• Computers and Concrete
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• 제32권4호
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• pp.365-371
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• 2023

On the basis of Flügge shell theory, the vibrations of single walled carbon nanotubes (SWCNTs) are investigated. The structure of armchair single walled carbon nanotubes are used here. Influences of length-to-diameter ratios and the two boundary conditions on the natural frequencies of armchair SWCNTs are examined. The Rayleigh-Ritz method is employed to determine eigen frequencies for single walled carbon nanotubes. The solution is obtained using the geometric characteristics and boundary conditions for natural frequencies of SWCNTs. The natural frequencies decrease as ratio of length to diameter increase and the effect of frequencies is less significant and more prominent for long tube. To assess the frequency confirmation carried out in this paper are compared with the earlier computations.

• Computers and Concrete
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• 제29권2호
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• pp.117-126
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• 2022

The vibrational characteristic of three-layered cylindrical shell (CS) submerged in fluid with the ring support has been studied. The inner and outer layer is supposed to construct by isotropic layer. The composition of central layer is of functionally graded material type. Acoustic Wave condition has been utilized to present the impact of fluid. The central layer of cylindrical shell (CS) varies by volume fraction law that has been expressed in terms of polynomial. The main shell frequency equation has been obtained by theory of Love's shell and Rayleigh-Ritz technique. The oscillation of natural frequency has been examined under a variety of end conditions. The dependence of axial model has been executed with the help of characteristic beam function. The natural frequencies (NFs) of functionally graded material (FGM) shell have been observed of cylindrical shell along the shell axial direction. Different physical parameters has been used to examine the vibration characteristics due to the effect of volume fraction law. MATLAB software has been used to get result.

• 복합신소재구조학회 논문집
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• 제1권3호
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• pp.17-23
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• 2010

본 연구는 비등방성 원통형 쉘의 휨문제에 대한 해석 기법을 제시하였다. 비등방성 원통형 쉘의 지배방정식을 해석하기 위해 유한요소법을 사용하였다. 두꺼운 쉘이론과 얇은 쉘이론을 사용하여 쉘의 폭-두께비 및 여러 가지 경계조건을 갖는 비등방성 원통형 쉘에 대한 해석결과를 비교 분석하였다. 본 연구의 수치해석 결과는 비등방성 원통형 쉘의 휨 거동 분석에 기여할 것으로 보인다.

• Composites Research
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• 제12권5호
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• pp.65-79
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• 1999

본 논문은 단순지지된 복합재료 사각판과 원통쉘이 결합된 구조물의 자유진동해석을 위한 해석적 방법에 대하여 기술하였다. 결합전 단순지시된 사각판과 원통쉘의 응답을 얻기 위하여 고전적 판이론과 Love의 얇은 쉘이론에 기초한 에너지법을 적용하였다. 결합구조물의 해석에는 동적응답법을 적용하였고, 길이방향 판과 쉘의 결합부에서의 동적 주기 하중과 모멘트는 Dirac 델타 함수와 정현 함수를 사용하였을 때 연속조건을 만족함을 보였다. 또한 원통쉘의 기하하적 매개변수인 쉘의 길이 대 반경비와 반경 대 두께비에 따른 진동특성의 변화를 고찰하였고, 복합재료의 섬유 방향각과 직교이방성 매개변수가 결합 원통쉘의 기본 진동수에 미치는 영향에 미치는 영향에 대하여 연구하였다.

• Steel and Composite Structures
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• 제43권5호
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• pp.603-623
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• 2022

This article is dedicated to predict the natural frequencies of joined conical shell structures made of Functionally Graded Material (FGM). The structure includes two conical segments. The equivalent material properties are found by using the rule of mixture based on Voigt model. In addition, three well-known patterns are employed for distribution of material properties throughout the thickness of the structure. The main objective of the present research is to propose a novel exponential pattern and obtain the related equivalent material properties. Furthermore, the Donnell type shell theory is used to obtain the governing equations of motion. Note that these equations are obtained by employing First-order Shear Deformation Theory (FSDT). In order to discretize the governing system of differential equations, well-known and efficient semi-analytical scheme, namely Generalized Differential Quadrature Method (GDQM), is utilized. Different boundary conditions are considered for various types of single and joined conical shell structures. Moreover, an applicable modification is considered for the continuity conditions at intersection position. In the first step, the proposed formulation is verified by solving some well-known benchmark problems. Besides, some new numerical examples are analyzed to show the accuracy and high capability of the suggested technique. Additionally, several geometric and material parameters are studied numerically.

• Advances in nano research
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• 제16권6호
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• pp.565-577
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• 2024

Vibration investigation of fluid-filled functionally graded cylindrical shells with ring supports is studied here. Shell motion equations are framed first order shell theory due to Sander. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Langrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is immersed in a fluid which is a non-viscous one. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. After these, ring supports are located at various positions along the axial direction round the shell circumferential direction. The influence of the ring supports is investigated at various positions. Effect of ring supports with empty and fluid-filled shell is presented using the Rayleigh - Ritz method with simply supported condition. The frequency behavior is investigated with empty and fluid-filled cylindrical shell with ring supports versus circumferential wave number and axial wave number. Also the variations have been plotted against the locations of ring supports for length-to-radius and height-to-radius ratio. Moreover, frequency pattern is found for the various position of ring supports for empty and fluid-filled cylindrical shell. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. It is found that due to inducting the fluid term frequency result down than that of empty cylinder. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Structural Engineering and Mechanics
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• 제50권3호
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• pp.403-417
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• 2014

The present paper addresses a general formulation for the thermo elastic analysis of a functionally graded cylindrical shell subjected to external loads. The shear deformation theory and energy method is employed for this purpose. This method presents the final relations by using a set of second order differential equations in terms of integral of material properties along the thickness direction. The proposed formulation can be considered for every distribution of material properties, whether functional or non functional. The obtained formulation can be used for manufactured materials or structures with numerical distribution of material properties which are obtained by using the experiments. The governing differential equation is applied for two well-known functionalities and some previous results are corrected with present true results.

• 대한기계학회논문집A
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• 제25권11호
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• pp.1802-1812
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• 2001

The theoretical method is developed to investigate the effects of ring stiffeners on free vibration characteristics and transient response for the ring stiffened composite cylindrical shells subjected to the impulse pressure Loading. In the theoretical procedure, the Love's thin shell theory combined with the discrete stiffener theory to consider the ring stiffening effect is adopted to formulate the theoretical model. The concentric or eccentric ring stiffeners are laminated with composite and have the uniform rectangular cross section. The modal analysis technique is used to develop the analytical solutions of the transient problem. The analysis is based on an expansion of the loads, displacements in the double Fourier series that satisfy the boundary conditions. The effect of stiffener's eccentricity, number, size, and position on transient response of the shells is examined. The results are verified by comparison with FEM results.

• 소음진동
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• 제9권3호
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• pp.485-492
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• 1999

The effects of boundary conditions on vibration characteristics for the ring stiffered composite cylindrical shells are investigated by theoretical and experimental method. In the theoretical procedure, the Love's thin shell theory combined with the discrete stiffener theory to consider the ring stiffening effect are adopted to derive the frequency equation. In experiment, the impact exciting method is used to obtain the vibraton results. Five different boundary conditions: clamped-clamped, simply supported-simply supported, free-free, clamped-free, clamped-simply supported are considered in this study.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.831-836
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• 2000

In this study, the Rayleigh inextensional theory and extensional theory for thin shells was employed to predict the natural frequencies of the hemi-spherical shell with free and simply. supported boundary condition. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS. In order to validate the theory, modal test was also performed by impact test and FFT analysis. Modal test and FEM analysis of the free, simply supported and clamped boundary condition was also carried out.