• Advances in concrete construction
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• v.9 no.6
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• pp.557-568
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• 2020

In this study, the impact of ring supports around the shell circumferential has been examined for their various positions along the shell axial length using Rayleigh-Ritz formulation. 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. The influence of the ring supports is investigated at various positions. These variations have been plotted against the locations of ring supports for three values of length-to-diameter ratios. Effect of ring supports with middle layer thickness is presented using the Rayleigh-Ritz procedure with three different conditions. The influence of the positions of ring supports for clamped-clamped is more visible than simply supported and clamped-free end conditions. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. The Lagrangian functional is created by adding the energy expressions for the shell and rings. The axial modal deformations are approximated by making use of the beam functions. The comparisons of frequencies have been made for efficiency and robustness for the present numerical procedure. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported frequency curves are higher than that of clamped-simply curves. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Computers and Concrete
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• v.25 no.5
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• pp.411-425
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• 2020

In this paper, the shell material has been taken as functionally graded material and their material quantity is located by the exponential volume fraction law. Moreover, the impact of ring supports around the shell circumference has been examined for their various positions along the shell axial length. These rings support restraints the radial displacement in the transverse direction. While the axial modal deformation functions have been estimated by characteristic beam functions and nature of materials used for construction of cylindrical shells. The fundamental natural frequency of cylindrical shell of parameter versus ratios of length- and height-to-radius for a wide range has been reported and investigated through the study. In addition, by increasing height-to-radius ratio resulting frequencies also increase and frequencies decrease on ratio of length-to-radius. Though the trends of frequency values of both ratios are converse to each other with three different boundary conditions. Also it is examined the position of ring supports with length-to radius ratio, height-to-radius ratio and varying the exponent of volume fraction. MATLAB software package has been utilized for extracting shell frequency spectra. The obtained results are confirmed by comparing with available literature.

• Steel and Composite Structures
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• v.35 no.2
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• pp.249-260
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• 2020

The main purpose of this research work is to investigate the free vibration of conical shell structures reinforced by graphene platelets (GPLs) and the elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. To this end, a shell model is developed based on Donnell's theory. To solve the problem, the analytical Galerkin method is employed together with beam mode shapes as weighting functions. Due to importance of boundary conditions upon mechanical behavior of nanostructures, the analysis is carried out for different boundary conditions. The effects of boundary conditions, semi vertex angle, porosity distribution and graphene platelets on the response of conical shell structures are explored. The correctness of the obtained results is checked via comparing with existing data in the literature and good agreement is eventuated. The effectiveness and the accuracy of the present approach have been demonstrated and it is shown that the Donnell's shell theory is efficient, robust and accurate in terms of nanocomposite problems.

• Steel and Composite Structures
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• v.42 no.3
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• pp.397-405
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• 2022

The existing researches on the dynamics of the fluid-conveying pipes only focus on stability and vibration problems, and there is no literature report on the wave propagation of the fluid-conveying pipes. Therefore, the purpose of this paper is to explore the propagation characteristics of longitudinal and flexural waves in the fluid-conveying pipes. First, it is assumed that the material properties of the fluid-conveying pipes vary based on a power function of the thickness. In addition, it is assumed that the material properties of both the fluid and the pipes are closely depended on temperature. Using the Euler-Bernoulli beam equation and based on the linear theory, the motion equations considering the thermal-mechanical-fluid coupling is derived. Then, the exact expressions of phase velocity and group velocity of longitudinal waves and bending waves in the fluid-conveying pipes are obtained by using the eigenvalue method. In addition, we also studied the free vibration frequency characteristics of the fluid-conveying pipes. In the numerical analysis, we successively studied the influence of temperature, functional gradient index and liquid velocity on the wave propagation and vibration problems. It is found that the temperature and functional gradient exponent decrease the phase and group velocities, on the contrary, the liquid flow velocity increases the phase and group velocities. However, for vibration problems, temperature, functional gradient exponent parameter, and fluid velocity all reduce the natural frequency.

• Advances in concrete construction
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• v.13 no.3
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• pp.223-231
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• 2022

The problem is formulated by applying the Kirchhoff's conception for shell theory. The longitudinal modal displacement functions are assessed by characteristic beam ones meet clamped-clamped end conditions applied at the shell edges. The fundamental natural frequency of rotating functionally graded cylindrical shells of different parameter versus ratios of length-to-diameter and height-to-diameter for a wide range has been reported and investigated through the study with fractions laws. The frequency first increases and gain maximum value with the increase of circumferential wave mode. By increasing different value of height-to-radius ratio, the resulting backward and forward frequencies increase and frequencies decrease on increasing height-to-radius ratio. Moreover, on increasing the rotating speed, the backward frequencies increases and forward frequencies decreases. The trigonometric frequencies are lower than that of exponential and polynomial frequencies. Stability of a cylindrical shell depends highly on these aspects of material. More the shell material sustains a load due to physical situations, the more the shell is stable. Any predicted fatigue due to burden of vibrations is evaded by estimating their dynamical aspects.

• Bulletin of the Society of Naval Architects of Korea
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• v.11 no.2
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• pp.15-22
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• 1974

As for the added mass moment of inertia of ships in torsional vibration, it seems that the works by T. Kumai[1,2] are the only systematic one available currently. The work[1] is for the calculation of the two dimensional correction factors with finitely-long elliptic cylinders as the mathematic model. In this work the authors recalculated the above factors, $J_{\tau}$, with the same mathematic model and the same problem formulation, and presented the numerical results in Fig. 1. The reason why the reinvestigation was done was that in Kumai's work he obtained the solutions of the Mathieu equations, which was derived from the problem formulation for the velocity potential, under the assumption that the dummy constant q involved in the equations was always far less than unity, whereas in fact it takes values within the region of $0<q{\leq}{\infty}$ in sequence. As a result the authors found two remarkable differences in general features of $J_{\tau}$(refer to Fg.3); one that the authors' numerical results are considerably higher than the results given in [2], and the other that for a given number of node those have properties of decreasing monotonically with increase of the beam-draft ratio while these rapidly decrease from a maximum value of near at B/T=2.00 with B/T becoming greater or less than ratio. It seems that the latter trend was resulted from the fact that the assumption of $q{\ll}1$ employed in [2] was more closely satisfied in the vicinity of B/T=2.00.