In-Plane Flexural Vibrations of Circular Rings

1969 ◽  
Vol 36 (3) ◽  
pp. 620-625 ◽  
Author(s):  
S. S. Rao ◽  
V. Sundararajan
Keyword(s):  
Natural Frequencies ◽  
Classical Equation ◽  
Circular Ring ◽  
Classical Formula ◽  
Free Ring ◽  
Circular Arcs ◽  
End Conditions ◽  
Circular Rings ◽  
Experimental Values ◽  
Fixed End

An equation of motion governing the free, in-plane vibrations of a circular ring is developed to include the effects of shear deformation and rotatory inertia. This equation is solved to find the natural frequencies of vibration of free rings and stiffened rings and the results compared with those given by a classical formula. The frequencies for a free ring are found to compare well with the experimental values of Kuhl [5]. Natural frequencies of circular arcs are calculated from the classical equation with hinged and fixed end conditions and the results compared with the approximate values given by Den Hartog [8, 9].

In-Plane Vibration of Simply Supported-Simply Supported Circular Ring Segments

1991 ◽  
Author(s):  
S. Azimi
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Circular Ring ◽  
Mode Shapes ◽  
Simply Supported ◽  
Plane Vibration ◽  
Ring Segment ◽  
Linear Spring ◽  
Circular Rings ◽  
Elastic Constraints

Abstract The general in-plane vibration problem of circular ring segments having linear and torsional elastic constraints at the ends has been studied. One of the interesting cases of concern for which there exists an exact solution is the case where the linear and torsional spring stiffnesses in the circumferential direction become zero (Ku = 0, Kt = 0) and the linear spring stiffness in the radial direction becomes infinity (Kw = ∞). This case is the so-called simply supported-simply supported case. The general form of the equations of motion of circular rings with the proper boundary conditions at the ends have been employed to investigate the vibration of the ring segment. Results for natural frequencies and mode shapes for different angles of the segment have been presented.

Influence of Geometric Imperfections on Vibrational Frequencies of Thin Rings

1975 ◽  
Vol 97 (4) ◽  
pp. 1199-1203
Author(s):  
Joseph R. Gartner ◽  
Shrikant T. Bhat
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Circular Ring ◽  
Body Motion ◽  
Mode Shapes ◽  
Geometric Imperfections ◽  
Modal Coupling ◽  
Truncated Fourier Series ◽  
Energy Formulation

A relatively thin—thickness to radius ratio—circular ring with rectangular cross section has been investigated to numerically evaluate the effect of eccentricity on the in plane bending natural frequencies and mode shapes. The assumed boundary conditions correspond to a ring freely supported in space such that it is free to translate and rotate with rigid body motion. A truncated Fourier series solution is assumed in an energy formulation to obtain numerical approximations of the eigenvalues and the corresponding eigenvectors for different eccentricities. Extensional and inextensional models for both Flu¨gge and Love-Timoshenko ring models were considered with two thickness to radius ratios. Results show different rates of decrease in the magnitudes of the natural frequencies for different mode configurations. Existence of closely spaced frequencies along with modal coupling are noticeable at 50 percent eccentricity.

Critical examination of various approaches used for analysing helical cables

1994 ◽  
Vol 29 (1) ◽  
pp. 43-55 ◽  
Author(s):  
M Raoof ◽  
I Kraincanic
Keyword(s):  
Large Diameter ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Critical Examination ◽  
First Order ◽  
Wide Range ◽  
End Conditions ◽  
Parametric Studies ◽  
The Individual ◽  
Fixed End

Using theoretical parametric studies covering a wide range of cable (and wire) diameters and lay angles, the range of validity of various approaches used for analysing helical cables are critically examined. Numerical results strongly suggest that for multi-layered steel strands with small wire/cable diameter ratios, the bending and torsional stiffnesses of the individual wires may safely be ignored when calculating the 2 × 2 matrix for strand axial/torsional stiffnesses. However, such bending and torsional wire stiffnesses are shown to be first order parameters in analysing the overall axial and torsional stiffnesses of, say, seven wire stands, especially under free-fixed end conditions with respect to torsional movements. Interwire contact deformations are shown to be of great importance in evaluating the axial and torsional stiffnesses of large diameter multi-layered steel strands. Their importance diminishes as the number of wires associated with smaller diameter cables decreases. Using a modified version of a previously reported theoretical model for analysing multilayered instrumentation cables, the importance of allowing for the influence of contact deformations in compliant layers on cable overall characteristics such as axial or torsional stiffnesses is demonstrated by theoretical numerical results. In particular, non-Hertzian contact formulations are used to obtain the interlayer compliances in instrumentation cables in preference to a previously reported model employing Hertzian theory with its associated limitations.

Free Vibration and Instability Analysis of Sandwich Plates with Carbon Nanotubes-Reinforced Composite Faces and Honeycomb Core

2021 ◽  
Author(s):  
Sushila Chowdhary ◽  
Mesfin Kebede Kassa ◽  
Yitbarek Gashaw Tadesse ◽  
Ananda Babu Arumugam ◽  
Rajeshkumar Selvaraj
Keyword(s):  
Finite Element ◽  
Glass Fiber ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Element Formulation ◽  
The Core ◽  
Glass Fiber Reinforced ◽  
End Conditions ◽  
Honeycomb Sandwich ◽  
Instability Regions

In this study, the instability regions of a honeycomb sandwich plate are investigated for different end conditions under periodic in-plane loading. The core layer of the sandwich plate is made of carbon nanotube (CNT)/glass fiber-reinforced honeycomb and the face layers of CNT/glass fiber- reinforced laminated composite. The governing equations are derived using classical laminated plate theory (CLPT) and solved numerically by using finite element formulation. The effectiveness of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies with those available in the literature. The effects of CNT wt.% on the core material, CNT wt.% on the skin material, ply orientation and various end conditions on the variation of natural frequencies, loss factors and instability regions are studied. Finally, some inferences for the effects of CNT reinforcement on the honeycomb sandwich plate subjected to the periodic in-plane loads are discussed.

A Study on a Vibratory Model of a Human Body

1987 ◽  
Vol 109 (2) ◽  
pp. 148-153 ◽  
Author(s):  
S. P. Nigam ◽  
M. Malik
Keyword(s):  
Human Body ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Male Body ◽  
Mass System ◽  
Modeling Procedure ◽  
Experimental Values

This paper is concerned with the modeling of the human body as a spring mass system. Based on certain assumptions, an analysis for evaluating the mass and stiffness values of the model is developed. As an illustration of the modeling procedure, a 15-degree-of-freedom model of a male body is considered. The computed natural frequencies of the model are found to be within the range of available experimental values.

scholarly journals Detection of multiple cracks in a beam by means natural frequencies of transverse vibrations

2020 ◽  
pp. 19-26
Author(s):  
Иван Михайлович Лебедев ◽  
Ефим Ильич Шифрин
Keyword(s):  
Arbitrary Number ◽  
Natural Frequencies ◽  
Multiple Cracks ◽  
Transverse Cracks ◽  
Numerical Examples ◽  
Transverse Vibrations ◽  
End Conditions

Рассматривается задача обнаружения множественных, поперечных трещин в стержне с помощью собственных частот поперечных колебаний. В недавней статье авторов доказано, что любое количество трещин однозначно восстанавливается по трем спектрам, отвечающим трем различным типам краевых условий. В статье также предложен алгоритм идентификации повреждений, вносимых трещинами. Помимо этого, высказано предположение, что для однозначной идентификации трещиноподобных дефектов на самом деле достаточно знать два спектра. Для проверки этого предположения разработана модификация предложенного ранее численного алгоритма. Рассмотрены численные примеры. Полученные результаты дают основание полагать, что высказанное предположение справедливо. A problem of detection of multiple transverse cracks in a beam by means of natural frequencies of transverse vibrations is considered. It is proved in the recent paper of the authors that an arbitrary number of cracks can be uniquely determined by three spectra corresponding to three types of the end conditions. An algorithm of reconstruction the damages corresponding the cracks is also developed. In addition, it was assumed that the cracks can be detected using only two spectra. To verify this supposition a modification of the previously developed algorithm is proposed. Numerical examples are considered. The obtained results confirm the assumption.

A Method for Determining the Flexural Effects of Statically Loaded Beams on Multiple Elastic Supports

1956 ◽  
Vol 23 (4) ◽  
pp. 503-508
Author(s):  
R. A. Di Taranto
Keyword(s):  
Beam Theory ◽  
Elastic Supports ◽  
Electronic Digital Computer ◽  
Simply Supported ◽  
Influence Coefficients ◽  
End Conditions ◽  
Desk Calculator ◽  
Simple Supports ◽  
Fixed End ◽  
Nonuniform Beam

Abstract Herein is presented a means for calculating the static deflections, slopes, moments, and shears of a nonuniform beam on two supports for any end conditions and on three simple supports when subjected to concentrated loads and/or concentrated moments. The method is an extension of a simple tabular procedure as used by Myklestad (1) for use on a desk calculator or electronic digital computer. The procedure is such that it may be easily carried out by one who need not have any knowledge of beam theory. Influence coefficients may be easily and directly calculated for nonuniform beams on two and three elastic supports. The two-support beam is formulated for simply supported one overhang, two supports with linear and torsional springs, and fixed-fixed end conditions. Extensions of this method to any other boundary conditions are indicated.

Flexural Vibrations of a Multi-Material Microhydraulic Hose Subjected to External Excitation. Experimental Research and Theoretical Description

2021 ◽  
Author(s):  
Marek Lubecki ◽  
Michał Stosiak ◽  
Mirosław Bocian ◽  
Kamil Urbanowicz
Keyword(s):  
Experimental Research ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Classical Equation ◽  
Analytical Description ◽  
Theoretical Description ◽  
Laser Vibrometer ◽  
Flexural Vibrations ◽  
Stiffness And Damping ◽  
Mathematica Software

Abstract The paper presents experimental research and mathematical modeling of flexural vibrations of a composite hydraulic microhose. The tested object was a Polyflex 2020N-013V30 hydraulic microhose, consisting of a braided aramid layer placed in a thermoplastic matrix. The vibrations were induced with an external electromagnetic exciter in the range from 0 Hz to 100 Hz using the sweep function. Using a laser vibrometer, the exciter’s displacement was measured in the above-mentioned range. Long exposure photographs were taken to identify the form of microhose’s vibrations as well as to measure it’s amplitude. The existence of considerable non-linearity in subsequent natural frequencies was shown. At the same time, mathematical simulations were carried out using the Mathematica software. For the analytical description of the object’s vibrations partial differential equations based on the string equation were used. A part responsible for damping in the material was added to the classical equation of the string. The dependence of the values of the stiffness and damping coefficients a on the excitation frequency made it possible to model nonlinearities manifested by the upward shift of higher natural frequencies and the suppression of the amplitudes of successive modes. Further development of the proposed model will allow for modeling the internal pressure in the hose and its effect on transverse vibrations. It will also allow to design of vibrations of composite microhoses and avoid the coupling of these vibrations with external excitations.

Force-length relation of isometric sarcomeres in fixed-end tetani

1993 ◽  
Vol 264 (1) ◽  
pp. C19-C26 ◽  
Author(s):  
A. Horowitz ◽  
G. H. Pollack
Keyword(s):  
Sarcomere Length ◽  
Production Capacity ◽  
Force Production ◽  
Length Change ◽  
Optical Diffraction ◽  
Tetanic Force ◽  
End Conditions ◽  
Linear Force ◽  
Fixed End

The higher force observed in fixed-end tetani relative to sarcomere-isometric tetani is commonly attributed to sarcomere length inhomogeneity; sarcomeres in the end regions of the fiber shorten extensively at the expense of the central sarcomeres. By shortening, these sarcomeres supposedly attain higher force production capacity and can thus account for the extra force. However, the fibers could also contain sarcomeres that stay isometric throughout most of the tetanic force plateau. If such sarcomeres undergo slight shortening before their isometric phase, their force-length relation should be elevated (A. Horowitz, H. P. M Wussling, and G. H. Pollack. Biophys. J. 63: 3-17, 1992). These sarcomeres may therefore account for the higher force in fixed-end tetani. To test this possibility, single frog semitendinosus fibers were tetanized under fixed-end conditions. Sarcomere length change during the tetanus was measured at different locations along the fiber by optical diffraction. Fibers stretched to average sarcomere lengths between 2.2 and 3.2 microns contained sarcomeres that, except for some initial shortening during the early part of the tetanus, remained isometric. These sarcomeres were located between the ends and the central region of the fibers. Their force-length relation was higher than the linear force-length relation based on sarcomere length clamps by an average of 14% between sarcomere lengths of 2.4-3.2 microns. Thus slight (1-5%) shortening may explain the relatively higher fixed-end force-length relation.

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