scholarly journals Asymptotic analysis of natural frequencies of axisymmetric oscillations of orthotropic cylindrical shells in an infinite elastic medium, liquid filled

2019 ◽  
Vol 15 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Famil A Seyfullayev ◽  
Gulnar R Mirzayeva ◽  
Shusha A Kerimova
Keyword(s):  
Asymptotic Analysis ◽  
Elastic Medium ◽  
Asymptotic Method ◽  
Natural Frequencies ◽  
Longitudinal Direction ◽  
Frequency Equation ◽  
Infinite Length ◽  
Dynamic Calculation ◽  
Thin Walled ◽  
Oscillatory Processes

Aim of the research. Free axisymmetric fluctuation of a cylindrical orthotropic cover, the infinite length contacting to the infinite elastic medium and filled with liquid is investigated. Methods. At design of the thin-walled shell designs which are widely applied in aviation, the missile and space equipment and various fields of the industry, an important task is dynamic calculation of the intense deformed condition of these designs. At a research of dynamics of covers it is necessary to determine own frequencies and forms of small fluctuations, and frequencies from the lower part of a range are of the greatest interest. It is supposed that the rigidity of material of a cover is a little more than rigidity of material of the environment. The solution of the equations of movements of the environment is considered in two options. Results. The frequency equation is received. The analysis of frequency and a form of fluctuations of a cover is carried out. The schedule of dependence of frequency of own axisymmetric fluctuations of a system on wave formation in the longitudinal direction is constructed. By means of an asymptotic method the frequency equations of the ridge cylindrical covers filled with liquid are constructed, the approximate frequencies of the equation and simple settlement formulas allowing to find values of the minimum own frequencies of fluctuations of the considered system are received, the forced fluctuations of the supported cover filled with liquid are investigated and defined is amplitude frequency characteristics of the considered oscillatory processes.

scholarly journals Spectral Dynamic Analysis of Torsional Vibrations of Thin-Walled Open Section Beams Restrained Against Warping at One End and Transversely Restrained at the Other End

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Chellapilla Kameswara Rao 1 ◽  
Lokavarapu Bhaskara Rao 2
Keyword(s):  
Dynamic Analysis ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
The Other ◽  
Graphical Form ◽  
Open Section ◽  
Torsional Frequency ◽  
Thin Walled ◽  
Spectral Frequency

The present paper deals with spectral dynamic analysis of free torsional vibration of doubly symmetric thin-walled beams of open section. Spectral frequency equation is derived in this paper for the case of rotationally restrained doubly-symmetric thin-walled beam with one end rotationally restrained and transversely restrained at the other end. The resulting transcendental frequency equation with appropriate boundary conditions is derived and is solved for varying values of warping parameter and the rotational and transverse restraint parameter. The influence of rotational restraint parameter, transverse restraint parameter and warping parameter on the free torsional vibration frequencies is investigated in detail. A MATLAB computer program is developed to solve the spectral frequency equation derived in this paper. Numerical results for natural frequencies for various values of rotational and transverse restraint parameters for various values of warping parameter are obtained and presented in both tabular as well as graphical form showing the influence of these parameters on the first fundamental torsional frequency parameter.

Vibrations of Spinning Rings With Radial and Circumferential Displacement Constraints

1991 ◽  
Author(s):  
Shyh-Chin Huang ◽  
Chen-Kai Su
Keyword(s):  
Natural Frequencies ◽  
Point Contact ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Complex Conjugate ◽  
Constrained System ◽  
Form Complex ◽  
Circumferential Displacement ◽  
On The Road ◽  
Displacement Constraints

Abstract The frequencies and mode shapes of rolling rings with radial and circumferential displacement constraints are investigated. The displacement constraints practically come from the point contact, e.g., rolling tire on the road, or other applications. The proposed approach to analysis is calculating the natural frequencies and modes of a non-contacted spinning ring, then employing the receptance method for displacement constraints. The frequency equation for the constrained system is hence obtained, and it can be solved numerically or graphically. The receptance matrix developed for the spinning ring is surprisingly found not symmetric as usual. Moreover, the cross receptances are discovered to form complex conjugate pairs. That is a feature that has never been described in literature. The results show that the natural frequencies for the spinning ring in contact, as expected, higher than those for the non-contacted ring. The variance of frequencies to rotational speeds are then illustrated. The analytic forms of mode shapes are also derived and sketched. The traveling modes are then shown for cases.

Axial Wave Propagation in Infinitely Long Periodic Curved Panels

2003 ◽  
Vol 125 (1) ◽  
pp. 24-30 ◽  
Author(s):  
C. Pany ◽  
S. Parthan
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Propagation Constant ◽  
Infinite Length ◽  
Approximate Methods ◽  
Bending Vibration ◽  
Element Analysis ◽  
Curved Panel ◽  
Propagation Of Waves ◽  
Curved Panels

Propagation of waves along the axis of the cylindrically curved panels of infinite length, supported at regular intervals is considered in this paper to determine their natural frequencies in bending vibration. Two approximate methods of analysis are presented. In the first, bending deflections in the form of beam functions and sinusoidal modes are used to obtain the propagation constant curves. In the second method high precision triangular finite elements is used combined with a wave approach to determine the natural frequencies. It is shown that by this approach the order of the resulting matrices in the FEM is considerably reduced leading to a significant decrease in computational effect. Curves of propagation constant versus natural frequencies have been obtained for axial wave propagation of a multi supported curved panel of infinite length. From these curves, frequencies of a finite multi supported curved panel of k segments may be obtained by simply reading off the frequencies corresponding to jπ/kj=1,2…k. Bounding frequencies and bounding modes of the multi supported curved panels have been identified. It reveals that the bounding modes are similar to periodic flat panel case. Wherever possible the numerical results have been compared with those obtained independently from finite element analysis and/or results available in the literature.

scholarly journals Investigation of natural frequencies of axially loaded thin-walled columns

2018 ◽  
Vol 219 ◽  
pp. 02018
Author(s):  
Łukasz Żmuda-Trzebiatowski
Keyword(s):  
Applied Load ◽  
Natural Frequencies ◽  
Elastic Buckling ◽  
Correlation Technique ◽  
Buckling Loads ◽  
Perfectly Plastic ◽  
Linear Buckling ◽  
Thin Walled ◽  
Elastic Perfectly Plastic ◽  
Flexural Torsional Buckling

The paper deals with correlation between natural frequencies of two steel thin-walled columns and the corresponding applied load. The structures are made of cold-formed lipped channel sections. The columns lengths were assumed to follow two buckling patterns – global flexural and flexural-torsional buckling. In the thicker structure two material models were considered – linearly-elastic and elastic-perfectly plastic. Numerical computations cover dynamic eigenvalue problem, linear buckling and geometrically (and materially) non-linear analysis. The correlation between squares of natural frequencies and the applied load is linear in both columns. The first natural frequencies drop to zero due to structural buckling. This method, called the Vibration Correlation Technique, allows to predict buckling loads on the basis of measured vibration frequencies of the structures. Plasticity does not affect the corresponding curves – the use of the presented technique is limited to the structures exhibiting elastic buckling behaviour.

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

scholarly journals The method of direct finite perturbation of numerical models for studying of the dynamic, stiffness and strength properties for thin-walled elements of engineering constructions.

2014 ◽  
Vol 2014 (4) ◽  
pp. 114-124
Author(s):  
Юрий Костенко ◽  
Yuriy Kostenko ◽  
Анатолий Чепурной ◽  
Anatoliy Chepurnoy ◽  
Александр Литвиненко ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Numerical Models ◽  
Dynamic Stiffness ◽  
Strength Properties ◽  
Test Problems ◽  
Finite Element Models ◽  
Direct Perturbation ◽  
Thin Walled

The methods of direct perturbation for finite element models of thin-walled engineering constructions for sensitivity analysis of their strength, stiffness and dynamic characteristics to the change in their thickness are proposed. The approach for prediction of distribution for natural frequencies migration as result of change in their thickness are presented. The applicability of the linearized models to determine displacements, stresses and natural frequencies slightly thinned design compared to the nominal (original) are shown. The examples of test problems are given.

Vibration Response of a Thin-Walled Cylindrical Pipe with Liquid

2012 ◽  
Vol 189 ◽  
pp. 345-349
Author(s):  
Yu Lan Wei ◽  
Bing Li ◽  
Li Gao ◽  
Ying Jun Dai
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Beam Model ◽  
Vibration Modes ◽  
Timoshenko Beam Model ◽  
Cylindrical Pipe ◽  
Bending Vibration ◽  
Beam Bending ◽  
Thin Walled

Vibration characteristics of the thin-walled cylindrical pipe are affected by the liquid within the pipe. The natural frequencies and vibration modes of the pipe without liquid are analyzed by the theory of beam bending vibration and finite element model, which is based on the Timoshenko beam model. The first three natural frequencies and vibration modes of the pipe with or without liquid are acquired by experiments. As shown in the experiment results, the natural frequencies of the containing liquid pipe are lower than the natural frequencies of the pipe without liquid.

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