Analytical and Experimental Studies of Orthotropic Corner-Supported Plates With Segmented In-Plane Actuators

2005 ◽  
Author(s):  
Hartono Sumali ◽  
Jordan E. Massad ◽  
Philip L. Reu ◽  
Pavel M. Chaplya ◽  
Jeffrey W. Martin
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Speckle Pattern ◽  
Experimental Studies ◽  
Electronic Speckle Pattern Interferometry ◽  
Two Dimensional ◽  
Dimensional Array ◽  
Laboratory Setup

This paper outlines a model for a corner-supported, thin, rectangular bimorph actuated by a two-dimensional array of segmented, orthotropic PVDF laminates; it investigates the realization and measurement of such a bimorph. First, a model is derived to determine the deflected shape of an orthotropic laminate for a given distribution of voltages over the actuator array. Then, boundary conditions are realized in a laboratory setup to approach the theoretical corner-supported boundary condition. Finally, deflection measurements of actuated orthotropic PVDF laminates are performed with Electronic Speckle Pattern Interferometry and are compared to the model results.

Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

Effect of plasticity at out-of-plane electronic speckle pattern interferometry diagnostics of axisymmetric stresses by the hole-drilling method

2017 ◽  
Vol 53 (1) ◽  
pp. 3-14 ◽  
Author(s):  
Alexander L Popov ◽  
Sergei E Alexandrov ◽  
Victor M Kozintsev ◽  
Alexander L Levitin ◽  
Dmitri A Chelyubeev
Keyword(s):  
Plastic Material ◽  
Speckle Pattern ◽  
Finite Thickness ◽  
Experimental Studies ◽  
Median Plane ◽  
Element Model ◽  
Electronic Speckle Pattern Interferometry ◽  
Hole Drilling ◽  
Disk Model ◽  
Blind Hole

Theoretical, calculated, and experimental results of studies on the registration of the accounting effect of plasticity in the diagnosis of axisymmetric stresses by the hole method and speckle-interferometric detection of the field of normal displacements in its vicinity are presented. Theoretical and computational studies were carried out on a disk model of finite thickness from an ideally elastic–plastic material. The theoretical model considers the formation of elastoplastic deformations in the vicinity of the through hole; the calculated finite element model considers in the vicinity of both through and blind holes of different depths. It was noted that at the blind hole, the most informative are the movements of the axisymmetric bend caused by the violation by the blind hole of symmetry of the disk with respect to its median plane. At the same time, an approximate analytical method has been developed to calculate the stresses that cause only elastic deformations. Experimental studies were carried out on a series of samples in the form of steel disks with axisymmetric stresses near the yield point. These stresses were induced by the hot fit of grinded rings from hardened high-strength steel onto disks made of steel with a low yield strength. Examples are given which show that the stress values determined from normal displacements in the vicinity of the probe holes from the calculated–theoretical and experimental are similar.

Investigation of Effect of Grains on Deformation of Wood under Shearing Loads Using Electronic Speckle Pattern Interferometry

2006 ◽  
Vol 326-328 ◽  
pp. 43-46
Author(s):  
Eisaku Umezaki
Keyword(s):  
Pseudotsuga Menziesii ◽  
Speckle Pattern ◽  
Electronic Speckle Pattern Interferometry ◽  
Two Dimensional ◽  
Annual Rings

The two-dimensional deformation of wood with different grains under shearing loads was measured using an electronic speckle pattern interferometry (ESPI) technique. The radical, tangential and end sections of Douglas firs (Pseudotsuga menziesii) were used as specimens. Results revealed that the deformation values significantly vary for every part of the specimens, and the ring directions of earlywood and latewood, which compose the annual rings, have an effect on the two-dimensional deformation of wood.

scholarly journals Properties of RG interfaces for 2D boundary flows

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Anatoly Konechny
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Variational Method ◽  
Boundary Conditions ◽  
The Other ◽  
Two Dimensional ◽  
Conformal Boundary ◽  
First Approximation ◽  
Local Operators

Abstract We consider RG interfaces for boundary RG flows in two-dimensional QFTs. Such interfaces are particular boundary condition changing operators linking the UV and IR conformal boundary conditions. We refer to them as RG operators. In this paper we study their general properties putting forward a number of conjectures. We conjecture that an RG operator is always a conformal primary such that the OPE of this operator with its conjugate must contain the perturbing UV operator when taken in one order and the leading irrelevant operator (when it exists) along which the flow enters the IR fixed point, when taken in the other order. We support our conjectures by perturbative calculations for flows between nearby fixed points, by a non-perturbative variational method inspired by the variational method proposed by J. Cardy for massive RG flows, and by numerical results obtained using boundary TCSA. The variational method has a merit of its own as it can be used as a first approximation in charting the global structure of the space of boundary RG flows. We also discuss the role of the RG operators in the transport of states and local operators. Some of our considerations can be generalised to two-dimensional bulk flows, clarifying some conceptual issues related to the RG interface put forward by D. Gaiotto for bulk 𝜙1,3 flows.

On the Formulation of Nonreflecting Boundary Conditions for Turbomachinery Configurations: Part II — Application and Analysis

2020 ◽  
Author(s):  
Nina Wolfrum ◽  
Patrick Bechlars ◽  
Maximilian Beck ◽  
Christian Frey ◽  
Daniel Schlüß
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Meridional Flow ◽  
Computational Domain ◽  
Two Dimensional ◽  
Elementary Model ◽  
Nonreflecting Boundary Conditions ◽  
First Case ◽  
Geometrical Features ◽  
Rotational Surfaces

Abstract The flow in turbomachinery components is complex due to the relative motion of rotating and non-rotating elements. A proper design and prediction of physical phenomena requires reliable CFD tools. One important aspect is the incorporation of sophisticated algorithms at the boundaries of the computational domain. For inviscid, one-dimensional and two-dimensional Euler-flows there exist analytical solutions for the formulation of a boundary condition. Realistic applications, however, are viscous and consist of a complex three-dimensional character. Nevertheless, the analytical 2D nonreflecting boundary conditions are commonly used in CFD codes for their high computational efficiency and numerical robustness. The application becomes more challenging when the boundaries are close to geometrical features such as blades and vanes. In practical applications, the position of the boundaries is dictated by geometrical constraints and hence the proximity to the blading cannot always be avoided. The interaction of rotating and non-rotating geometrical features in a turbomachine produces complex flow patterns that propagate in the form of acoustic, vorticity and entropy waves. A boundary condition must be implemented in such a way that waves can propagate undisturbed out of the computational domain. Any reflection may unphysically affect the solution within the computational domain which is especially harmful to sensitive values such as unsteady aeroelastic quantities. But also steady-state computations may suffer from errors produced by reflective boundary conditions. The following paper is the second of two papers on the formulation of unsteady boundary conditions based on a two-dimensional analytical approach. The first part of this paper [6] explains how to extend 2D nonreflecting boundary conditions to real 3D annular domains by applying them in certain conical rotational surfaces. Two different formulations are discussed referring to the orientation of said rotational surfaces. In the first case the surfaces are oriented perpendicular to the boundary panel. In the second case the surfaces are aligned with the circumferentially averaged meridional flow velocity. In the present paper a thorough analysis of the two different approaches will be given. Both formulations of the boundary algorithm are validated on the basis of several elementary model flows. The behavior is analyzed for various unsteady wave patterns of different propagation directions with respect to the boundary. It will be shown that the alignment of the rotational surfaces with the meridional flow has a beneficial effect on the reflective behavior for the majority of the investigated flow conditions. The boundary conditions are then tested on realistic turbomachinery components in order to analyze their applicability on complex flows.

scholarly journals Classifying boundary conditions in JT gravity: from energy-branes to α-branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Akash Goel ◽  
Luca V. Iliesiu ◽  
Jorrit Kruthoff ◽  
Zhenbin Yang
Keyword(s):  
Boundary Condition ◽  
Black Holes ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Ensemble Averaging ◽  
Matrix Integral ◽  
Two Dimensional Model ◽  
Definition Of ◽  
Extremal Black Holes

Abstract We classify the possible boundary conditions in JT gravity and discuss their exact quantization. Each boundary condition that we study will reveal new features in JT gravity related to its matrix integral interpretation, its factorization properties and ensemble averaging interpretation, the definition of the theory at finite cutoff, its relation to the physics of near-extremal black holes and, finally, its role as a two-dimensional model of cosmology.

A Localized Finite-Element Method for Two-Dimensional Steady Potential Flows with a Free Surface

1978 ◽  
Vol 22 (04) ◽  
pp. 216-230
Author(s):  
Kwang June Bai
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Boundary Conditions ◽  
Complex Geometry ◽  
The Body ◽  
Finite Domain ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Test Functions ◽  
Infinite Domain

A numerical method is presented for solving two-dimensional uniform flow problems with a linearized free-surface boundary condition. The boundary-value problem governed by Laplace's equation is replaced by a weak formulation (also known as Galerkin's method) with certain essential boundary conditions. The infinite domain of the fluid is reduced to a finite domain by utilizing known solution spaces in certain subdomains. The bases for the trial and test functions are chosen from the same subspace of the polynomial function space in the reduced subdomain. The essential boundary conditions are properly taken into account by an unconventional choice of the basis for the trial functions, which is different from that for the test functions in other subdomains. This method is applied to two-dimensional steady flow past a submerged elliptic section, a hydrofoil at an arbitrary angle of attack, and a bump on the bottom. In each example the body boundary condition is satisfied exactly. Both subcritical and supercritical flows are treated. We present the numerical results of wave resistance, lift force, moment, circulation strength, and flow blockage parameter. The computed pressure distributions on the hydrofoil and wave profiles are shown. The test results obtained by the present method agree very well with existing results. The main advantage of this method is that any complex geometry of the boundary can be easily accommodated.

scholarly journals Investigation on Non-Linear Vibration Response of Cantilevered Thin Plates with Crack Using Electronic Speckle Pattern Interferometry

Proceedings ◽  
2018 ◽  
Vol 2 (8) ◽  
pp. 539
Author(s):  
Nan Tao ◽  
Yinhang Ma ◽  
Hanyang Jiang ◽  
Meiling Dai ◽  
Fujun Yang
Keyword(s):  
Mode Shape ◽  
Speckle Pattern ◽  
Experimental Studies ◽  
Forced Response ◽  
Thin Plates ◽  
Mode Shapes ◽  
Electronic Speckle Pattern Interferometry ◽  
Intact Specimen ◽  
Harmonic Resonance ◽  
Super Harmonic Resonance

The time-averaged electronic speckle pattern interferometry (ESPI) is employed to measure the frequencies and mode shapes of thin, cantilevered plates with root-slit. The first 12 order linear resonance frequency and mode shape of an intact cantilevered plate is determined by using FEM calculation. The dynamic response of the intact specimen forced by a PZT actuator is measured and its super-harmonic resonance of forced response is investigated experimentally. The results show that the principal mode shape of super-harmonic vibration is similar to its natural modal. In contrast to linear forcing vibration, the threshold of force for super-harmonic resonance is much higher than that of the former. In addition, linear free response of four cantilevered root-slit plates with variation length of slit are analyzed by applying the FEM calculation, and their responses of forcing vibration were measured by using the ESPI method. The validity and accuracy of the numerical prediction are confirmed through experimental studies. The present work shows that the ESPI technique can provide whole-field and real-time measurement for vibration analysis and can also be employed for validation of the FEM calculation.

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