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1.
The present study is concerned with the dynamic anomalous response of an elastic-plastic column struck axially by a massm with an initial velocityv
0. This simple example is considered in order to clarify the influence of the impact characteristics and the material plastic properties on the dynamic buckling phenomenon and particularly on the final vibration amplitudes of the column when it shakes down to a wholly elastic behaviour. The material is assumed to have a linear strain hardening with a plastic with a plastic reloading allowed. These material properties are the reason a number of elastic-plastic cycles to be realized prior to any wholly elastic stable behaviour, which causes different amounts of energy to be absorbed due to the plastic deformations.The column exhibits two types of behaviour over the range of the impact masses — a quasi-periodic and a chaotic response. The chaotic behaviour is caused by the multiple equilibrium states of the column when any small changes in the loading parameters cause small changes in the plastic strains which result in large changes in the response behaviour. The two types of behaviour are represented by displacement-time and phase-plane diagrams. The sensitivity to the load parameters is illustrated by the calculation of a Lyapunov-like exponent. Poincaré maps are shown for three particular cases.Notation
c
elastic wave propagation speed
-
m
impact mass
-
m
c
column mass
-
s
step of the spatial discretization
-
t
time
-
u(x,t)
axial displacement
-
v
0
initial velocity
-
w
0(x)
initial imperfections
-
w(x,t)+w
0(x)
total lateral displacements
-
x
axial axis
-
z
axis along the column thickness
-
A
cross-section areahb
-
E
Young's modulus
-
E
t
hardening modulus (Figure 2)
-
M(x,t)
bending moment
-
N(x,t)
axial force
-
impact mass ratiom/m
c
-
(x,z)
strain
-
Lyapunov-like exponent
-
material density
-
(x,z)
stress 相似文献
2.
We investigate the equations of anisotropic incompressible viscous fluids in , rotating around an inhomogeneous vector B(t, x
1, x
2). We prove the global existence of strong solutions in suitable anisotropic Sobolev spaces for small initial data, as well
as uniform local existence result with respect to the Rossby number in the same functional spaces under the additional assumption
that B = B(t, x
1) or B = B(t, x
2). We also obtain the propagation of the isotropic Sobolev regularity using a new refined product law. 相似文献
3.
An investigation of the flow over a three-dimensional (3-D) double backward-facing step is presented using a combination of
both quantitative measurements from a particle image velocimetry (PIV) system and qualitative oil-flow visualizations. The
arrangement of the PIV instrument allows for snap-shots of the (x, y) and (y, z) planes at various axial and spanwise positions. The measurements illustrate characteristics that are found in both two-dimensional
(2-D) backward-facing steps and 3-D flows around wall mounted cubes. In particular, the development of a horseshoe vortex
is found after each step alongside other vortical motions introduced by the geometry of the model. Large turbulence levels
are found to be confined to a region in the center of the backstep; their mean square levels being much larger than what has
been observed in 2-D backward-facing steps. The large turbulent fluctuations are attributed to a quasi-periodic shedding of
the horseshoe vortex as it continuously draws energy from the spiral nodes of separation, which form to create the base of
the horseshoe vortex. A combination of effects including the shedding of the first horseshoe vortex, the horizontal entrainment
of air and the presence of two counter rotating vortices initiated at reattachment, are shown to cause the steering vector
of the flow to jettison away from the surface in the first redeveloping region and along the center at z/h = 0. Oil-flow visualizations confirm these observations.
相似文献
C. E. Tinney (Corresponding author)Email: |
L. S. UkeileyEmail: |
4.
Tanja Siegmann-Hegerfeld Stefan Albensoeder Hendrik C. Kuhlmann 《Experiments in fluids》2008,45(5):781-796
Two- and three-dimensional flows in nearly cuboidal cavities are investigated experimentally. A tight cavity is formed in
the gap between two long and parallel cylinders of large radii by adding rigid top, bottom, and end walls. The cross-section
perpendicular to the axes of the cylinders is nearly rectangular with aspect ratio Γ. The axial aspect ratio Λ > 10 is large
to suppress end-wall effects. The fluid motion is driven by independent and steady rotation of the cylinders about their axes
which defines two Reynolds numbers Re
1,2. Stability boundaries of the nearly two-dimensional steady flow have been determined as functions of Re
1,2 for Γ = 0.76 and Γ = 1. Up to six different three-dimensional supercritical modes have been identified. The critical thresholds
for the onset of most of the three-dimensional modes, three of which have been observed for the first time, agree well with
corresponding linear-stability calculations. Particular attention is paid to the flow for Γ = 1 under symmetric and parallel
wall motion. In that case the basic flow consists of two mirror symmetric counter-rotating parallel vortices. They become
modulated in span-wise direction as the driving increases. Detailed LDV measurements of the supercritical three-dimensional
velocity field and the bifurcation show an excellent agreement with numerical simulations.
相似文献
Tanja Siegmann-Hegerfeld (Corresponding author)Email: |
Stefan AlbensoederEmail: |
Hendrik C. KuhlmannEmail: |
5.
Recently a third-order existence theorem has been proven to establish the sufficient conditions of periodicity for the most general third-order ordinary differential equation
x+f(t,x,x′,x″)=0