Dynamic Stability of Truncated Conical Shells Under Pulsating Torsion

1981 ◽  
Vol 48 (2) ◽  
pp. 391-398 ◽  
Author(s):  
J. Tani
Keyword(s):  
Dynamic Stability ◽  
Practical Importance ◽  
Low Frequency ◽  
Instability Region ◽  
Wave Number ◽  
Vibration Modes ◽  
Conical Shells ◽  
Instability Regions ◽  
The Galerkin Method ◽  
Circumferential Wave

The dynamic stability of clamped, truncated conical shells under periodic torsion is analyzed by the Galerkin method in conjunction with Hsu’s results. The instability regions of practical importance are clarified for relatively low frequency ranges. Numerical results indicate that under the purely periodic torsion only the combination instability region exists but that with an increase in the static torsion the principal instability region becomes most significant. The relative openness of the instability regions is found to depend sensitively on the circumferential phase difference of two vibration modes excited simultaneously at the resonance with the same circumferential wave number.

Dynamic Stability of Annular Plates Under Pulsating Torsion

1980 ◽  
Vol 47 (3) ◽  
pp. 595-600 ◽  
Author(s):  
J. Tani ◽  
T. Nakamura
Keyword(s):  
Dynamic Stability ◽  
Low Frequency ◽  
Instability Region ◽  
Simultaneous Action ◽  
Vibration Modes ◽  
Relative Width ◽  
Annular Plates ◽  
Parametric Resonances ◽  
Instability Regions ◽  
The Galerkin Method

The dynamic stability of annular plates under periodic torsion is analyzed by means of the Galerkin method in conjunction with Hsu’s procedure. The instability regions associated with both principal and combination parametric resonances are clarified for relatively low frequency ranges. It is found that under the purely periodic torsion only the combination instability region exists, while under the simultaneous action of the static torsion the principal instability region exists also. The circumferential phase difference of two vibration modes excited simultaneously at the resonance is also found to change remarkably the relative width of the instability region.

Refined Dynamic Stability Theory of Laminated Isotropic Circular Plates

1998 ◽  
Vol 65 (2) ◽  
pp. 334-340 ◽  
Author(s):  
G. Krizhevsky ◽  
Y. Stavsky
Keyword(s):  
Variational Principle ◽  
Dynamic Stability ◽  
Transverse Shear ◽  
Rotational Inertia ◽  
Trigonometric Functions ◽  
Circular Plates ◽  
Analytic Expressions ◽  
Transversally Isotropic ◽  
Instability Regions ◽  
The Galerkin Method

Hamilton’s variational principle is used for the derivation of transversally isotropic laminated circular plates motion. Nonlinear strain-displacements relations are considered. Linearized dynamic stability equations are obtained for circular plates subjected to the same uniformly distributed periodic radial loads. The effects of transverse shear and rotational inertia are included. The exact solutions of vibrations and buckling problems are given initially in the terms of Bessel, power, and trigonometric functions. The vibrational modal functions are used then as a basis in the Galerkin method that reduced the study of dynamic stability to investigation of bounds of instability of Mathieu’s equations. Analytic expressions for the bounds of both principal and combination-type instability regions are obtained using the methods of Bolotin and Tamir. A new effect—sensitivity of certain instability regions to slight imperfections in the symmetry of lamination—is found out and discussed here.

Nonlinear Free Vibrations Analysis of Delaminated Composite Conical Shells

2019 ◽  
Vol 20 (01) ◽  
pp. 2050010 ◽  
Author(s):  
Abbas Kamaloo ◽  
Mohsen Jabbari ◽  
Mehdi Yarmohammad Tooski ◽  
Mehrdad Javadi
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Laminated Composite ◽  
Middle Surface ◽  
Free Vibrations ◽  
Wave Number ◽  
Vertex Angle ◽  
Conical Shells ◽  
Circumferential Wave ◽  
Delamination Length

This paper examines the nonlinear free vibration of laminated composite conical shells throughout the circumferential delamination. First, based on the energy method, the governing equation of motion for the shell was derived. To simplify the analysis, the nonlinear partial differential equations were reduced into a system of coupled ordinary differential equations using Galerkin’s method. Consequently, the results were obtained by the numerical methods. Finally, the effects of delamination, variations in the delamination length, conical shells characteristics, materials property and circumferential wave number on the nonlinear response of delaminated composite conical shells were examined. The results show that the presence of delamination leads to increase in the amplitude of oscillations for the shells. Besides, the increase in the delamination length and decrease of the circumferential wave number, number of layers, and half vertex angle of the cone and orthotropy bring about a decrease in the nonlinearity of delaminated composite conical shells. However, an increase of the middle surface radius of the shell leads to a reduction of the nonlinearity as well as an increase of the amplitude.

OPTIMIZATION OF ULTRASOUND MEDICAL PARAMETERS TOOLS

2021 ◽  
pp. 147-154
Author(s):  
Елена Петровна Белоусова
Keyword(s):  
Dynamic Stability ◽  
Low Frequency ◽  
Mathieu Equation ◽  
Parameter Method ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Bending Vibrations ◽  
Medical Instruments ◽  
Instability Regions ◽  
The Stability

Для многих видов медицинских вмешательств требуется применение ультразвуковых инструментов с различными характеристиками. Используются инструменты, совершающие продольные колебания, значительно реже - инструменты с изгибами и крутильными колебаниями, либо достаточно длинные ультразвуковые медицинские инструменты, либо короткие, но тонкие. В таких инструментах часто наблюдается так называемая динамическая потеря устойчивости, когда прямолинейный инструмент, совершающий продольные колебания, внезапно начинает совершать изгибные колебания, амплитуда которых бывает настолько высока, что приводит к разрушению инструмента. Такое явление также называют параметрическим резонансом ультразвуковых инструментов. Цель статьи - анализ условий и параметров, позволяющих минимизировать травматичность применения ультразвуковых медицинских инструментов, исследование в динамике устойчивости ультразвуковых низкочастотных медицинских инструментов. Для определения оптимального набора параметров динамической устойчивости изгибных колебаний ультразвуковых низкочастотных медицинских инструментов используется уравнение Матье-Хилла. В этом аспекте решение задачи сводится к определению: 1) границ областей неустойчивости уравнения Матье; 2) границ областей неустойчивости при разных значениях коэффициента возбуждения; 3) границ областей неустойчивости с применением метода малого параметра. Для исследования динамической устойчивости уравнения колебаний прямолинейного стержня переменного сечения достаточно выполнить расчет коэффициентов уравнения Матье и использовать диаграмму Айнса-Стретта для нахождения точек попадания в область устойчивости. Результаты расчетов показали, что инструменты, изготовленные из титана, обладают высокой динамической устойчивостью, что практически исключает вероятность их разрушения при проведении медицинских операций. Полученные характеристики медицинских инструментов указывают на эффективность их применения в медицинской практике Many types of medical interventions require the use of ultrasound instruments with different characteristics. Instruments that perform longitudinal vibrations are used, much less often-instruments with bends and torsional vibrations, or rather long ultrasound medical instruments, or short, but thin. In such instruments, the so-called dynamic loss of stability is often observed, when a straight-line tool that performs longitudinal vibrations suddenly begins to make bending vibrations, the amplitude of which is so high that it leads to the destruction of the tool. This phenomenon is also called parametric resonance of ultrasonic instruments. The purpose of the article is to analyze the conditions and parameters that allow minimizing the traumaticity of the use of ultrasonic medical instruments, to study the dynamics of the stability of ultrasonic low-frequency medical instruments. The Mathieu-Hill equation is used to determine the optimal set of parameters for the dynamic stability of bending vibrations of ultrasonic low-frequency medical instruments. In this aspect, the solution of the problem is reduced to the definition of: 1) the boundaries of the instability regions of the Mathieu equation; 2) the boundaries of the instability regions at different values of the excitation coefficient; 3) the boundaries of the instability regions using the small parameter method. To study the dynamic stability of the equation of oscillations of a rectilinear rod of variable cross-section, it is sufficient to calculate the coefficients of the Mathieu equation and use the Ains-Strett diagram to find the points of falling into the stability region. The results of the calculations showed that the instruments made of titanium have a high dynamic stability, which practically eliminates the possibility of their destruction during medical operations. The obtained characteristics of medical instruments indicate the effectiveness of their use in medical practice

Dynamic Stability of Liquid-Filled Cylindrical Shells Under Periodic Shearing Forces

1989 ◽  
Vol 111 (4) ◽  
pp. 420-427 ◽  
Author(s):  
M. Chiba ◽  
T. Yamashida ◽  
H. Sugiyama ◽  
J. Tani
Keyword(s):  
Dynamic Stability ◽  
Velocity Potential ◽  
Filling Ratio ◽  
Simultaneous Action ◽  
Mathieu’S Equation ◽  
Instability Regions ◽  
Dynamic Version ◽  
The Galerkin Method ◽  
Theoretical Analyses ◽  
Equations Of Motions

Theoretical analyses are presented for the dynamic stability of a cylindrical shell partially filled with liquid, under periodic shearing forces. In the analyses, the dynamic version of the Donnell equations and the velocity potential theory are used for the motions of the shell and the contained liquid, respectively. The problem was solved by using the Galerkin method and the equations of motions coupling the shell and the liquid were derived from a type of coupled Mathieu’s equation. The instability boundaries where parametric resonance occurs were determined by using Hsu’s method. Numerical calculations were carried out for cylinders with various dimensions, i.e., radius-thickness and length-radius ratios. The effects of the liquid-filling ratio and the static shearing forces on the instability boundaries were clarified. It is found that the instability regions enlarge with increasing liquid and that the principal instability regions appear under the simultaneous action of the static shearing force.

Donor-acceptor complexes formed by perfluoro-organo bromides and iodides with nitrogenous and other bases. II. Band shapes and widths in the absorption spectrum of gaseous CF3I-N(CH3)3

1971 ◽  
Vol 24 (12) ◽  
pp. 2493 ◽  
Author(s):  
A Mishra ◽  
ADE Pullin
Keyword(s):  
Vibrational Mode ◽  
Low Frequency ◽  
Molecular Complexes ◽  
Wave Number ◽  
Centrifugal Distortion ◽  
Band Shape ◽  
Gaseous Mixtures ◽  
Factors Affecting ◽  
Donor Acceptor ◽  
Vibration Rotation

The absorption band centred at c. 77 cm-1 in gaseous mixtures of CF3I and N(CH3)3 previously reported and attributed to the N-I stretching mode of the complex CF3I-N(CH3)3 has been carefully re-examined. This band is of interest as an example of a low frequency ?dissociative type? vibrational mode of a weak molecular complex. The band is asymmetric and apparently structureless with a half intensity width at room temperature of 28-30 cm-1. The width of the band may be accounted for as arising from transitions vi + vi+1 where vi is the vibrational quantum number of the N-I stretching mode with vi up to c. 10 making appreciable contribution to the intensity on the low wave-number side. Centrifugal distortion in the complex is considered. Centrifugal stretching and consequent weakening of the bond may shift the band envelope 2-3 cm-1 to lower wave numbers. Assessment of these and other factors affecting the band shape suggest that the fundamental frequency is probably c. 90 cm-1. The band shape of the vibrational mode of the complex at c. 272 cm-1 is briefly discussed. Many of the considerations presented in this paper should apply to vibration-rotation band shapes in other weak molecular complexes. Some general consequences of anharmonicity for the interpretation of the spectra of weak molecular complexes are discussed.

scholarly journals Alternating (AC) Loop Current Attacks Against the KLJN Secure Key Exchange Scheme

2021 ◽  
pp. 2150050
Author(s):  
Mutaz Y. Melhem ◽  
Christiana Chamon ◽  
Shahriar Ferdous ◽  
Laszlo B. Kish
Keyword(s):  
Electromagnetic Interference ◽  
High Frequency ◽  
Practical Importance ◽  
Low Frequency ◽  
Key Exchange ◽  
Power Density Spectrum ◽  
Voltage Source ◽  
Loop Current ◽  
Johnson Noise ◽  
Density Spectrum

Recently, several passive and active attack methods have been proposed against the Kirchhoff–Law–Johnson–Noise (KLJN) secure key exchange scheme by utilizing direct (DC) loop currents. The DC current attacks are relatively easy, but their practical importance is low. On the other hand, parasitic alternating (AC) currents are virtually omnipresent in wire-based systems. Such situations exist due to AC ground loops and electromagnetic interference (EMI). However, utilizing AC currents for attacks is a harder problem. Here, we introduce and demonstrate AC current attacks in various frequency ranges. The attacks exploit a parasitic/periodic AC voltage-source at either Alice’s or Bob’s end. In the low-frequency case, the procedure is the generalized form of the former DC ground-loop-based attack. In the high-frequency case, the power density spectrum of the wire voltage is utilized. The attack is demonstrated in both the low and the high-frequency situations. Defense protocols against the attack are also discussed.

Free Vibration of Moderately Thick Conical Shells Using a Higher Order Shear Deformable Theory

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
R. D. Firouz-Abadi ◽  
M. Rahmanian ◽  
M. Amabili
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
First Time ◽  
Circumferential Wave ◽  
Shear Deformable

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential wave numbers for clamped (C), and simply supported (SS) boundary conditions.

An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang ◽  
Jianhui Wang
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Higher Order ◽  
Wave Number ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Circular Cylindrical Shells ◽  
Geometrical Factors ◽  
Circumferential Wave

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

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