Thermally Induced Instability of Laminated Beams and Plates

1996 ◽  
Vol 63 (4) ◽  
pp. 884-890 ◽  
Author(s):  
A. Tylikowski ◽  
R. B. Hetnarski
Keyword(s):  
Stochastic Stability ◽  
Direct Method ◽  
Wide Band ◽  
Temperature Fields ◽  
Time And Space ◽  
Thermally Induced ◽  
Stability Problems ◽  
Linear Elastic ◽  
Liapunov Direct Method ◽  
Short Time

A theoretical investigation of dynamic stability for linear elastic structures due to non-uniform, time and space-dependent stochastic temperature fields is presented. The study is based on the reformulation of stochastic stability problems as a stability of Itoˆ type equations in some appropriate Hilbert space and is adopted for stability problems of structures with time and space-dependent stochastic coefficients. Uniform stochastic stability criteria of the structure equilibrium are derived using the Liapunov direct method. The energy-like functional and the generalized ltoˆ lemma are used to derive the sufficient stability conditions of the equilibrium state. A symmetrically laminated crossply plate subjected to the wide-band Gaussian temperature distribution and a laminated beam subjected to local short-time heatings are analysed in detail.

Thermally Induced Flow in a Rotating Annulus Filled With a Compressible Fluid

1988 ◽  
Vol 110 (2) ◽  
pp. 134-139 ◽  
Author(s):  
M. A. Ortega ◽  
J. T. Sielawa
Keyword(s):  
Flow Field ◽  
Inner Core ◽  
Temperature Fields ◽  
Bottom Plate ◽  
Rossby Number ◽  
Thermally Induced ◽  
Coaxial Cylinders ◽  
Induced Flow ◽  
Velocity And Temperature Fields ◽  
Induced Velocity

The thermally induced flow field, in a rapidly rotating container consisting of a pair of coaxial cylinders bounded on the top and bottom by horizontal end plates, is considered. The top plate is heated and the bottom plate is cooled, both by small amounts, so that the thermal Rossby number is small, and the cylinders are supposed to be conductive. The induced velocity and temperature fields are determined by subdivision of the flow field; the equation for the central part, the inner core, is solved numerically as well as analytically.

scholarly journals A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 282
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equations ◽  
Direct Method ◽  
General Theorem ◽  
Stability Problems ◽  
General Stability ◽  
Stability Theorems ◽  
Additive Type ◽  
The Stability

We prove general stability theorems for n-dimensional quartic-cubic-quadratic-additive type functional equations of the form by applying the direct method. These stability theorems can save us the trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

scholarly journals Free radially expanding liquid sheet in air: time- and space-resolved measurement of the thickness field

2015 ◽  
Vol 764 ◽  
pp. 428-444 ◽  
Author(s):  
C. Vernay ◽  
L. Ramos ◽  
C. Ligoure
Keyword(s):  
High Speed ◽  
Liquid Sheet ◽  
Radial Position ◽  
Maximum Diameter ◽  
Time And Space ◽  
Level Measurement ◽  
Time Regime ◽  
Long Time ◽  
Short Time ◽  
Thickness Field

AbstractThe collision of a liquid drop against a small target results in the formation of a thin liquid sheet that extends radially until it reaches a maximum diameter. The subsequent retraction is due to the air–liquid surface tension. We have used a time- and space-resolved technique to measure the thickness field of this class of liquid sheet, based on the grey-level measurement of the image of a dyed liquid sheet recorded using a high-speed camera. This method enables a precise measurement of the thickness in the range $10{-}450~{\rm\mu}\text{m}$, with a temporal resolution equal to that of the camera. We have measured the evolution with time since impact, $t$, and radial position, $r$, of the thickness, $h(r,t)$, for various drop volumes and impact velocities. Two asymptotic regimes for the expansion of the sheet are evidenced. The scalings of the thickness with $t$ and $r$ measured in the two regimes are those that were predicted by Rozhkov et al. (Proc. R. Soc. Lond. A, vol. 460, 2004, pp. 2681–2704) for the short-time regime and Villermaux and Bossa (J. Fluid Mech., vol. 668, 2011, pp. 412–435) for the long-time regime, but never experimentally measured before. Interestingly, our experimental data also provide evidence for the existence of a maximum of the film thickness $h_{max}(r)$ at a radial position $r_{h_{max}}(t)$ corresponding to the cross-over of these two asymptotic regimes. The maximum moves with a constant velocity of the order of the drop impact velocity, as expected theoretically. Thanks to our visualization technique, we also provide evidence of an azimuthal thickness modulation of the liquid sheets.

Prediction of thermally induced postbuckling of clutch disks using the finite element method

2020 ◽  
pp. 135065012090197
Author(s):  
Zhuo Chen ◽  
Yun-Bo Yi ◽  
Ke Bao
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Temperature Fields ◽  
Frictional Heat ◽  
Temperature Dependent ◽  
Displacement Fields ◽  
Element Analysis ◽  
Nonlinear Buckling ◽  
Thermally Induced ◽  
Linear Buckling

Buckling and postbuckling of automotive clutch disks can be excited by the temperature fields caused by frictional heat generation during engagement of clutch systems. Linear and nonlinear buckling finite element analyses are performed to evaluate the thermal postbuckling of clutch metal disks. The dominant buckling modes are first obtained through performing linear buckling finite element analysis (FEA) analyses. The scaled displacement fields obtained from the linear buckling FEA analyses are added to the original geometries to generate the perturbed meshes. The postbuckling is then investigated by performing nonlinear buckling FEA analyses. The commercial FEA software ABAQUS is used in the current study. The effects of the temperature-dependent material properties are studied. It is concluded that the temperature dependence of material properties affects the postbuckling behaviors significantly.

Short-Time-Scale Thermal Mapping of Microdevices Using a Scanning Thermoreflectance Technique

1998 ◽  
Vol 120 (2) ◽  
pp. 306-313 ◽  
Author(s):  
Y. S. Ju ◽  
K. E. Goodson
Keyword(s):  
Temperature Distribution ◽  
Time Scale ◽  
Silicon On Insulator ◽  
Temperature Fields ◽  
Scanning Laser ◽  
Transient Temperature ◽  
Drift Region ◽  
Short Time Scale ◽  
Short Time ◽  
The Impact

The performance and reliability of microdevices can be strongly influenced by the peak temperature rise and spatial temperature distribution during brief electrical overstress (EOS) phenomena, which can occur at sub-microsecond time scales. The present study investigates short-time-scale laser reflectance thermometry of micro devices by examining the impact of passivation overlayers on the thermoreflectance signal and by demonstrating a calibration method suitable for metallization. This manuscript also describes a scanning laser thermometry facility that captures temperature fields in microdevices with 10 ns temporal resolution and 1 μm spatial resolution. The facility combines scanning laser optics with electrical stressing capability to allow simultaneous interrogation of the thermal and electrical behavior of devices. Data show the transient temperature distribution along the drift region of silicon-on-insulator (SOI) power transistors and along metal interconnects subjected to brief electrical stresses. The theory and experimental capability developed in this study are useful for studying short-time-scale thermal phenomena in microdevices and verifying models employed for their simulation.

The Large Deflection and Post-Buckling Behaviour of Some Laminated Plates

1973 ◽  
Vol 24 (2) ◽  
pp. 77-86 ◽  
Author(s):  
G J Turvey ◽  
W H Wittrick
Keyword(s):  
Large Deflection ◽  
Middle Surface ◽  
Laminated Plates ◽  
Dynamic Relaxation ◽  
Orthotropic Plates ◽  
Stability Problems ◽  
Linear Elastic ◽  
Dr Method ◽  
Post Buckling ◽  
Coupling Phenomena

SummaryThe Dynamic Relaxation (DR) method is applied to the solution of geometrically non-linear, elastic, laminated plate, flexural and stability problems. Two categories of plate are considered, namely, those that are symmetrically and unsymmetrically laminated with respect to the plate middle surface. Whereas the former category exhibits a bending – twisting coupling phenomenon, the latter exhibits an extensional – flexural type of coupling. The effects of these coupling phenomena are evaluated by comparing the plate responses with those of corresponding homogeneous, specially orthotropic plates. With the exception of uniaxially compressed plates of the latter category in the post-buckling regime, it is found that for both flexural and stability problems the coupling phenomena cause a reduction in stiffness and the extent of this reduction is dependent on the lay-up of the laminate.

Estimation of the Crack Behaviour in the Compressive Layer of the Alumina-Zirconia Ceramic Laminate

2014 ◽  
Vol 627 ◽  
pp. 41-44
Author(s):  
Luboš Náhlík ◽  
Bohuslav Máša ◽  
Pavel Hutař
Keyword(s):  
Crack Propagation ◽  
Direct Method ◽  
Zirconia Ceramic ◽  
Finite Element Models ◽  
Linear Elastic ◽  
Dimensional Finite Element ◽  
Density Factor ◽  
Elastic Fracture ◽  
Energy Density Factor ◽  
Good Agreement

This paper deals with a description of the crack behaviour in the layered alumina-zirconia ceramic laminate. The main aim is to investigate the crack behaviour in the compressive layer. The crack propagation was investigated on the basis of linear elastic fracture mechanics. Two dimensional finite element models were developed in order to obtain a stress distribution around the crack tip. The stress intensity factors were computed numerically employing the direct method. The change in the crack propagation direction was estimated using criterion based on the strain energy density factor. Sharp crack deflection in the compressive layer was predicted by mentioned approach. The determined crack behaviour is qualitatively in a good agreement with experimental observations.

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