Size-Effect Analysis on Vibrational Response of Functionally Graded Annular Nano-Plate Based on Nonlocal Stress-Driven Method
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Dynamic analysis of functionally graded size-dependent annular nano-plate is the main concern in this study. To obtain the vibrational behavior of this plate, the stress-driven nonlocal integral elasticity, as well the strain gradient theory were used in conjunction with the classical plate theory. The resulting equilibrium equations were solved using the generalized differential quadrature rule (GDQR) and the influences of various parameters such as; size-effect parameter, material heterogeneity index, the aspect ratio of the inner to outer radii, and the effects of different boundary conditions were investigated on the vibrational behavior of the nano-plate, based on different types of boundary conditions. Results indicate that the natural frequencies increase with an increase in the heterogeneity index [Formula: see text] and the increase in size-effect parameter shows a similar effect in both models. Additionally, for the simply supported and free-edge boundary conditions (for both edges), as well as the free and knife-edges, and simply supported-free edges, the strain gradient theory predicts higher values of frequency ratios as [Formula: see text] was increased. Similar results were obtained for the remaining types of boundary conditions, with a higher sensitivity to [Formula: see text], provided the stress-driven model is used. This behavior can be interpreted as the sensitivity of the nano-plate to [Formula: see text] that is manifested by the use of the stress-driven model for the prediction of vibrational behavior of the nano-plate.Keywords:
Plate theory
Aspect ratio (aeronautics)
Elasticity
Many defects are generated during micro- and nano-fabrication processes, especially for high aspect ratio structures. The aspect ratio of structures is an important parameter for subsequent processes. However, the top of high aspect ratio structures usually adheres to each other; moreover, pattern with high aspect ratio even can collapse or peel off from the substrate during the drying process, which is mainly ascribed to the capillary force. In this paper, a new method that puts supporting structures on the fabrication structures to reduce collapse has been proposed. The conventional method and new method were compared by calculating the deformations for different line widths and aspect ratios. The new method was also applied in fabricating nanostructures. The results indicated that the new method can effectively decrease the deformation and increase the aspect ratio.
Aspect ratio (aeronautics)
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In this paper, static analysis of a nano rectangular plate subjected to uniform distributed load is studied based on modified couple stress theory (MSCT) by using Generalized Differential Quadrature (GDQ) Method. The inclusion of an additional material parameter enables the new plate model to capture the size effect. The new non-classical plate model reduces to the classical plate model when the length scale parameter is set to zero. In deriving of the governing equations, the minimum total potential energy principle is used. In the solution of the governing equations, the DQM method is used for simply-supported nano plate within the Kirchhoff-Love plate theory. In the numerical results, the influences the material length scale parameter and the dimension parameters of the plate on the static deflection of the nano plate is presented. Also, the difference between the classical theory (CT) and MSCT is investigated for static responses of nano plate.
Plate theory
Quadrature (astronomy)
Length scale
Bending of plates
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Plate theory
Length scale
Elasticity
Aspect ratio (aeronautics)
Quadrature (astronomy)
Poisson's ratio
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Orthotropic material
Plate theory
Quadrature (astronomy)
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A debate is currently taking place over the appropriate aspect ratio for advanced television displays. Any selected aspect ratio is inherently incompatible with any other and will require the use of some form of accommodation technique. The derivation of the 16:9 (1.78:1) aspect ratio from accommodation techniques and display modes is explained. The relationship between aspect ratio and display memory is also explained. Research into the history of aspect ratios indicates that the 1.78:1 aspect ratio was adopted by the standards committee of the Society of Motion Picture Engineers in 1930. It also indicates that the factors that may have led to widescreen motion picture systems may no longer be applicable. The research for this paper found no clear indication of a preference for any particular aspect ratio for moving images nor any physiological reason to favor one over another. The research did show that cinematographers have not always favored a particular aspect ratio.
Aspect ratio (aeronautics)
Contrast ratio
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A debate is currently taking place over the appropriate aspect ratio for advanced television displays. Any selected aspect ratio is inherently incompatible with any other and will require the use of some form of accommodation technique. The derivation of the 16:9 (1.78:1) aspect ratio from accommodation techniques and display modes is explained, as is the relationship between aspect ratio and display memory. Research into the history of aspect ratios indicates that the 1.78:1 aspect ratio was adopted by the Standards Committee of the Society of Motion Picture Engineers (SMPE) in 1930. It also indicates that the factors that may initially have led to widescreen motion picture systems may no longer be applicable. The research for this paper found no clear indication of a preference for any particular aspect ratio for moving images nor any physiological reason to favor one over another. The research did show that cinematographers have not always favored the same aspect ratio.
Aspect ratio (aeronautics)
Contrast ratio
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Abstract A simple numerical experiment was performed to investigate the result published in many papers that measurements indicate that aggregates may be well represented as oblate spheroids with mean aspect ratio (semiminor axis to semimajor axis length) of 0.6. The aspect ratio measurements are derived from two-dimensional projections of complex three-dimensional aggregates. Here, aggregates were modeled as ellipsoids with semiprincipal axes of length a , b , and c , which include oblate spheroids ( a = b ) as a class, and the projected aspect ratios of large numbers of two-dimensional projections of them were sampled. When sampling oblate spheroids with aspect ratio 0.6 over random orientations, the mean projected aspect ratio is 0.746. A mean projected aspect ratio of 0.6 is obtained for an oblate spheroid with aspect ratio of 0.33. When sampling randomly oriented ellipsoids with semiminor axes ( b , c ) varying from 0.10 to 1.00 in steps of 0.01, representing many complex shapes, the mean projected aspect ratio is 0.595, close to the measured mean projected aspect ratio of aggregates of 0.6. These experiments demonstrate that the conclusion one may safely draw from the projected aspect ratio measurements is that the mean aspect ratio of aggregates is lower than 0.6. Moreover, the projected aspect ratio distributions from measurements suggest a mixture of aggregate shapes, rather than only oblate spheroids as is often assumed.
Aspect ratio (aeronautics)
Oblate spheroid
Ellipsoid
Spheroid
Axial ratio
Shape factor
Particle (ecology)
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Aspect ratio (aeronautics)
Morphology
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Differential Quadrature Method (DQM) is employed to obtain natural frequencies and mode shapes of nonhomogeneous rectangular orthotropic plates of linearly varying thickness resting on two -parameter foundation (Pasternak). The analysis is based on classical plate theory. Numerical results are presented for various values of plate parameters for different boundary conditions. Convergence studies have been made to ensure accuracy of the results. A comparison of our results with those available in the literature shows the versatility and accuracy of DQM
Orthotropic material
Plate theory
Natural frequency
Quadrature (astronomy)
Foundation (evidence)
Transverse vibration
Vibration of plates
Bending of plates
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Synopsis The relationship between the aspect ratio and physical fields in aluminium reduction cells wase studied numerically. The aspect ratio was firstly defined and 7 kinds of 320 kA cells with different aspect ratios were put forward. By using numerical simulation, the relationship between the aspect ratio and the electric-magnetic flow fields, magnetohydrodynamic stabilities, and thermal stability was discussed. It is concluded that the electric-magnetic flow field distributions are greatly affected by the aspect ratio. From the perspective of magnetohydrodynamics stability, the larger the aspect ratio is, the more stable the cell will be. A larger aspect ratio is more beneficial for the thermal stability under the same current density.
Aspect ratio (aeronautics)
Thermal Stability
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