Parametric Resonance Oscillations of Flexible Slender Cylinders in Harmonically Perturbed Axial Flow—Part 2: Experiments

1980 ◽  
Vol 47 (4) ◽  
pp. 715-719 ◽  
Author(s):  
M. P. Paidoussis ◽  
N. T. Issid ◽  
M. Tsui
Keyword(s):  
Flow Velocity ◽  
Parametric Resonance ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Primary Resonance ◽  
Second Mode ◽  
Flow Part ◽  
Resonance Oscillations

This paper examines experimentally the dynamical behavior of a flexible slender cylinder in axial flow, perturbed harmonically in time. Parametric resonance oscillations were found to exist over certain ranges of frequencies and amplitudes of flow-velocity perturbations. The most prominent of the resonances, in these experiments, were associated with the second-mode principal primary resonance, and were studied extensively. Agreement with theory was found to be quite good.

Parametric Resonance Oscillations of Flexible Slender Cylinders in Harmonically Perturbed Axial Flow—Part 1: Theory

1980 ◽  
Vol 47 (4) ◽  
pp. 709-714 ◽  
Author(s):  
M. P. Paidoussis ◽  
N. T. Issid ◽  
M. Tsui
Keyword(s):  
Boundary Conditions ◽  
Flow Velocity ◽  
Dynamical Behavior ◽  
Parametric Instability ◽  
Axial Flow ◽  
Mean Flow ◽  
Parametric Resonances ◽  
Flow Part ◽  
The Mean ◽  
Resonance Oscillations

This paper studies theoretically the dynamical behavior of a flexible slender cylinder in pulsating axial flow. The dynamics of the system in steady, unperturbed flow are examined first. For various sets of boundary conditions the eigenfrequencies of the system at any given flow velocity are determined, and the critical flow velocities are established, beyond which buckling (divergence) would occur. The behavior of the system in pulsating flow is examined next, establishing the existence of parametric resonances. The effects of the mean flow velocity, boundary conditions, dissipative forces, and virtual (hydrodynamic) mass on the extent of the parametric instability zones are then discussed.

Nonlinear Dynamics of a Slender Flexible Cylinder in Axial Flow

2011 ◽  
Vol 130-134 ◽  
pp. 761-765
Author(s):  
Ji Duo Jin ◽  
N. Li ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Flow Velocity ◽  
Nonlinear Model ◽  
Dynamic Instability ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Viscous Force ◽  
Flexible Cylinder ◽  
Flutter Instability ◽  
The Stability

The stability and nonlinear dynamics are studied for a slender flexible cylinder subjected to axial flow. A nonlinear model is presented, based on the corresponding linear equation of motion, for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the additional axial force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain, with this relatively simple nonlinear model, the flutter instability found in experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the buckled configuration becomes unstable at higher flow leading to post-divergence flutter. As the flow velocity increases further, the system is restabilized in the buckled configuration prior to another dynamic instability at higher flow.

Nonlinear Dynamics of Supported Cylinder Subjected to Axial Flow

2011 ◽  
Vol 243-249 ◽  
pp. 4712-4717
Author(s):  
Ji Duo Jin ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Flow Velocity ◽  
Nonlinear Model ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Equation Of Motion ◽  
Flexible Cylinder ◽  
Chaotic Motions ◽  
Flutter Instability ◽  
The Stability

In this paper, the stability and nonlinear dynamics are studied for a slender flexible cylinder subjected to axial flow. A nonlinear model is presented, based on the corresponding linear equation of motion, for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are only the additional axial force induced by the lateral motions of the cylinder. Using six-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain, with this relatively simple nonlinear model, the flutter instability found in experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. As the flow velocity increases further, the quasiperiodic motion around the buckled position occurs, and this evolves into chaotic motions at higher flow.

Flow through axial-flow-turbomachinery blading

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Flow Velocity ◽  
Compressible Flow ◽  
Dimensional Analysis ◽  
Incompressible Flow ◽  
Compressible Fluid ◽  
Axial Flow ◽  
Linear Cascade ◽  
Dimensional Parameters ◽  
Flow Through

This chapter is concerned primarily with the flow of a compressible fluid through stationary and moving blading, for the most part using the analysis introduced in Chapter 11. The principles of dimensional analysis are applied to determine the appropriate non-dimensional parameters to characterise the performance of a turbomachine. The analysis of incompressible flow through a linear cascade of aerofoil-like blades is followed by the analysis of compressible flow. Velocity triangles for flow relative to blades, and Euler’s turbomachinery equation, are introduced to analyse flow through a rotor. The concepts introduced are applied to the analysis of an axial-turbomachine stage comprising a stator and a rotor, which applies to either a compressor or a turbine.

Dynamics of a Supported Cylinder in Axial Flow

2011 ◽  
Vol 99-100 ◽  
pp. 1059-1062
Author(s):  
Ji Duo Jin ◽  
Ning Li ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Analysis ◽  
Numerical Simulations ◽  
Nonlinear Model ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Viscous Force ◽  
Friction Drag ◽  
Flutter Instability ◽  
Nonlinear Force

The nonlinear dynamics are studied for a supported cylinder subjected to axial flow. A nonlinear model is presented for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the structural nonlinear force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain the flutter instability found in the experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. The effect of the friction drag coefficients on the behavior of the system is investigated.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

2009 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis ◽  
Fadi M. Alsaleem ◽  
Ronald Miles ◽  
Weili Cui
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Model Equations

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

LINEAR AND NONLINEAR DYNAMICS OF CANTILEVERED CYLINDERS IN AXIAL FLOW. PART 3: NONLINEAR DYNAMICS

2002 ◽  
Vol 16 (6) ◽  
pp. 739-759 ◽  
Author(s):  
C. SEMLER ◽  
J.L. LOPES ◽  
N. AUGU ◽  
M.P. PAÏDOUSSIS
Keyword(s):  
Nonlinear Dynamics ◽  
Axial Flow ◽  
Flow Part ◽  
Linear And Nonlinear

Analysis of Parametric Resonances in In-Plane Vibrations of Electrostrictive Hyperelastic Plates

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Electric Field ◽  
Parametric Resonance ◽  
Mechanical Response ◽  
Element Model ◽  
Mode Shapes ◽  
Principal Parametric Resonance ◽  
Parametric Resonances ◽  
Second Mode ◽  
Electrostrictive Polymer ◽  
Large Amplitude Vibrations

Electrostriction is a recent actuation mechanism which is being explored for a variety of new micro- and millimeter scale devices along with macroscale applications such as artificial muscles. The general characteristics of these materials and the nature of actuation lend itself to possible production of very rich nonlinear dynamic behavior. In this work, principal parametric resonance of the second mode in in-plane vibrations of appropriately designed electrostrictive plates is investigated. The plates are made of an electrostrictive polymer whose mechanical response can be approximated by Mooney Rivlin model, and the induced strain is assumed to have quadratic dependence on the applied electric field. A finite element model (FEM) formulation is used to develop mode shapes of the linearized structure whose lowest two natural frequencies are designed to be close to be in 1:2 ratio. Using these two structural modes and the complete Lagrangian, a nonlinear two-mode model of the electrostrictive plate structure is developed. Application of a harmonic electric field results in in-plane parametric oscillations. The nonlinear response of the structure is studied using averaging on the two-mode model. The structure exhibits 1:2 internal resonance and large amplitude vibrations through the route of parametric excitation. The principal parametric resonance of the second mode is investigated in detail, and the time response of the averaged system is also computed at few frequencies to demonstrate stability of branches. Some results for the case of principal parametric resonance of the first mode are also presented.

scholarly journals Normal forces exerted upon a long cylinder oscillating in an axial flow

2014 ◽  
Vol 752 ◽  
pp. 649-669 ◽  
Author(s):  
L. Divaret ◽  
O. Cadot ◽  
P. Moussou ◽  
O. Doaré
Keyword(s):  
Flow Velocity ◽  
Normal Force ◽  
Pressure Coefficient ◽  
Axial Flow ◽  
Fluid Forces ◽  
Normal Forces ◽  
Pressure Distributions ◽  
Damping Rate ◽  
Static Approach ◽  
Yaw Angle

AbstractThis work aims to improve understanding of the damping induced by an axial flow on a rigid cylinder undergoing small lateral oscillations within the framework of the quasistatic assumption. The study focuses on the normal force exerted on the cylinder for a Reynolds number of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}=24\, 000$ (based on the cylinder diameter and axial flow velocity). Both dynamic and static approaches are investigated. With the static approach, fluid forces, pressure distributions and velocity fields are measured for different yaw angles and cylinder lengths in a wind tunnel. It is found that for yaw angles smaller than $5{^\circ }$, the normal force varies linearly with the angle and is fully dominated by its lift component. The lift originates from the high pressure coefficient at the front of the cylinder, which is found to depend linearly on the angle, and from a base pressure coefficient that remains close to zero independent of the yaw angle. At the base, a flow deficit and two counter-rotating vortices are observed. A numerical simulation using a $k\mbox{--}\omega $ shear stress transport turbulence model confirms the static experimental results. A dynamic experiment conducted in a water tunnel brings out damping-rate values during free oscillations of the cylinder. As expected from the linear dependence of the normal force on the yaw angle observed with the static approach, the damping rate increases linearly with the axial flow velocity. Satisfactory agreement is found between the two approaches.

Experimental Investigation of the Flow-Induced Vibrations of a Rod Cluster Control Assembly Inside Guides With Enlarged Gaps

2019 ◽  
Author(s):  
Pierre Moussou ◽  
Vincent Fichet ◽  
Luc Pastur ◽  
Constance Duhamel ◽  
Yannick Tampango
Keyword(s):  
Experimental Investigation ◽  
Flow Velocity ◽  
Nuclear Power ◽  
Axial Flow ◽  
Fretting Wear ◽  
Pressurized Water Reactor ◽  
Test Rig ◽  
Pressurized Water ◽  
Control Assembly ◽  
Control Rods

Abstract In order to better understand the mechanisms of fretting wear damage of guide cards in some Pressurized Water Reactor (PWR) Nuclear Power Plant (NPP), an experimental investigation is undertaken at the Magaly facility in Le Creusot. The test rig consists of a complete Rod Cluster with eleven Guide Cards, submitted to axial flow inside a water tunnel. In order to mimic the effect of fretting wear, the four lower guide cards have enlarged gaps, so that the Control Rods are free to oscillate. The test rig is operated at ambient temperature and pressure, and Plexiglas walls can be arranged along its upper part, and a series of camera records the vibrations of the control rods above and below the guide cards. The vertical flow velocity is in the range of a few m/s. Beam-like pinned-pinned modes at about 5 Hz are observed, and oscillations of several mm of the central rods are measured, which come along with impacts at the higher flow velocities. A simple non-linear calculation reveals that the main effect of the impacts between Control Rods and Guide Cards is an increase of the natural frequency of the rods by about 10%. Furthermore, as the vibration spectra collapse remarkably well with the flow velocity, the experiments prove that turbulent forcing is responsible for the large oscillations of the control rods, no other mechanism being involved.

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