Mode Localization in Coupled Circular Plates

1994 ◽  
Vol 116 (3) ◽  
pp. 286-294 ◽  
Author(s):  
C. O. Orgun ◽  
B. H. Tongue
Keyword(s):  
Periodic Structures ◽  
Qualitative Change ◽  
Disk Drive ◽  
Circular Plates ◽  
Mode Localization ◽  
Infinite Dimensional ◽  
Write Heads ◽  
The Individual ◽  
Support Motion ◽  
Computer Disk

When analyzing structures that are comprised of many similar pieces (periodic structures), it is common practice to assume perfect periodicity. Such an assumption will lead to the existence of eigenmodes that are global in character, i.e., the structural deflections will occur throughout the system. However, research in structural mechanics has shown that, when only weak coupling is present between the individual pieces of the system, small amounts of disorder can produce a qualitative change in the character of the eigenmodes. A typical eigenmode of such a system will support motion only over a limited extend of the structure. Often only one or two of the smaller pieces that make up the structure show any motion, the rest remain quiescent. This phenomenon is known as “mode localization”, since the modes become localized at particular locations on the overall structure. This paper will examine the behavior of several circular plates that are coupled together through springs, a system that models a multiple disk computer disk drive. These drives typically consist of several disks mounted on a single spindle, coupled by read/write heads, which act as weak springs, thus leading one to suspect the possibility of localization. Since such an effect would impact accurate read/write operations at small fly heights, the problem deserves attention. Although computer disk drives contain space fixed read/write heads, this paper will consider springs that are fixed to the plates in order to understand the effect of localization on a set of infinite dimensional structures (the circular plates). Later work will extend the model to the case of space fixed springs and the wave behavior and destabilizing effects that such a configuration will induce.

Piezoelectric Networks for Vibration Suppression of Mistuned Bladed Disks

2007 ◽  
Vol 129 (5) ◽  
pp. 559-566 ◽  
Author(s):  
Hongbiao Yu ◽  
K. W. Wang
Keyword(s):  
Vibration Suppression ◽  
Periodic Structures ◽  
Electric Circuit ◽  
Forced Response ◽  
Bladed Disks ◽  
Vibration Localization ◽  
Network Concept ◽  
Engine Order ◽  
The Individual ◽  
Local Circuits

Extensive investigations have been conducted to study the vibration localization phenomenon and the excessive forced response that can be caused by mistuning in bladed disks. Most previous researches have focused on analyzing∕predicting localization or attacking the mistuning issue via mechanical tailoring. Few have focused on developing effective vibration control methods for such systems. This study extends the piezoelectric network concept, which has been utilized for mode delocalization in periodic structures, to the control of mistuned bladed disks under engine order excitation. A piezoelectric network is synthesized and optimized to effectively suppress vibration in bladed disks. One of the merits of such an approach is that the optimum design is independent of the number of spatial harmonics, or engine orders. Local circuits are first formulated by connecting inductors and resistors with piezoelectric patches on the individual blades. Although these local circuits can function as conventional damped absorber when properly tuned, they do not perform well for bladed disks under all engine order excitations. To address this issue, capacitors are introduced to couple the individual local circuitries. Through such networking, an absorber system that is independent of the engine order can be achieved. Monte Carlo simulation is performed to investigate the effectiveness of the network for a bladed disk with a range of mistuning level of its mechanical properties. The robustness issue of the network in terms of detuning of the electric circuit parameters is also studied. Finally, negative capacitance is introduced and its effect on the performance and robustness of the network is investigated.

Optimal Control of Nonlinear Parametrically Excited Beam Vibrations by Spatially Distributed Sensors and Actors

1997 ◽  
Author(s):  
Andreas Kugi ◽  
Kurt Schlacher ◽  
Hans Irschik
Keyword(s):  
Axial Strain ◽  
Equations Of Motion ◽  
Nonlinear Formulation ◽  
Control Laws ◽  
Distributed Sensors ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Piezoelectric Layers ◽  
Spatially Distributed ◽  
Support Motion

Abstract This contribution is focused on a straight composite beam with multiple piezoelectric layers under the action of an axial support motion. In the sense of v. Karman a nonlinear formulation for the axial strain is used and the equations of motion are derived by means of the Hamilton formalism. This system turns out to be a special class of infinite dimensional systems, the so called Hamilton AI-systems with external inputs. In order to suppress the excited vibrations two infinite control laws are proposed. The first one is an infinite PD-feedback law and the second one is based on the nonlinear H∞-design, where an exact solution of the corresponding Hamilton Jacobi Isaacs equation is presented. The necessary quantities for the control laws can be measured by appropriate space-wise shaped sensors and the asymptotic stability of the equilibrium point can be proved.

Investigation of Mistuned Oscillating Cascade Using Fully-Coupled Method

2021 ◽  
Author(s):  
H. M. Phan ◽  
L. He
Keyword(s):  
Striking Difference ◽  
Influence Coefficient ◽  
Aeroelastic Stability ◽  
Mode Localization ◽  
Coupled Method ◽  
Reduced Frequency ◽  
Systematic Understanding ◽  
Cascade Flutter ◽  
The Individual ◽  
Fully Coupled

Abstract The uncoupled phase-shifted single-passage simulation is commonly used for turbomachinery aeroelastic problems. However, it has difficulties in dealing with unconventional phenomena such as strong fluid-structure interaction effects as well as blade mistuning effects. Regarding mistuning effects, structural mistuning has been studied extensively while aerodynamic mistuning has received far less attention. There seems to be a lack of clear and systematic understanding of physical behaviour and mechanisms of mistuned bladerows, particularly in the context of the aerodynamic mistuning versus structural one. In the present work, direct fully-coupled method is adopted to investigate the dynamics mechanism of a mistuned oscillating cascade. Both structurally and aerodynamically mistuned cascades show that the blades would couple and oscillate at a unique frequency and a constant inter-blade phase angle regardless of the individual blade’s eigen-frequency. The vibration amplitudes of blades of a mistuned row are different when excited. For structural mistuning, the mode localization effect is seen to be responsible for a monotonic increase of cascade aeroelastic stability with mistuning. On the other hand, the aerodynamically mistuned cascade shows a stabilizing effect at small amount of mistuning but exhibits a destabilizing effect at large mistuning. Such non-monotonic tendency could be explained using the aero-damping decomposition by the influence coefficient approach. At low reduced frequency, there is a striking difference between the tuned and aero-mistuned cascade. Although the tuned cascade is stable, the aero-mistuned cascade may experience flutter. A close inspection of the aero-mistuned cascade flutter reveals that there are two oscillating waves forming a beating signal.

The ultrastructure of Methanothrix concilii, a mesophilic aceticlastic methanogen

1986 ◽  
Vol 32 (9) ◽  
pp. 703-710 ◽  
Author(s):  
Terry J. Beveridge ◽  
Girish B. Patel ◽  
Bob J. Harris ◽  
G. Dennis Sprott
Keyword(s):  
Cell Wall ◽  
Plasma Membrane ◽  
Circular Plates ◽  
A Cell ◽  
Granular Matrix ◽  
A Chain ◽  
The Individual

Methanothrix concilii strain GP6 consists of a chain of rod-shaped cells, ca. 2.5 μm in length and 0.8 μm in width, which are encased in a tubular proteinaceous sheath. The sheath is composed of annular hoops, ca. 8.0 nm wide and 9.0 nm thick, which are stacked together to form the tube. The ends of the sheath, and therefore the cell filament, are blocked by single, multilayered, 13.5 nm thick, circular plates, designated as "spacer plugs," which contain a series of concentric rings; these also separate the individual cells within each filament. Each cell is therefore bounded by a tubular section of sheath and two spacer plugs. Completely encapsulating each cell, and lying between the sheath and cell, is an amorphous granular matrix. Overlying the plasma membrane and surrounding each protoplast is a thin veil of material which resembles a cell wall, but which is unable to maintain the rod shape when cells are extruded from the sheath.

Geometric Mistuning Reduced-Order Model Development Utilizing Bayesian Surrogate Models for Component Mode Calculations

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Emily B. Carper ◽  
Daniel L. Gillaugh
Keyword(s):  
Periodic Structures ◽  
Model Development ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Order Model ◽  
Mode Localization ◽  
Reduced Order ◽  
Structural Periodicity ◽  
Computationally Intensive

AbstractIntegrally bladed rotors (IBRs) are meant to be rotationally periodic structures. However, unique variations in geometries and material properties from sector-to-sector, called mistuning, destroy the structural periodicity. This results in mode localization that can induce forced response levels greater than what is predicted with a tuned analysis. Furthermore, mistuning and mode localization are random processes that require stochastic treatments when analyzing the distribution of fleet responses. Generating this distribution can be computationally intensive when using the full finite element model (FEM). To overcome this expense, reduced-order models (ROMs) have been developed to accommodate fast calculations of mistuned forced response levels for a fleet of random IBRs. Usually, ROMs can be classified by two main families: frequency-based and geometry-based methods. Frequency-based ROMs assume mode shapes do not change due to mistuning. However, this assumption has been shown to cause errors that propagate to the fleet distribution. To circumvent these errors, geometry-based ROMs have been developed to provide accurate predictions. However, these methods require recalculating modal data during ROM formulations. This increases the computational expense in computing fleet distributions. A new geometry-based ROM is presented to reduce this cost. The developed ROM utilizes a Bayesian surrogate model in place of sector modal calculations required in ROM formulations. The method, surrogate modal analysis for geometry mistuning assessments (SMAGMA), will propagate uncertainties of the surrogate prediction to forced response. ROM accuracies are compared to the true forced response levels and results computed by a frequency-based ROM.

Adaptive and Repetitive Control for Rejecting Repeatable and Non-Repeatable Runout in Rotating Devices

2007 ◽  
Author(s):  
Ne´stor O. Pe´rez Arancibia ◽  
Chi-Ying Lin ◽  
Tsu-Chin Tsao ◽  
James S. Gibson
Keyword(s):  
High Performance ◽  
Disk Drive ◽  
Minimum Variance ◽  
Experimental Results ◽  
Recursive Least Squares ◽  
Broad Bandwidth ◽  
Periodic Disturbances ◽  
Write Heads ◽  
Control Scheme ◽  
Control Schemes

This paper presents a control scheme for rejecting both repeatable and non-repeatable runout components of disturbances occurring in rotational devices. To exemplify this method, implementation and experimental results for track following control of a computer hard disk drive (HDD) read/write heads are presented. Aiming for high performance, the control design involves two steps. The first is the design and tuning of a recursive least-squares (RLS) based scheme intended to achieve minimum variance performance. The second step integrates repetitive and adaptive control schemes in a real-time implementation to compensate for variations and changes in the disturbance dynamics. The repetitive part of this controller targets specific periodic disturbances. The adaptive part compensates for broad bandwidth stochastic disturbances. The key element in this design is the formulation of an appropriate optimization problem, solvable recursively by applying recursive adaptive algorithms. Experimental results obtained from the implementation of this method in a commercial HDD demonstrates the effectiveness of this approach.

Luther and Literacy

PMLA ◽  
1976 ◽  
Vol 91 (5) ◽  
pp. 816-828 ◽  
Author(s):  
H. G. Haile
Keyword(s):  
Qualitative Change ◽  
Individual Life ◽  
The Bible ◽  
Great Relevance ◽  
The Individual

Luther studies have traditionally been confessionally oriented. Today, this author's significance is also secular, and it is most readily interpreted by disinterested literature teachers. Disputes about his writings radically increased European literacy rates. His songs and pamphlets engaged popular tradition in order to achieve broad, democratic appeal. Aside from the increase in readership after 1518, Luther as critic and interpreter brought about a more important qualitative change in literacy. In this way, he influenced writings of other lands and of later centuries. He treated the Bible as literature with great relevance to the individual life. Karl Holl and Heinrich Bornkamm give excellent accounts of his hermeneutics, but the literature student is most impressed by Luther's imaginative participation in the text. He took his contemporaries and countrymen into account, and their experiences, in order to achieve a meeting between their passions and those of the biblical authors.

scholarly journals Periodic textures for enhanced current in thin film silicon solar cells

2008 ◽  
Vol 1101 ◽  
Author(s):  
Franz-Josef Haug ◽  
Thomas Söderström ◽  
Oscar Cubero ◽  
Vanessa Terrazzoni-Daudrix ◽  
Xavier Niquille ◽  
...  
Keyword(s):  
Thin Film ◽  
Solar Cells ◽  
Periodic Structures ◽  
Plastic Substrate ◽  
Silicon Solar Cells ◽  
Sinusoidal Grating ◽  
Thin Film Silicon ◽  
Wide Range ◽  
The Individual ◽  
High Degree

AbstractFor thin film silicon solar cells it is vital to increase the optical path of light in the absorber because this allows for thinner cells with better stability and higher production throughput. We discuss the effect of periodically textured interfaces for the case of thin film silicon solar cells in n-i-p configuration using embossed plastic substrate which allows us studying the effect of a wide range of random or periodic textures. Due to the moderate thickness of the individual layers the texture is carried into each interface with a high degree of conformity even for the front contact which is the last layer. Solar cells on periodic structures show excellent performance; in a microcrystalline cell on a simple sinusoidal grating we achieved a gain in current density of 30%. Furthermore, the periodicity serves as a useful tool for the study of light management because the underlying phenomena like diffraction or grating coupling to plasma excitations of the metallic back reflector are governed by a relatively low number of well defined parameters like the periodicity and the amplitude of the grating.

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