Dynamic Stability of Poroelastic Columns

1999 ◽  
Vol 67 (2) ◽  
pp. 360-362 ◽  
Author(s):  
G. Cederbaum
Keyword(s):  
Dynamic Stability ◽  
Multiple Scales ◽  
Transversely Isotropic ◽  
Axial Direction ◽  
Periodic Force ◽  
Stability Boundaries ◽  
Coupled Equations ◽  
Column Material ◽  
The Stability ◽  
Fluid Diffusion

The dynamic stability of a poroelastic column subjected to a longitudinal periodic force is investigated. The column material is assumed to be transversely isotropic with respect to the column axis, and the pore fluid flow is possible in the axial direction only. The motion of the column is governed by two coupled equations, for which the stability boundaries are determined analytically by using the multiple-scales method. It is shown that due to the fluid diffusion the stability regions are expanded, relative to the elastic (drained) case. The critical (minimum) loading amplitude, for which instability occurs, is also given. [S0021-8936(00)00902-8]

Dynamic Stability of a Spinning Timoshenko Beam Subjected to a Moving Mass-Spring-Damper Unit

2010 ◽  
Author(s):  
T. H. Young ◽  
M. S. Chen
Keyword(s):  
Dynamic Stability ◽  
Timoshenko Beam ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Longitudinal Axis ◽  
Moving Mass ◽  
The Stability ◽  
The Galerkin Method ◽  
Mass Spring

This paper investigates the dynamic stability of a finite Timoshenko beam spinning along its longitudinal axis and subjected to a moving mass-spring-damper (MSD) unit traveling in the axial direction. The mass of the moving MSD unit makes contact with the beam all the time during traveling. Due to the moving MSD unit, the beam is acted upon by a periodic, parametric excitation. In this work, the equations of motion of the beam are first discretized by the Galerkin method. The discretized equations of motion are then partially uncoupled by the modal analysis procedure suitable for gyroscopic systems. Finally the method of multiple scales is used to obtain the stability boundaries of the beam. Numerical results show that if the displacement of the MSD unit is equal to only one of the two transverse displacements of the beam, very large unstable regions may appear at main resonances.

Parametric Stability of Axially Accelerating Viscoelastic Beams With the Recognition of Longitudinally Varying Tensions

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Li-Qun Chen ◽  
You-Qi Tang
Keyword(s):  
Governing Equation ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Finite Support ◽  
Governing Equations ◽  
Parametric Stability ◽  
Stability Boundaries ◽  
Axial Acceleration ◽  
The Stability ◽  
Longitudinally Varying Tension

In this paper, the parametric stability of axially accelerating viscoelastic beams is revisited. The effects of the longitudinally varying tension due to the axial acceleration are highlighted, while the tension was approximately assumed to be longitudinally uniform in previous studies. The dependence of the tension on the finite support rigidity is also considered. The generalized Hamilton principle and the Kelvin viscoelastic constitutive relation are applied to establish the governing equations and the associated boundary conditions for coupled planar motion of the beam. The governing equations are linearized into the governing equation in the transverse direction and the expression of the longitudinally varying tension. The method of multiple scales is employed to analyze the parametric stability of transverse motion. The stability boundaries are derived from the solvability conditions and the Routh-Hurwitz criterion for principal and sum resonances. In terms of stability boundaries, the governing equations with or without the longitudinal variance of tension are compared and the effects of the finite support rigidity are also examined. Some numerical examples are presented to demonstrate the effects of the stiffness, the viscosity, and the mean axial speed on the stability boundaries. The differential quadrature scheme is developed to numerically solve the governing equation, and the computational results confirm the outcomes of the method of multiple scales.

Dynamic Stability of a Rotor Filled or Partially Filled With Liquid

1996 ◽  
Vol 63 (1) ◽  
pp. 101-105 ◽  
Author(s):  
Wen Zhang ◽  
Jiong Tang ◽  
Mingde Tao
Keyword(s):  
Dynamic Stability ◽  
Dynamic Pressure ◽  
Flow Analysis ◽  
Previous Literature ◽  
Stability Criteria ◽  
Stability Boundaries ◽  
Planar Flow ◽  
Harmonic Motion ◽  
Analytical Stability ◽  
The Stability

The dynamic stability of a high-spinning liquid-filled rotor with both internal and external damping effects involved in is investigated in this paper. First, in the case of the rotor subjected to a transverse harmonic motion, the dynamic pressure of the liquid acting on the rotor is extracted through a planar flow analysis. Then the equation of perturbed motion for the liquid-filled rotor is derived. The analytical stability criteria as well as the stability boundaries are given. The results are extensions of those given by previous literature.

Determining Stability Boundaries Using Gyroscopic Eigenfunctions

2003 ◽  
Vol 125 (3) ◽  
pp. 405-407 ◽  
Author(s):  
Anthony A. Renshaw
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Stability Boundaries ◽  
Parametrically Excited ◽  
The Stability ◽  
Simplified Procedure ◽  
Gyroscopic Systems

By taking advantage of modal decoupling and reduction of order, we derive a simplified procedure for applying the method of multiple scales to determine the stability boundaries of parametrically excited, gyroscopic systems. The analytic advantages of the procedure are illustrated with three examples.

Dynamic Stability of Disks With Periodically Varying Spin Rates Subjected to Stationary In-Plane Edge Loads

2004 ◽  
Vol 71 (4) ◽  
pp. 450-458 ◽  
Author(s):  
T. H. Young ◽  
M. Y. Wu
Keyword(s):  
Dynamic Stability ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Parametric Instability ◽  
Stress Distributions ◽  
The Finite Element Method ◽  
Nodal Diameter ◽  
The Stability ◽  
Small Periodic ◽  
Small Periodic Perturbation

This paper presents an analysis of dynamic stability of an annular plate with a periodically varying spin rate subjected to a stationary in-plane edge load. The spin rate of the plate is characterized as the sum of a constant speed and a small, periodic perturbation. Due to this periodically varying spin rate, the plate may bring about parametric instability. In this work, the initial stress distributions caused by the periodically varying spin rate and the in-plane edge load are analyzed first. The finite element method is applied then to yield the discretized equations of motion. Finally, the method of multiple scales is adopted to determine the stability boundaries of the system. Numerical results show that combination resonances take place only between modes of the same nodal diameter if the stationary in-plane edge load is absent. However, there are additional combination resonances between modes of different nodal diameters if the stationary in-plane edge load is present.

Experimental and Numerical Analyses for Auto-Parametric Internal Resonance of a Framed Structure

2020 ◽  
pp. 2150012
Author(s):  
Yuchun Li ◽  
Wei Liu ◽  
Chao Shen ◽  
Xiaojun Yang
Keyword(s):  
Internal Resonance ◽  
Vibration Exciter ◽  
Engineering Structures ◽  
Periodic Force ◽  
Stability Boundaries ◽  
Horizontal Beam ◽  
Resonance Response ◽  
Vertical Beam ◽  
The Common ◽  
The Stability

The auto-parametric internal resonance experiment of a [Formula: see text]-shaped frame is first conducted in this research. A non-contact electromagnetic vibration exciter is used to exert a periodic force on the vertical beam of the frame. The phenomena of internal resonance and non-internal resonance are observed and measured in this test. A common resonance of the vertical beam is excited by the external electromagnetic force, and the auto-parametric internal resonance of the horizontal beam is subsequently induced by the common resonance. The numerical method is also used to simulate the internal resonance and non-internal resonance. The stability boundaries of internal resonance and non-internal resonance are numerically and experimentally determined and compared. The numerical stability boundaries are in agreement with the experimental results. The results indicate that a small external excitation can excite a strong internal resonance response of a framed structure. The unstable domain of the internal resonance is much bigger than that of the non-internal resonance. The auto-parametric internal resonance is much more dangerous than the non-internal resonance. The risk of auto-parametric internal resonance should be emphasized and avoided in the designs of engineering structures.

The Coupled Longitudinal and Bending Vibrations on Stability in a Cracked Blade-Disk

2001 ◽  
Author(s):  
B. W. Huang ◽  
J. H. Kuang
Keyword(s):  
Dynamic Stability ◽  
Coriolis Force ◽  
Multiple Scales ◽  
Coupling Effect ◽  
Disk System ◽  
Bending Vibrations ◽  
Mode Localization ◽  
The Stability ◽  
The Galerkin Method ◽  
Blade Crack

The effect of coriolis force on the stability in a rotational blade-disk with a cracked blade was presented in this paper. A disk comprising of periodically shrouded blades was used to simulate the weakly coupled periodic structure. The mode localization phenomenon introduced by the blade crack on the longitudinal and bending vibrations on the rotating blades are considered. The Galerkin method was used to derive the unperturbation equations for the system. The boundaries of instability zones of the mistuned system were approximated by employing the so called multiple scales method. The effects of coriolis force and the magnitude of crack on the variation of the dynamic stability zones in a cracked blade-disk system are investigated numerically. Numerical results indicate that the coriolis force and the coupling effect between longitudinal and bending vibrations could affect the dynamic stability in a mistuned system significantly.

Combination Resonances of Traveling Unidirectional Plates Partially Immersed in Fluid with Time-Dependent Axial Velocity and Axially Varying Tension

2021 ◽  
Author(s):  
Hongying Li ◽  
Xibo Wang ◽  
Shumeng Zhang ◽  
Jian Li
Keyword(s):  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Complex Dynamics ◽  
Axial Direction ◽  
Mean Velocity ◽  
Velocity Amplitude ◽  
Study Results ◽  
Axially Moving ◽  
The Stability ◽  
The Galerkin Method

Abstract Nonlinear vibrations of axially moving plates partially immersed in fluid are investigated in this paper. The system has time dependency in velocity as well as tension in axial direction. The Galerkin method is used to solve the nonlinear vibration differential equation. The method of multiple scales and Runge-Kutta method are applied to solve the nonlinear vibration response of the system. Additionally, the stability conditions of trivial and nontrivial solutions are analyzed using the Routh-Hurwitz criterion. The effects of mean velocity, amplitude of pulsating velocity, mean tension, amplitude of pulsating tension and pulsating frequency on the complex dynamics of the system are obtained. The study results reveal rich dynamic behaviors of fluid-structure coupling system.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

scholarly journals Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai
Keyword(s):  
Numerical Stability ◽  
Bragg Gratings ◽  
Stability Boundaries ◽  
Quintic Nonlinearity ◽  
Numerical Stability Analysis ◽  
Gap Solitons ◽  
The Stability ◽  
Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

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