Nonlinear Theory for Flexural Motions of Thin Elastic Plate—Part 2: Boundary-Layer Theory Near the Edge

1981 ◽  
Vol 48 (2) ◽  
pp. 383-390 ◽  
Author(s):  
N. Sugimoto
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Elastic Plate ◽  
Order Theory ◽  
Higher Order ◽  
Boundary Layer Theory ◽  
Thin Elastic Plate ◽  
Boundary Layer Problem ◽  
Higher Order Theory ◽  
Layer Problem

This paper deals with, as a continuation of Part 1 of this series, the boundary-layer theory for flexural motions of a thin elastic plate. In the framework of the higher-order theory developed in Part 1, three independent boundary conditions at the edge of the plate are too many to be imposed on the essentially fourth order differential equations. To overcome this difficulty, a boundary layer appearing in a narrow region adjacent to the edge is introduced. Using the matched asymptotic expansion method, uniformly valid solutions for a full plate problem are sought. The boundary-layer problem consists of the torsion problem and the plane problem. Three types of the edge conditions are treated, the built-in edge, the free edge, and the hinged edge. Depending on the type of edge condition, the nature of the boundary layer is characterized. After solving the boundary-layer problem, “reduced” boundary conditions relevant to the higher-order theory are established.

Nonlinear Theory for Flexural Motions of Thin Elastic Plate—Part 1: Higher-Order Theory

1981 ◽  
Vol 48 (2) ◽  
pp. 377-382 ◽  
Author(s):  
N. Sugimoto
Keyword(s):  
Elastic Plate ◽  
Finite Thickness ◽  
Expansion Method ◽  
Order Theory ◽  
Higher Order ◽  
Thin Elastic Plate ◽  
Characteristic Wavelength ◽  
Higher Order Terms ◽  
The Moment ◽  
Higher Order Theory

This paper develops a comprehensive higher-order theory for flexural motions of a thin elastic plate, in which the effect of finite thickness of the plate and that of small but finite deformation are taken into account. Based on the theory of nonlinear elasticity for a homogeneous and isotropic solid, the nonlinear equations for the flexural motions coupled with the extensional motions are systematically derived by the moment asymptotic expansion method. Denoting by ε the ratio of the thickness of the plate to a characteristic wavelength of flexural motions, an order of characteristic deflection is assumed to be ε2 and that of a characteristic strain ε3. The displacement and stress components are sought consistently up to the next higher-order terms than those in the classical theory.

Boundary Conditions for the Turbulent Mixing Layer Between Two Parallel Streams

1974 ◽  
Vol 41 (1) ◽  
pp. 25-28 ◽  
Author(s):  
T. E. Unny ◽  
Norio Hayakawa
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Eddy Viscosity ◽  
Outer Boundary ◽  
Mixing Layer ◽  
Turbulent Mixing Layer ◽  
Boundary Layer Problem ◽  
Finite Distance ◽  
Layer Problem

The boundary conditions of the boundary-layer problem between two parallel turbulent streams are investigated solving higher-order terms of the inner and outer boundary-layer expansion. It is shown that the assumption that the eddy viscosity is proportional to longitudinal distance x fails to yield the third boundary condition of the boundary-layer problem. In this paper this boundary condition has been derived based on the consideration that the eddy viscosity attains a constant value at large but finite distance. The result applies to compressible as well as incompressible flow.

scholarly journals On Solutions for a Generalized Differential Equation Arising in Boundary Layer Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Layer ◽  
Existence And Uniqueness ◽  
Shooting Method ◽  
Boundary Layer Theory ◽  
Boundary Layer Problem ◽  
Blasius Problem ◽  
Generalized Differential Equation ◽  
Generalized Differential ◽  
Uniqueness Of A Solution ◽  
Layer Problem

We treat the existence and uniqueness of a solution for the generalized Blasius problem which arises in boundary layer theory. The shooting method is used in the proof of our main result. An example is included to illustrate the results.

Consciousness, Metacognition, & Perceptual Reality Monitoring

2019 ◽  
Author(s):  
Hakwan Lau
Keyword(s):  
Epistemic Justification ◽  
Order Theory ◽  
Higher Order ◽  
Belief Formation ◽  
Reality Monitoring ◽  
Conscious Perception ◽  
Brute Fact ◽  
Higher Order Theory ◽  
Subjective Level

I introduce an empirically-grounded version of a higher-order theory of conscious perception. Traditionally, theories of consciousness either focus on the global availability of conscious information, or take conscious phenomenology as a brute fact due to some biological or basic representational properties. Here I argue instead that the key to characterizing the consciousness lies in its connections to belief formation and epistemic justification on a subjective level.

Dual Aspect Theory

2018 ◽  
Author(s):  
J. Christopher Maloney
Keyword(s):  
Phenomenal Character ◽  
Order Theory ◽  
Higher Order ◽  
Normal Variation ◽  
Perceptual Representations ◽  
Order Representation ◽  
Management Conflicts ◽  
Higher Order Theory

Carruthers proposes a subtle dispositionalist rendition of higher order theory regarding phenomenal character. The theory would distinguish unconscious movement management from conscious attitude management as perceptual processes. Each process takes perceptual representations as inputs. A representation subject to attitude management is apt to induce a higher order representation of itself that secures a self-referential aspect of its content supposedly determinative of phenomenal character. Unfortunately, the account requires a problematic cognitive ambiguity while failing to explain why attitude, but not movement, management, determines character. Moreover, normal variation in attitudinal management conflicts with the constancy typical of phenomenal character. And although an agent denied perceptual access to a scene about which she is otherwise well informed would suffer no phenomenal character, dispositionalist theory entails otherwise. Such problems, together with the results of the previous chapters, suggest that, whether cloaked under intentionalism or higher order theory, representationalism mistakes content for character.

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