with an end mass is studied. We have already clarified the nonplanar vibrations with a single frequency component when the pipe conveys fluid whose velocity is slightly over the critical value, above which the lateral vibration of the pipe is self-excited due to the internal flow. Moreover, for the case that the upper end of the pipe is excited periodically in the horizontal direction, we have shown in the previous paper that the nonplanar limit cycle motions start complex spatial transients and settle down to stationary planar forced-excited vibration when the excitation frequency is near the nonplanar limit cycle frequency. The purpose of this paper is to examine the stability of the nonplanar pipe vibrations when the nonplanar self-excited pipe vibrations are subjected to the excitation at the upper end. A set of ordinary differential equations, which govern the amplitudes and phases of unstable mode vibration and contain the effect of excitation at the upper end are derived. Stability analysis of these equations clarifies the nonlinear interactions between nonplanar self-excited pipe vibrations and the forced excitation. Second, the experiments are conducted with a silicon rubber pipe conveying water, confirming the dynamic features of pipe vibrations for the horizontal excitation.

Nonplanar Vibration of a Vertical Fluid-Conveying Pipe (Effect of Horizontal Excitation at the Upper End)

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Kiyotaka Yamashita ◽  
Hiroaki Furuya ◽  
Hiroshi Yabuno ◽  
Masatsugu Yoshizawa
Keyword(s):  
Limit Cycle ◽  
Excitation Frequency ◽  
Horizontal Direction ◽  
Pipe Conveying Fluid ◽  
Lateral Vibration ◽  
Ccd Cameras ◽  
Cycle Frequency ◽  
Excited Vibration ◽  
Nonplanar Vibration ◽  
Conveying Fluid

Nonlinear and nonplanar lateral vibration of a self-excited vertical cantilevered pipe conveying fluid is studied for the case that the upper end of the pipe is periodically excited in the horizontal direction. The modulation equations, which are coupled with nonlinear terms and govern the amplitudes and phases of nonplanar vibration, are analytically derived. When the excitation frequency is near the nonplanar limit cycle frequency, the nonplanar self-excited vibration is quenched to the excitation, and the amplitude of lateral vibration in the direction perpendicular to the horizontal excitation is decreased. Experiments were conducted and spatial pipe behaviors were observed using two CCD cameras. The theoretically predicted effects of horizontal excitation were confirmed qualitatively.

On Multiple Hopf Bifurcations of Airflow Excited Vibration of a Translating String

2007 ◽  
Author(s):  
Yuefang Wang ◽  
Lefeng Lu¨ ◽  
Yingxi Liu
Keyword(s):  
Limit Cycle ◽  
Harmonic Balance ◽  
Equilibrium Configuration ◽  
Transverse Motion ◽  
Hopf Bifurcations ◽  
Flip Bifurcation ◽  
Excited Vibration ◽  
Incremental Harmonic Balance ◽  
The Stability ◽  
Bifurcation Behavior

This paper presents the stability and bifurcation of transverse motion of translating strings excited by a steady wind flowfield. The stability of the equilibrium configuration is presented for loss of stability and generation of limit cycles via the Hopf bifurcation. It is demonstrated that there are single, double and quadruple Hopf bifurcations in the parametric space that lead to the limit cycle motion. The method of Incremental Harmonic Balance is used to solve the limit cycle response of which the stability is determined by computation of the Floquet multipliers. For the forced vibration, it is pointed out that the periodic and quasi-periodic motions exist as parameters are changed. The quench frequency and the Neimark-Sacker (NS) bifurcation and flip bifurcation are obtained. The continuity software MATCONT is adopted and the Resonance 1:1, 1:3 and 1:4 as well as NS to NS bifurcations are presented. The bifurcation behavior reveals the complexity of the string’s motion response induce by aerodynamic excitations.

Energy Harvesting Under Combined Aerodynamic and Base Excitations

2012 ◽  
Author(s):  
Amin Bibo ◽  
Mohammed F. Daqaq
Keyword(s):  
Limit Cycle ◽  
Output Voltage ◽  
Excitation Frequency ◽  
The Self ◽  
Combined Loading ◽  
Dimensional System ◽  
Base Excitation ◽  
Cycle Frequency ◽  
Center Manifold Reduction ◽  
Flutter Instability

This paper investigates the transduction of a piezoaeroelastic energy harvester under combined base and aerodynamic loadings. The harvester consists of a typical rigid airfoil supported by hardening flexural and torsional springs. The airfoil is placed in an incompressible air flow and subjected to a harmonic base excitation in the plunge direction. Considering a nonlinear quasi-steady aerodynamic model, the response behavior and electric output of the harvester are analyzed near the flutter instability. A center manifold reduction is implemented to reduce the original five-dimensional system into one nonlinear first-order ordinary differential equation. Subsequently, the normal form of the reduced system is derived to study slow modulation of the voltage amplitude and phase. Several case studies are presented indicating a considerable improvement in the output voltage of the harvester under the combined loading even when the air speed is below the flutter velocity, i.e., even when the harvester cannot maintain steady-state periodic oscillations in the absence of the harmonic base excitation. It is also shown that, when the base-excitation amplitude is sufficiently large and its frequency is close to the frequency of the self-sustained limit-cycle oscillations emanating from the flutter instability, the periodic solution resulting from the base excitation entrains the self-sustained oscillations yielding a periodic output voltage. However, when the excitation frequency is far from the limit-cycle frequency, or the amplitude of base excitation is small, the voltage is two-period quasiperiodic.

DEVELOPMENT OF THE BASIC CRITERIA FOR RUSSIAN COASTS TYPIFICATION

2017 ◽  
Author(s):  
Рубен Косян ◽  
Ruben Kosyan ◽  
Viacheslav Krylenko ◽  
Viacheslav Krylenko
Keyword(s):  
Coastal Zone ◽  
Coastal Area ◽  
Economic Activity ◽  
Basic Information ◽  
Dynamic Features ◽  
Static State ◽  
Evolutionary Features ◽  
Coastal Features ◽  
The Stability

There are many types of coasts classifications that indicate main coastal features. As a rule, the "static" state of the coasts is considered regardless of their evolutionary features and ways to further transformation. Since the most part of the coastal zone studies aimed at ensuring of economic activity, it is clear that the classification of coast types should indicate total information required by the users. Accordingly, the coast classification should include the criterion, characterizing as dynamic features of the coast and the conditions and opportunities of economic activity. The coast classification, of course, should be based on geomorphological coast typification. Similar typification has been developed by leading scientists from Russia and can be used with minimal modifications. The authors propose to add to basic information (geomorphological type of coast) the evaluative part for each coast sector. It will include the estimation of the coast changes probability and the complexity of the coast stabilization for economic activity. This method will allow to assess the dynamics of specific coastal sections and the processes intensity and, as a result – the stability of the coastal area.

Study on Self-Excited Vibration Mechanism of Wheel-Rail Lateral Contact System

2013 ◽  
Vol 427-429 ◽  
pp. 257-261
Author(s):  
Li Xia Sun ◽  
Jian Wei Yao ◽  
Fu Guo Hou ◽  
Xin Zhao
Keyword(s):  
Feedback Mechanism ◽  
Point Of View ◽  
Contact System ◽  
Vibration System ◽  
Lateral Contact ◽  
System A ◽  
Vibration Model ◽  
Excited Vibration ◽  
Vibration Mechanism ◽  
The Stability

In order to investigate self-excited vibration mechanism of wheel-rail lateral contact system, a two DOF elasticity position wheelset lateral vibration model is established which considers the dry friction; the mechanism of the wheelset lateral self-excited vibration is investigated from the energy point of view. It shows that: the bifurcation diagram of this wheel-rail lateral contact system has a supercritical Hopf bifurcation. The energy of self-excited vibration derives from a part of traction energy; the creep rate in the wheel-rail system act as a feedback mechanism in the wheelset lateral self-excited vibration system. The stability of the wheelset self-excited vibration system depends mainly on the total energy removed from and imported into the system.

Numerical Investigation of the Influence of Friction Coefficient on Brake Groan

2010 ◽  
Vol 44-47 ◽  
pp. 1923-1927 ◽  
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Friction Coefficient ◽  
Degrees Of Freedom ◽  
Equilibrium Points ◽  
Static Friction ◽  
Kinetic Friction ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model ◽  
The Stability

A two degrees of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction of brake disk and pads is built firstly, the stability of vibration system at the equilibrium points is analyzed using the nonlinear dynamics theory. Finally the numerical method is taken to study the impacts of friction coefficient on brake groan. The calculation result shows that with the increase of kinetic friction coefficient /or the decrease of difference value between static friction coefficient and kinetic friction coefficient can prevent or restrain self-excited vibration from happening.

scholarly journals STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD

2020 ◽  
Vol 2 (1) ◽  
pp. 27-31
Author(s):  
Abdulghafoor Jasim Salim ◽  
Kais Ismail Ebrahem ◽  
Suhirman
Keyword(s):  
Singular Point ◽  
Limit Cycle ◽  
Autoregressive Model ◽  
Stable Limit Cycle ◽  
Linearization Method ◽  
Stable Limit ◽  
Local Linearization ◽  
Non Linear ◽  
The Stability ◽  
Local Linearization Method

Abstract: In this paper we study the stability of one of a non linear autoregressive model with trigonometric term  by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude  that the proposed model under certain conditions have a non-zero singular point which is  a asymptotically salable ( when  0 ) and have an  orbitaly stable limit cycle . Also we give some examples in order to explain the method. Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.

scholarly journals Investigating the effect of vibration on the stability of the three-wheeled scooter taxi

2021 ◽  
Vol 39 (4) ◽  
pp. 1117-1122
Author(s):  
S.J. Ojolo ◽  
O.O. Ajayi ◽  
G.A. Asuelinmen
Keyword(s):  
Excitation Frequency ◽  
Vehicle Safety ◽  
Asian Countries ◽  
Wheeled Vehicle ◽  
Safety Margins ◽  
Schematic Layout ◽  
Analysis Design ◽  
The Stability ◽  
The Impact ◽  
Selection Of

The present three wheeled scooter taxi (TWST) that are widespread in Africa and Asian Countries are fuel economical and inexpensive. However, they are unstable due to their schematic layout. This instability places limitation on the usage of the vehicle. Researchers have investigated the rollover and lateral stabilities of this vehicle, including the effect of vibration on the comfort of the riders. However, not much work has been done on the impact of vibration on the stability of the vehicle. These instabilities could be induced by trenches, potholes, uneven and ungraded roads that are prevalent in developing countries. Therefore, this work modelled and analysed the effect of vibration on a TWST using a standard road bump as reference point. The results proved the vehicle to be unstable in the vicinity of excitation frequency of 15.95rad/sec and spring constant of 68,600N/m due to resonance. This would affect safety of life and property. Therefore, it would be appropriate for some of the manufacturers of these vehicles to provide for enough safety margins in the design and selection of springs where the vehicles are rollover and laterally unstable. This will enhance the vehicle safety and receptivity. Keywords: Three wheeled Vehicle, Vibration Modelling and Analysis, Design, Safety of Life and Property

THE INFLUENCES OF TEMPERATURE AND CHAIN–CHAIN INTERACTION ON FEATURES OF SOLITONS EXCITED IN α-HELIX PROTEIN MOLECULES WITH THREE CHANNELS

2009 ◽  
Vol 23 (10) ◽  
pp. 2303-2322 ◽  
Author(s):  
XIAO-FENG PANG ◽  
MEI-JIE LIU
Keyword(s):  
Energy Transport ◽  
Initial Conditions ◽  
Dynamic Features ◽  
New Model ◽  
Protein Molecules ◽  
Long Time ◽  
The Stability ◽  
Α Helix ◽  
Increasing Temperature ◽  
Chain Interaction

The dynamic features of soliton transporting the bio-energy in the α-helix protein molecules with three channels under influences of temperature of systems and chain–chain interaction among these channels have been numerically studied by using the dynamic equations in a new model and the fourth-order Runge–Kutta method. This result obtained shows that the chain–chain interaction depresses the stability of the soliton due to the dispersed effect, but the stability of the soliton in the case of simultaneous motivation of three channels by an initial conditions is better than that in another initial condition. We also find from this investigation that the new soliton can transport steadily over 1000 amino acid residues in the cases of motion of long time of 120 ps, and retain their shapes and energies to travel towards the protein molecules after mutual collision of the solitons at the biological temperatures of 300 K. Therefore the soliton is very robust against the thermal perturbation of the α-helix protein molecules at 300 K. From the investigation of changes of features of the soliton with increasing temperature, we find that the amplitudes and velocities of the solitons decrease with increasing temperature of proteins, but the soliton disperses in the cases of higher temperature of 325 K and larger structure disorders. Thus we find that the critical temperature of the soliton occurring in the α-helix protein molecules is about 320 K. Therefore we can conclude that the soliton in the new model can play an important role in the bio-energy transport in the α-helix protein molecules with three channels at biological temperature, and the new model is possibly a candidate for the mechanism of this transport.

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