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

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.

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.

IN-PLANE VIBRATION OF CIRCULAR ARCHES WITH VARYING CROSS-SECTIONS

2013 ◽  
Vol 13 (01) ◽  
pp. 1350003 ◽  
Author(s):  
EKREM TUFEKCI ◽  
OZNUR OZDEMIRCI YIGIT
Keyword(s):  
Exact Solution ◽  
Cross Section ◽  
Cross Sections ◽  
Free Vibrations ◽  
Transverse Shear Deformation ◽  
Mode Transition ◽  
Rotatory Inertia ◽  
Initial Value ◽  
Inertia Effects ◽  
Circular Arch

The in-plane free vibration of circular arches with continuously varying cross-sections is studied by means of the exact solution. The exact solution can be obtained only for a circular arch with constant cross-section. As an approximation, the circular arch with varying cross-sections is divided into a number of arch elements with constant cross-sections. The cross-section of each arch element is determined by averaging the upper and lower cross-sections. Then, the exact solution of free vibrations for each arch element can be obtained by using the initial value method. The axial extension, transverse shear deformation and rotatory inertia effects are included in the analysis. As the number of the arch elements increases, the fast convergence of the frequencies to those of the original arch is observed. Clamped–clamped (CC), hinged–hinged (HH), hinged–clamped (HC), clamped–free (CF) and free–free (FF) boundary conditions are studied for different opening angles, taper types and taper ratios. A detailed parametric study is performed, by which the mode transition phenomenon is observed. The results obtained are compared with those available in the literature.

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.

Free Vibrations of Functionally Graded Graphene-Reinforced Composite Blades with Varying Cross-Sections

2020 ◽  
pp. 2043006
Author(s):  
Jie Chen ◽  
Pai Cui ◽  
Qiu-Sheng Li
Keyword(s):  
Cross Sections ◽  
Mass Density ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Composite Blades

In this paper, free vibrations of functionally graded (FG) graphene-reinforced composite blades with varying cross-sections are investigated. Considering the cantilever boundary conditions, the dynamic model of a rotating blade is simplified as a varying cross-sections plate with pre-installed angle and pre-twisted angle. As a reinforcement, the graphene platelets (GPLs) are distributed either uniformly or gradiently on the plate along its thickness direction. The effective Young’s modulus is formulated by the modified Halpin–Tsai model. The rule of mixture is applied to calculate the effective Poisson’s ratio and mass density. The equations of motion are established by using the first-order shear deformation theory and von Karman geometric nonlinear theory. Based on the Rayleigh–Ritz method, the natural frequencies of the rotating FG blade reinforced with the GPLs are obtained. The accuracy of the present method is verified by comparing the obtained results with those of the finite element method and published literature. A comprehensive parametric study is conducted, with a particular focus on the effects of distribution pattern, weight fraction, and geometries size of the GPLs together with dimensional parameters of varying cross-sections blade on the dynamics of the FG blades reinforced with the GPLs.

scholarly journals Analysis of free vibrations of cantilever bars with parabolically variable cross-sections using the Rayleigh’s method

2018 ◽  
Vol 16 (4) ◽  
pp. 5-14
Author(s):  
Olga Szlachetka ◽  
◽  
Marek Chalecki ◽  
Jacek Jaworski, ◽  
◽  
...  
Keyword(s):  
Cross Sections ◽  
Free Vibrations ◽  
Variable Cross
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