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.

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.

Canonical formulation of Pais–Uhlenbeck action and resolving the issue of branched Hamiltonian

2017 ◽  
Vol 14 (03) ◽  
pp. 1750038 ◽  
Author(s):  
Kaushik Sarkar ◽  
Nayem Sk ◽  
Ranajit Mandal ◽  
Abhik Kumar Sanyal
Keyword(s):  
Scalar Curvature ◽  
Canonical Transformation ◽  
Auxiliary Variable ◽  
Order Theory ◽  
Higher Order ◽  
End Points ◽  
Canonical Formulation ◽  
Higher Order Terms ◽  
Theory Of Gravity ◽  
Higher Order Theory

Canonical formulation of higher order theory of gravity requires to fix (in addition to the metric), the scalar curvature, which is acceleration in disguise, at the boundary. On the contrary, for the same purpose, Ostrogradski's or Dirac's technique of constrained analysis, and Horowit'z formalism, tacitly assume velocity (in addition to the co-ordinate) to be fixed at the end points. In the process when applied to gravity, Gibbons–Hawking–York term disappears. To remove such contradiction and to set different higher order theories on the same footing, we propose to fix acceleration at the endpoints/boundary. However, such proposition is not compatible to Ostrogradski's or Dirac's technique. Here, we have modified Horowitz's technique of using an auxiliary variable, to establish a one-to-one correspondence between different higher order theories. Although, the resulting Hamiltonian is related to the others under canonical transformation, we have proved that this is not true in general. We have also demonstrated how higher order terms can regulate the issue of branched Hamiltonian.

Nonlinear Vibration Analysis of Shear Deformable Functionally Graded Ceramic-Metal Plates Using an Improved Higher Order Theory

2010 ◽  
Author(s):  
Mohammad Talha ◽  
B. N. Singh
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Normal Strain ◽  
Higher Order Terms ◽  
Higher Order Theory ◽  
Shear Deformable

In the present study, an improved higher order theory in conjunction with finite element method (FEM) is presented and is applied to study the nonlinear vibration analysis of shear deformable functionally graded material (FGMs) plates. The present structural model kinematics assumes the cubically varying in-plane displacement over the entire thickness, while the transverse displacement varies quadratically to achieve the accountability of normal strain and its derivative in calculation of transverse shear strains. The theory also satisfies zero transverse strains conditions at the top and bottom faces of the plate, and the geometric nonlinearity is based on Green-Lagrange assumptions. All higher order terms appearing from nonlinear strain displacement relations are incorporated in the formulation. The material properties of the plates are assumed to vary smoothly and continuously throughout the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. A C0 continuous isoparametric nonlinear FEM with 13 degrees of freedom per node is proposed for the accomplishment of the improved elastic continuum. Numerical results with different system parameters and boundary conditions are accomplished, to show the importance and necessity of the higher order terms in the nonlinear formulations.

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.

Higher Order Theory

2018 ◽  
Author(s):  
J. Christopher Maloney
Keyword(s):  
Phenomenal Character ◽  
Order Theory ◽  
Higher Order ◽  
Cognitive State ◽  
Unconscious Perception ◽  
Higher Order Theory ◽  
Order State

Rosenthal's rendition of representationalism denies intentionalism. His higher order theory instead asserts that a perceptual state's phenomenal character is set by that state's being related to, because represented by, another, but higher order, cognitive state. The theory arises from the doubtful supposition of unconscious perception and mistakenly construes intrinsic phenomenal character extrinsically, as one state's serving as the content of another. Yet it remains mysterious how and why a higher order state might be so potent as to determine phenomenal character at all. Better to resist higher order theory’s embrace of dubious unconscious perceptual states and account for states so-called simply in terms of humdrum mnemonic malfeasance. Moreover, since the suspect theory allows higher order misrepresentation, it implies sufferance of impossible phenomenal character. Equally problematic, representationalism pitched at the higher order entails the existence of bogus phenomenal character when upstairs states represent downstairs nonperceptual states.

Seeming to Seem

2018 ◽  
Author(s):  
David Rosenthal
Keyword(s):  
Mental States ◽  
Order Theory ◽  
Higher Order ◽  
Psychological State ◽  
Intentional Stance ◽  
First Person ◽  
Psychological States ◽  
Third Person ◽  
Higher Order Theory ◽  
The Third Person

Dennett’s account of consciousness starts from third-person considerations. I argue this is wise, since beginning with first-person access precludes accommodating the third-person access we have to others’ mental states. But Dennett’s first-person operationalism, which seeks to save the first person in third-person, operationalist terms, denies the occurrence of folk-psychological states that one doesn’t believe oneself to be in, and so the occurrence of folk-psychological states that aren’t conscious. This conflicts with Dennett’s intentional-stance approach to the mental, on which we discern others’ mental states independently of those states’ being conscious. We can avoid this conflict with a higher-order theory of consciousness, which saves the spirit of Dennett’s approach, but enables us to distinguish conscious folk-psychological states from nonconscious ones. The intentional stance by itself can’t do this, since it can’t discern a higher-order awareness of a psychological state. But we can supplement the intentional stance with the higher-order theoretical apparatus.

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