• Structural Engineering and Mechanics
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• 제39권4호
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• pp.449-463
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• 2011

A free vibration analysis is made of a moderately-thick toroidal shell based on a shear deformation (Timoshenko-Mindlin) shell theory. This work represents an extension of earlier work by the authors which was based on a thin (Kirchoff-Love) shell theory. The analysis uses a modal approach in the circumferential direction, and numerical results are found using the differential quadrature method (DQM). The analysis is first developed for a shell of revolution of arbitrary meridian, and then specialized to a complete circular toroidal shell. A second analysis, based on the three-dimensional theory of elasticity, is presented to cover thick shells. The shear deformation theory is validated by comparing calculated results with previously published results for fifteen cases, found using thin shell theory, moderately-thick shell theory, and the theory of elasticity. Consistent agreement is observed in the comparison of different results. New frequency results are then given for moderately-thick and thick toroidal shells, considered to be completely free. The results indicate the usefulness of the shear deformation theory in determining natural frequencies for toroidal shells.

• Advances in concrete construction
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• 제14권5호
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• pp.309-315
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• 2022

This paper depicts the diagram of cylindrical shells as an essential idea. It centers around an outline of exploration and use of cylindrical shell in expansive current circumstance. In view of investigation of the current and prospect of model as a piece of present exploration work, a straightforward contextual analysis is examined with Love's shell theory based on Galerkin's method. The cylindrical shells are attached from one end of the cylindrical shells. The frequencies of ring support shells are investigated against the half axial wave mode. The frequencies increase on increasing the half axial wave mode. Also, the frequencies are downsized with ring supports. The software MATLAB is preferred to others because in this software computing coding is very easy to do. Just single command 'eig' furnishes shell frequencies and mode shapes by calculating eigenvalues and eigenvectors respectively. The shell vibration frequencies for cylindrical shells are compared with those results found in the open literature.

• Computers and Concrete
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• 제30권4호
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• pp.269-276
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• 2022

In this paper, frequency vibrations of double-walled carbon nanotubes (CNTs) has been investigated based upon nonlocal elastic theory. The inference of small scale is being perceived by establishing nonlocal Love shell model. The wave propagation approach has been operated to frame the governing equations as eigen value system. An innovational nonlocal model to examine the scale effect on vibrational behavior of armchair, zigzag and chiral of double-walled CNTs. An appropriate selection of material properties and nonlocal parameter has been considered. The influence of dimensionless nonlocal parameter has been studied in detail. The dominance of end condition via nonlocal parameter is explained graphically. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

• Structural Engineering and Mechanics
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• 제90권6호
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• pp.601-610
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• 2024

Free vibration of layered conical shell frusta of thickness filled with fluid is investigated. The shell is made up of isotropic or specially orthotropic materials. Three types of thickness variations are considered, namely linear, exponential and sinusoidal along the radial direction of the conical shell structure. The equations of motion of the conical shell frusta are formulated using Love's first approximation theory along with the fluid interaction. Velocity potential and Bernoulli's equations have been applied for the expression of the pressure of the fluid. The fluid is assumed to be incompressible, inviscid and quiescent. The governing equations are modified by applying the separable form to the displacement functions and then it is obtained a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by cubic and quintics splines along with the boundary conditions to get generalized eigenvalue problem. The generalized eigenvalue problem is solved numerically for frequency parameters and then associated eigenvectors are calculated which are spline coefficients. The vibration of the shells with the effect of fluid is analyzed for finding the frequency parameters against the cone angle, length ratio, relative layer thickness, number of layers, stacking sequence, boundary conditions, linear, exponential and sinusoidal thickness variations and then results are presented in terms of tables and graphs.

• Advances in concrete construction
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• 제16권5호
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• pp.243-254
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• 2023

Microtubules in the cell are influenced by internal and external stimulation and play an important part in conveying protein substances and in carrying out medications to the intended targets. Waves are produced during these functions and in order to control the biological cell functions, it is important to know the wave velocities of microtubules. Owing to cylindrical shell shaped and mechanically elastic and orthotropic, cylindrical shell model based on gradient elasticity theory has been used. Wave velocities of the protein microtubule are carried out by considering Love's thin shell theory and Navier solution. Also the effect of size parameter and other variables on the results are investigated.

• Advances in concrete construction
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• 제13권6호
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• pp.471-479
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• 2022

In this paper, vibrational attributes of double-walled carbon nanotubes (CNTs) has been studied based upon nonlocal elastic shell theory. The implication of small scale is being perceived by establishing nonlocal Love shell model. The wave propagation approach has been operated to frame the governing equations as eigen value system. The comparison of local and nonlocal model has been overtly explored by means of scaling parameter. An appropriate selection of material properties and nonlocal parameter has been considered. The influence of changing mechanical parameter Young's modulus has been studied in detail. The dominance of end condition via nonlocal parameter is explained graphically. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

• 대한기계학회논문집A
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• 제23권11호
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• pp.2040-2049
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• 1999

The Rayleigh-Ritz method is used to investigate the natural frequencies and mode shapes of the ring stiffened cylindrical shells with a rectangular cutout. The cutout is located on the center of the shell. The Love's thin shell theory combined with the discrete stiffener theory is adopted to formulate the analytical model of the shell. The effect of stiffener eccentricity, number, and position on vibration characteristics of the shell is examined. Also the effect of cutout size is examined. By comparison with previously published analytical and new FEM results, it is shown that natural frequencies and mode shapes can be determined with adequate accuracy.

• 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.

• 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.

• Advances in nano research
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• 제16권6호
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• pp.601-613
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• 2024

A new analytical buckling solution of a thermo-electro-magneto-elastic (TEME) cylindrical nano-shell made of BiTiO₃-CoFe₂O₄ materials is obtained based on Hamiltonian approach. The Winkler and Pasternak elastic foundations as well as thermo-electro-magneto-mechanical loadings are applied, and two different types of edge conditions are taken into the investigation. According to nonlocal strain gradient theory (NSGT) and surface elasticity theory in conjunction with the Kirchhoff-Love theory, governing equations of the nano-shell are acquired, and the buckling bifurcation condition is obtained by adopting the Navier's method. The detailed parameter study is conducted to investigate the effects of axial and circumferential wave numbers, scale parameters, elastic foundations, edge conditions and thermo-electro-magnetic loadings on the buckling behavior of the nano-shell. The proposed model can be applied in design and analysis of TEME nano components with multi-field coupled behavior, multiple edge conditions and scale effect.