A Quasi-3D Higher-Order Theory for Bending of FG Nanoplates Embedded in an Elastic Medium in a Thermal Environment

This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered where the variation of the material properties of the FG nanoplate are considered only in thickness direction. Unlike other shear and deformations theories in which the number of unknown functions is five and more, the present work uses shear and deformations theory with only four unknown functions. The four-unknown normal and shear deformations model, associated with Eringen nonlocal elasticity theory, is used to derive the equations of equilibrium utilizing the principle of virtual displacements. The effects due to nonlocal coefficient, side-to-thickness ratio, aspect ratio, normal and shear deformations, thermal load and elastic foundation parameters, as well as the gradation in FG nanoplate bending, are investigated. In addition, for validation, the results obtained from the present work are compared to ones available in the literature.

On wave propagation and free vibration of piezoelectric sandwich plates with perfect and porous functionally graded substrates

This paper aims to develop analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers. The effect of porosities, which occur in FG materials, is rarely reported in the literature of smart FG plates but included in the present modeling. The modified rule of mixture is therefore considered for variation of effective material properties within the FG substrate. Based on a four-variable higher-order theory, the electromechanical model of the system is established through the use of Hamilton’s principle, and Maxwell’s equation. This theory drops the need of any shear correction factor, and results in less governing equations compared to the conventional higher-order theories. Analytical solutions are applied to the obtained equations to extract the results for two investigations: (I) the plane wave propagation of infinite smart plates and (II) the free vibration of smart rectangular plates with different boundary conditions. After verifying the model, extensive numerical results are presented. Numerical results demonstrate that the wave characteristics of the system, including wave frequency and phase velocity along with the natural frequencies of its bounded counterpart, are highly influenced by the plate parameters such as power-law index, porosity, and piezoelectric characteristics.

Ultraproducts and Higher Order Models

<p>The programme of work for this thesis began with the somewhat genenal intention of parallelling in the context of higher order models the ultraproduct construction and its consequences as developed in the literature for first order models. Something of this was, of course, already available in the ultrapower construction of W.A.J. Luxemburg used in Non Standand Analysis. It may have been considered that such a genenal intention was not likely to yield anything of significance oven and above what was already available from viewing the higher order situation as a 'many sorted' first order one and interpreting the first order theory accordingly. In the event, however, I believe this has proved not to be so. In particular the substructure concepts developed in Chapter II of this thesis together with the various embedding theorems and their applications are not immediately available fnom the first order theory and seem to be of sufficient worth to warrant developing the higher order theory in its own terms. This, anyway, is the basic justification for the approach and content of the thesis.</p>

Canonical equivalence, quantization and inflation for higher-order theory of gravity

Canonical formulation of higher-order theory of gravity has been attempted over decades. Different routes lead to different phase-space structures of the Hamiltonian. Although, these Hamiltonians are canonically equivalent at the classical level, their quantum counterparts may not be same, due to nonlinearity. Earlier, it has been proved that ‘Dirac constraint analysis’ (after taking care of divergent terms) and ‘Modified Horowitz’ Formalism’ lead to identical phase-space structure of the Hamiltonian for the gravitational action with scalar curvature squared terms. For the sake of completeness, this paper expatiates the extension of the same work for a general fourth-order gravitational action. Canonical quantization and semiclassical approximation are performed to explore that such a quantum theory transits successfully to a classical de-Sitter Universe. Inflation is also studied. Inflationary parameters show excellent agreement with the recently released Planck’s data.

Durand of St.-Pourçain on Reflex Acts and State Consciousness

Some of my mental states are conscious and some of them are not. Sometimes I am so focused on the wine in front of me that I am unaware that I am thinking about it. But sometimes, of course, I take a reflexive step back and become aware of my thinking about the wine in front of me. What marks the difference between a conscious mental state and an unconscious one? In this article, the author focuses on Durand of St.-Pourçain’s rejection of the higher-order theory of state consciousness, according to which a mental act is conscious when there is another, suitably related, mental (reflex) act that exists at the same time with it. Durand rejects such higher-order theories on the grounds that they violate the thesis that a given mental power can have or elicit only one mental act at a given time. The author first goes over some of Durand’s general arguments for this thesis. He then turns to Durand’s application of the thesis to the issue of state consciousness and reflex acts. He closes by considering the objection that Durand’s same-order theory of state consciousness makes consciousness ubiquitous.