scholarly journals Free Vibrations of Anisotropic Nano-Objects with Rounded or Sharp Corners

Nanomaterials ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1838
Author(s):  
Lucien Saviot
Keyword(s):  
Variational Method ◽  
Cross Sections ◽  
Free Vibrations ◽  
Plane Convex ◽  
Single Nanoparticle ◽  
Vibrational Spectroscopies ◽  
Sharp Corners

An extension of the Rayleigh–Ritz variational method to objects with superquadric and superellipsoid shapes and cylinders with cross-sections delimited by a superellipse is presented. It enables the quick calculation of the frequencies and displacements for shapes commonly observed in nano-objects. Original smooth shape variations between objects with plane, convex, and concave faces are presented. The validity of frequently used isotropic approximations for experimentally relevant vibrations is discussed. This extension is expected to facilitate the assignment of features observed with vibrational spectroscopies, in particular in the case of single-nanoparticle measurements.

scholarly journals GEOMETRIC MODELING OF A SHAPE OF PARALLELOGRAM PLATES IN A PROBLEM OF FREE VIBRATIONS USING CONFORMAL RADII

2021 ◽  
pp. 143-159
Author(s):  
A.A. Chernyaev ◽  
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Interpolation Method ◽  
Geometric Characteristic ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Constant Thickness ◽  
Basic Frequency ◽  
Plate Vibrations ◽  
The Subject

The paper considers a method of geometric modeling applied when solving basic twodimensional problems of the theory of elasticity and structural mechanics, in particular the applied problems of engineering. The subject of this study is vibrations of thin elastic parallelogram plates of constant thickness. To determine a basic frequency of vibrations, the interpolation method based on the geometric characteristic of the shape of plates (membrane, cross sections of a rod) is proposed. This characteristic represents a ratio of interior and exterior conformal radii of the plate. As is known from the theory of conformal mappings, conformal radii are those obtained by mapping of a plate onto the interior and exterior of a unit disk. The paper presents basic terms, tables, and formulas related to the considered geometric method with a comparative analysis of the curve diagrams obtained using various interpolation formulas. The original computer program is also developed. The main advantage of the proposed method of determining the basic frequency of plate vibrations is a graphic representation of results that allows one to accurately determine the required solution on the graph among the other solutions corresponding to the considered case of parallelogram plates. Although there are many known approximate approaches, which are used to solve the considered problems, only geometric modeling technique based on the conformal radii ratio gives such an opportunity.

A Variational Method for Fully Developed Laminar Heat Transfer in Ducts

1959 ◽  
Vol 81 (2) ◽  
pp. 157-164 ◽  
Author(s):  
E. M. Sparrow ◽  
R. Siegel
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Variational Method ◽  
Cross Section ◽  
Cross Sections ◽  
Axial Direction ◽  
Circular Sector ◽  
Thermal Boundary Conditions ◽  
Temperature Distributions ◽  
Good Agreement

A variational method is presented for determining fully developed velocity and temperature distributions for laminar flow in noncircular ducts. The heat addition to the fluid is taken to be uniform in the axial direction, but a variety of thermal boundary conditions are considered around the periphery of the duct cross section. Several illustrative examples are given, and comparisons are made which show good agreement with available exact solutions. These examples include ducts of rectangular and circular-sector cross sections.

The Elastic Moduli of Fiber-Reinforced Materials

1964 ◽  
Vol 31 (2) ◽  
pp. 223-232 ◽  
Author(s):  
Zvi Hashin ◽  
B. Walter Rosen
Keyword(s):  
Variational Method ◽  
Cross Sections ◽  
Elastic Moduli ◽  
Numerical Results ◽  
Exact Results ◽  
Effective Elastic Moduli ◽  
Fiber Reinforced ◽  
Random Array ◽  
Fiber Reinforced Materials ◽  
Hexagonal Arrays

Bounds and expressions for the effective elastic moduli of materials reinforced by parallel hollow circular fibers have been derived by a variational method. Exact results have been obtained for hexagonal arrays of identical fibers and approximate results for random array of fibers, which may have unequal cross sections. Typical numerical results have been obtained for technically important elastic moduli.

scholarly journals Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Erasmo Viola ◽  
Marco Miniaci ◽  
Nicholas Fantuzzi ◽  
Alessandro Marzani
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Internal Boundary ◽  
Radius Of Curvature ◽  
Inertia Effects ◽  
Circular Arch

AbstractThis paper investigates the in-plane free vibrations of multi-stepped and multi-damaged parabolic arches, for various boundary conditions. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The constitutive equations relating the stress resultants to the corresponding deformation components refer to an isotropic and linear elastic material. Starting from the kinematic hypothesis for the in-plane displacement of the shear-deformable arch, the equations of motion are deduced by using Hamilton’s principle. Natural frequencies and mode shapes are computed using the Generalized Differential Quadrature (GDQ) method. The variable radius of curvature along the axis of the parabolic arch requires, compared to the circular arch, a more complex formulation and numerical implementation of the motion equations as well as the external and internal boundary conditions. Each damage is modelled as a combination of one rotational and two translational elastic springs. A parametric study is performed to illustrate the influence of the damage parameters on the natural frequencies of parabolic arches for different boundary conditions and cross-sections with localizeddamage.Results for the circular arch, derived from the proposed parabolic model with the derivatives of some parameters set to zero, agree well with those published over the past years.

Numerical Simulation of Vortex-Induced Vibration and Torsional Flutter of Rectangular Cross-Sections by k-ε Model

2003 ◽  
Author(s):  
Kenji Shimada ◽  
Takeshi Ishihara
Keyword(s):  
Numerical Simulation ◽  
Numerical Analysis ◽  
Cross Sections ◽  
Present Method ◽  
Free Vibrations ◽  
Shear Layer Instability ◽  
Vortex Induced Vibration ◽  
Vortex Induced Vibrations ◽  
Karman Vortex ◽  
Occurrence Mechanism

In this paper, torsional aeroelastic vibration is investigated by wind tunnel experiment and numerical analysis which incorporates 2-dimensional modified k-ε model. Experimental results shows that the torsional vortex-induced vibration are classified into several groups. Harmonics and of the Karman-vortex or impinging-shear-layer-instability are found to be involved with the occurrence mechanism of these instabilities. Two types of rectangular cross-sections are chosen to examine the applicability of the numerical method. Unsteady wind forces, pressure distribution and free vibrations are compared with experiments. Although the present method is 2-dimensional, vortex-induced vibrations and torsional flutter were well simulated by the method.

Measurement and modelling of torsional warping free vibrations of beams with rectangular hollow cross-sections

2017 ◽  
Vol 136 ◽  
pp. 68-76 ◽  
Author(s):  
Justin Murin ◽  
Vladimir Goga ◽  
Mehdi Aminbaghai ◽  
Juraj Hrabovsky ◽  
Tibor Sedlar ◽  
...  
Keyword(s):  
Cross Sections ◽  
Free Vibrations
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