Vibration and Buckling of Rotating, Pretwisted, Preconed Beams Including Coriolis Effects

1986 ◽  
Vol 108 (2) ◽  
pp. 140-149 ◽  
Author(s):  
K. B. Subrahmanyam ◽  
K. R. V. Kaza
Keyword(s):  
Equations Of Motion ◽  
Energy Functional ◽  
Solution Procedure ◽  
Thickness Ratio ◽  
The Other ◽  
Collective Effects ◽  
Coriolis Forces ◽  
Coriolis Effects ◽  
Axis Of Rotation ◽  
Setting Angle

The effects of pretwist, precone, setting angle and Coriolis forces on the vibration and buckling behavior of rotating, torsionally rigid, cantilevered beams are studied in this investigation. The beam is considered to be clamped on the axis of rotation in one case, and off the axis of rotation in the other. Two methods are employed for the solution of the vibration problem: one based upon a finite-difference approach using second-order central differences for solution of the equations of motion, and the other based upon the minimum of the total potential energy functional with a Ritz type of solution procedure making use of complex forms of shape functions for the dependent variables. Numerical results obtained by using these methods are compared to those existing in the literature for specialized simple cases. Results indicating the individual and collective effects of pretwist, precone, setting angle, thickness ratio, and Coriolis forces on the natural frequencies and the buckling boundaries are presented and discussed. Furthermore, it is shown that the inclusion of Coriolis effects is necessary for blades of moderate-to-large thickness ratios while these effects are not so important for small thickness ratio blades. Finally, the results show the possibility of buckling due to centrifugal softening terms for large values of precone and rotation.

Heat Transfer in Rotating Serpentine Passages With Selected Model Orientations for Smooth or Skewed Trip Walls

1994 ◽  
Vol 116 (4) ◽  
pp. 738-744 ◽  
Author(s):  
B. V. Johnson ◽  
J. H. Wagner ◽  
G. D. Steuber ◽  
F. C. Yeh
Keyword(s):  
Heat Transfer ◽  
Turbine Blades ◽  
The Other ◽  
First Passage ◽  
Forward Flow ◽  
Coriolis Forces ◽  
The Third ◽  
Axis Of Rotation ◽  
Trailing Edges ◽  
Serpentine Passages

Experiments were conducted to determine the effects of model orientation as well as buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. Turbine blades have internal coolant passage surfaces at the leading and trailing edges of the airfoil with surfaces at angles that are as large as ±50 to 60 deg to the axis of rotation. Most of the previously presented, multiple-passage, rotating heat transfer experiments have focused on radial passages aligned with the axis of rotation. The present work compares results from serpentine passages with orientations 0 and 45 deg to the axis of rotation, which simulate the coolant passages for the midchord and trailing edge regions of the rotating airfoil. The experiments were conducted with rotation in both directions to simulate serpentine coolant passages with the rearward flow of coolant or with the forward flow of coolant. The experiments were conducted for passages with smooth surfaces and with 45 deg trips adjacent to airfoil surfaces for the radial portion of the serpentine passages. At a typical flow condition, the heat transfer on the leading surfaces for flow outward in the first passage with smooth walls was twice as much for the model at 45 deg compared to the model at 0 deg. However, the differences for the other passages and with trips were less. In addition, the effects of buoyancy and Coriolis forces on heat transfer in the rotating passage were decreased with the model at 45 deg, compared to the results at 0 deg. The heat transfer in the turn regions and immediately downstream of the turns in the second passage with flow inward and in the third passage with flow outward was also a function of model orientation with differences as large as 40 to 50 percent occurring between the model orientations with forward flow and rearward flow of coolant.

Free Vibrations of Laminated Composite Noncircular Thin Cylindrical Shells

1994 ◽  
Vol 61 (4) ◽  
pp. 861-871 ◽  
Author(s):  
K. Suzuki ◽  
G. Shikanai ◽  
A. W. Leissa
Keyword(s):  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Power Series Expansion ◽  
Laminated Composite ◽  
Energy Functional ◽  
Solution Procedure ◽  
Free Vibrations ◽  
Layer Stacking ◽  
Kinetic Energy Functional ◽  
Energy Principles

An exact solution procedure is presented for solving free vibration problems for laminated composite noncircular cylindrical shells. Based on the classical lamination theory, strain energy and kinetic energy functional are first derived for shells having arbitrary layer stacking sequences. These functional are useful for a general analysis based upon energy principles. However, in the present work equations of motion and boundary conditions are obtained from the minimum conditions of the Lagrangian (Hamilton’s principle). The equations of motion are solved exactly by using a power series expansion for symmetrically laminated, cross-ply shells having both ends freely supported. Frequencies are presented for a set of elliptical cylindrical shells, and the effects of various parameters upon them are discussed.

Heat Transfer in Rotating Serpentine Passages With Selected Model Orientations for Smooth or Skewed Trip Walls

1993 ◽  
Author(s):  
B. V. Johnson ◽  
J. H. Wagner ◽  
G. D. Steuber ◽  
F. C. Yeh
Keyword(s):  
Heat Transfer ◽  
Turbine Blades ◽  
The Other ◽  
First Passage ◽  
Forward Flow ◽  
Coriolis Forces ◽  
The Third ◽  
Axis Of Rotation ◽  
Trailing Edges ◽  
Serpentine Passages

Experiments were conducted to determine the effects of model orientation as well as buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. Turbine blades have internal coolant passage surfaces at the leading and trailing edges of the airfoil with surfaces at angles which are as large as +/−50 to 60 degrees to the axis of rotation. Most of the previously–presented, multiple–passage, rotating heat transfer experiments have focused on radial passages aligned with the axis of rotation. The present work compares results from serpentine passages with orientations 0 and 45 degrees to the axis of rotation which simulate the coolant passages for the midchord and trailing edge regions of the rotating airfoil. The experiments were conducted with rotation in both directions to simulate serpentine coolant passages with the rearward flow of coolant or with the forward flow of coolant. The experiments were conducted for passages with smooth surfaces and with 45 degree trips adjacent to airfoil surfaces for the radial portion of the serpentine passages. At a typical flow condition, the heat transfer on the leading surfaces for flow outward in the first passage with smooth walls was twice as much for the model at 45 degrees compared to the model at 0 degrees. However, the differences for the other passages and with trips were less. In addition, the effects of buoyancy and Coriolis forces on heat transfer in the rotating passage were decreased with the model at 45 degrees, compared to the results at 0 degrees. The heat transfer in the turn regions and immediately downstream of the turns in the second passage with flow inward and in the third passage with flow outward was also a function of model orientation with differences as large as 40 to 50 percent occurring between the model orientations with forward flow and rearward flow of coolant.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

Concise Equations for Rotor Dynamics Analysis

1995 ◽  
Author(s):  
W. J. Chen
Keyword(s):  
Equations Of Motion ◽  
Rotor Dynamics ◽  
Memory Storage ◽  
The Other ◽  
Dynamics Analysis ◽  
Real Domain ◽  
The Matrix ◽  
System Equations ◽  
Ordering Algorithms ◽  
Matrix Bandwidth

Abstract Concise equations for rotor dynamics analysis are presented. Two coordinate ordering methods are introduced in the element equations of motion. One is in the real domain and the other is in the complex domain. The two proposed ordering algorithms lead to more compact element matrices. A station numbering technique is also proposed for the system equations during the assembly process. This numbering technique can minimize the matrix bandwidth, the memory storage and can increase the computational efficiency.

LES Simulations of Rotating Two-Pass Ribbed Duct With Coriolis and Centrifugal Buoyancy Forces at Re=100,000

2016 ◽  
Author(s):  
Cody Dowd ◽  
Danesh Tafti
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Large Eddy Simulations ◽  
The Other ◽  
Coriolis Forces ◽  
Flow And Heat Transfer ◽  
Large Eddy ◽  
Buoyancy Forces ◽  
First Pass ◽  
Duct Geometry

The focus of this research is to predict the flow and heat transfer in a rotating two-pass duct geometry with staggered ribs using Large-Eddy Simulations (LES). The geometry consists of a U-Bend with 17 ribs in each pass. The ribs are staggered with an e/Dh = 0.1 and P/e = 10. LES is performed at a Reynolds number of 100,000, a rotation number of 0.2 and buoyancy parameters (Bo) of 0.5 and 1.0. The effects of Coriolis forces and centrifugal buoyancy are isolated and studied individually. In all cases it is found that increasing Bo from 0.5 to 1.0 at Ro = 0.2 has little impact on heat transfer. It is found that in the first pass, the heat transfer is quite receptive to Coriolis forces which augment and attenuate heat transfer at the trailing and leading walls, respectively. Centrifugal buoyancy, on the other hand has a bigger effect in augmenting heat transfer at the trailing wall than in attenuating heat transfer at the leading wall. On contrary, it aids heat transfer in the second half of the first pass at the leading wall by energizing the flow near the wall. The heat transfer in the second pass is dominated by the highly turbulent flow exiting the bend. Coriolis forces have no impact on the augmentation of heat transfer on the leading wall till the second half of the passage whereas it attenuates heat transfer at the trailing wall as soon as the flow exits the bend. Contrary to phenomenological arguments, inclusion of centrifugal buoyancy augments heat transfer over Coriolis forces alone on both the leading and trailing walls of the second pass.

Effects of Viewing Distance on the Responses of Vestibular Neurons to Combined Angular and Linear Vestibular Stimulation

1999 ◽  
Vol 81 (5) ◽  
pp. 2538-2557 ◽  
Author(s):  
Chiju Chen-Huang ◽  
Robert A. McCrea
Keyword(s):  
Eye Movements ◽  
Eye Movement ◽  
Vestibular Stimulation ◽  
The Other ◽  
Viewing Distance ◽  
Vestibuloocular Reflex ◽  
Horizontal Canal ◽  
Head Velocity ◽  
Vestibular Neurons ◽  
Axis Of Rotation

Effects of viewing distance on the responses of vestibular neurons to combined angular and linear vestibular stimulation. The firing behavior of 59 horizontal canal–related secondary vestibular neurons was studied in alert squirrel monkeys during the combined angular and linear vestibuloocular reflex (CVOR). The CVOR was evoked by positioning the animal’s head 20 cm in front of, or behind, the axis of rotation during whole body rotation (0.7, 1.9, and 4.0 Hz). The effect of viewing distance was studied by having the monkeys fixate small targets that were either near (10 cm) or far (1.3–1.7 m) from the eyes. Most units (50/59) were sensitive to eye movements and were monosynaptically activated after electrical stimulation of the vestibular nerve (51/56 tested). The responses of eye movement–related units were significantly affected by viewing distance. The viewing distance–related change in response gain of many eye-head-velocity and burst-position units was comparable with the change in eye movement gain. On the other hand, position-vestibular-pause units were approximately half as sensitive to changes in viewing distance as were eye movements. The sensitivity of units to the linear vestibuloocular reflex (LVOR) was estimated by subtraction of angular vestibuloocular reflex (AVOR)–related responses recorded with the head in the center of the axis of rotation from CVOR responses. During far target viewing, unit sensitivity to linear translation was small, but during near target viewing the firing rate of many units was strongly modulated. The LVOR responses and viewing distance–related LVOR responses of most units were nearly in phase with linear head velocity. The signals generated by secondary vestibular units during voluntary cancellation of the AVOR and CVOR were comparable. However, unit sensitivity to linear translation and angular rotation were not well correlated either during far or near target viewing. Unit LVOR responses were also not well correlated with their sensitivity to smooth pursuit eye movements or their sensitivity to viewing distance during the AVOR. On the other hand there was a significant correlation between static eye position sensitivity and sensitivity to viewing distance. We conclude that secondary horizontal canal–related vestibuloocular pathways are an important part of the premotor neural substrate that produces the LVOR. The otolith sensory signals that appear on these pathways have been spatially and temporally transformed to match the angular eye movement commands required to stabilize images at different distances. We suggest that this transformation may be performed by the circuits related to temporal integration of the LVOR.

On the flow properties of a fluid between concentric spheres

1971 ◽  
Vol 47 (4) ◽  
pp. 799-809 ◽  
Author(s):  
S. G. H. Philander
Keyword(s):  
Outer Sphere ◽  
Azimuthal Velocity ◽  
Ekman Layer ◽  
Shear Layers ◽  
The Other ◽  
Axial Motion ◽  
Flow Properties ◽  
Axis Of Rotation ◽  
Concentric Spheres ◽  
Angular Velocities

Proudman (1956) and Stewartson (1966) analyzed the dynamical properties of a fluid occupying the space between two concentric rotating spheres when the angular velocities of the spheres are slightly different, in other words, when the motion relative to a reference frame rotating with one of the spheres is due to an imposed azimuthal velocity which is symmetric about the equator. The consequences of forcing motion across the equator are explored here. Whereas the flow inside the cylinder [Cscr ] circumscribing the inner sphere and having generators parallel to the axis of rotation is similar to that which results when the driving is symmetric, the flow outside [Cscr ] is quite different. The Ekman layer on the outer sphere persists outside [Cscr ] - its dynamics is modified in the vicinity of the equator - and is instrumental in transferring fluid from one hemisphere to the other. The divergence of this Ekman layer causes slow, axial motion in the inviscid region outside [Cscr ]. On [Cscr ], two shear layers of thicknessO(R−2/7) andO(R−1/3) (whereRis the Reynolds number, assumed large) remove discontinuities in the flow field and return fluid from one hemisphere to the other (rather than one Ekman layer to the other as is the case when the driving is azimuthal).

Experimental Analysis of a Planar Reconfigurable Mechanism With a Variable Joint

2016 ◽  
Author(s):  
Peter W. Malak ◽  
Anthony J. Buchta ◽  
Philip A. Voglewede
Keyword(s):  
Optimal Control ◽  
Transition Point ◽  
Physical Mechanism ◽  
Equations Of Motion ◽  
Angular Position ◽  
The Other ◽  
Simplified Model ◽  
Physical Prototype ◽  
Kinetics Of ◽  
Kinematics And Kinetics

Previously a specific planar reconfigurable mechanism with a variable joint (RRRR1 -RRRP2 Mechanism) was dynamically modeled. The RRRR-RRRP Mechanism functions as a RRRR mechanism in one configuration and as a in RRRP mechanism the other. The kinematics and kinetics of the RRRP and RRRR configurations were previously analyzed with a Lagrangian approach. The developed equations of motion will be validated with a physical prototype in this paper. In addition, a simplified model of the RRRR-RRRP Mechanism is also developed and compared to the experimental results. The experimental angular position of each joint on the RRRR-RRRP Mechanism will be compared to the model position analysis. Particular attention will be given to the transition point when the physical mechanism changes from an RRRR mechanism to RRRP mechanism and vice versa as it is vital to knowing this point for optimal control of the mechanism.

scholarly journals COMPARATIVE STUDY OF VARIATIONAL CHAOS INDICATORS AND ODEs' NUMERICAL INTEGRATORS

2012 ◽  
Vol 22 (10) ◽  
pp. 1230033 ◽  
Author(s):  
L. A. DARRIBA ◽  
N. P. MAFFIONE ◽  
P. M. CINCOTTA ◽  
C. M. GIORDANO
Keyword(s):  
Numerical Technique ◽  
Equations Of Motion ◽  
General System ◽  
Detailed Comparison ◽  
Dynamical Problem ◽  
Point Of View ◽  
The Other ◽  
Numerical Integrators ◽  
Fast Lyapunov Indicator ◽  
The Times

The reader can find in the literature a lot of different techniques to study the dynamics of a given system and also, many suitable numerical integrators to compute them. Notwithstanding the recent work of [Maffione et al., 2011b] for mappings, a detailed comparison among the widespread indicators of chaos in a general system is still lacking. Such a comparison could lead to select the most efficient algorithms given a certain dynamical problem. Furthermore, in order to choose the appropriate numerical integrators to compute them, more comparative studies among numerical integrators are also needed. This work deals with both problems. We first extend the work of [Maffione et al., 2011b] for mappings to the 2D [Hénon & Heiles, 1964] potential, and compare several variational indicators of chaos: the Lyapunov Indicator (LI); the Mean Exponential Growth Factor of Nearby Orbits (MEGNO); the Smaller Alignment Index (SALI) and its generalized version, the Generalized Alignment Index (GALI); the Fast Lyapunov Indicator (FLI) and its variant, the Orthogonal Fast Lyapunov Indicator (OFLI); the Spectral Distance (D) and the Dynamical Spectra of Stretching Numbers (SSNs). We also include in the record the Relative Lyapunov Indicator (RLI), which is not a variational indicator as the others. Then, we test a numerical technique to integrate Ordinary Differential Equations (ODEs) based on the Taylor method implemented by [Jorba & Zou, 2005] (called taylor), and we compare its performance with other two well-known efficient integrators: the [Prince & Dormand, 1981] implementation of a Runge–Kutta of order 7–8 (DOPRI8) and a Bulirsch–Stöer implementation. These tests are run under two very different systems from the complexity of their equations point of view: a triaxial galactic potential model and a perturbed 3D quartic oscillator. We first show that a combination of the FLI/OFLI, the MEGNO and the GALI 2N succeeds in describing in detail most of the dynamical characteristics of a general Hamiltonian system. In the second part, we show that the precision of taylor is better than that of the other integrators tested, but it is not well suited to integrate systems of equations which include the variational ones, like in the computing of almost all the preceeding indicators of chaos. The result which induces us to draw this conclusion is that the computing times spent by taylor are far greater than the times consumed by the DOPRI8 and the Bulirsch–Stöer integrators in such cases. On the other hand, the package is very efficient when we only need to integrate the equations of motion (both in precision and speed), for instance to study the chaotic diffusion. We also notice that taylor attains a greater precision on the coordinates than either the DOPRI8 or the Bulirsch–Stöer.

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