• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.366-375
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• 1991

In this study, vibrational behavior of uniform pipe carrying a moving medium is studied by using a transfer matrix and the displacement function derived from the conventional beam theory. In various boundary conditions, flow velocity and mechanical property change of the variation of natural frequency are investigated. The Coriolis term in the original differential equation of motion has been ignored in the investigation. This method is used to study the variation of natural frequency with flow velocity for clamped-clamped, cantilevered, clamped-pinned, pinned-pinned, free-free straight pipe element. It is shown that clamped-clamped, free-free pipe have the highest natural frequency and critical velocity values while cantilevered pipe have the smallest natural frequency for the same mechanical properties. From the vibration effects of mechanical property variation, it is shown that bending stiffness and pipe length variation has large influence on natural frequency and critical velocity. Since the order of transfer matrix is not changed with boundary conditions of pipe element, this method proposed can be easily applied to personal-computer for vibration analysis of pipe element. Furthermore, this method can be extended to three-dimensional system by using a coordinate transformation for the analysis of piping systems.

• Steel and Composite Structures
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• v.42 no.3
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• pp.353-361
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• 2022

In this study, an estimation regarding nonlocal shell model based on wave propagation approach has been considered for vibrational behavior of the double walled carbon nanotubes with distinct nonlocal parameters. Vibrations of double walled carbon nanotubes for chiral indices (8, 3) have been analyzed. The significance of small scale is being perceived by developing nonlocal Love shell model. The influence of changing mechanical parameter Poisson's ratio has been investigated in detail. The dominance of boundary conditions via nonlocal parameter is shown graphically. It is found that on increasing the Poisson's ratio, the frequencies increases. It is noted that the frequencies of clamped-clamped frequencies are higher than that of simply-supported and clamped-free edge conditions. The outcomes of frequencies are tested with earlier computations.

• Journal of Mechanical Science and Technology
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• v.17 no.3
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• pp.370-379
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• 2003

A study of free vibration of rectangular Mindlin plates is presented. The analysis is based on the Chebyshev pseudospectral method, which uses test functions that satisfy the boundary conditions as basis functions. The result shows that rapid convergence and accuracy as well as the conceptual simplicity are achieved when the pseudospectral method is applied to the solution of eigenvalue problems. Numerical examples of rectangular Mindlin plates with clamped and simply supported boundary conditions are provided for various aspect ratios and thickness-to length ratios.

• Geomechanics and Engineering
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• v.32 no.5
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• pp.541-551
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• 2023

Snap-buckling is one of the main failure modes of structures, because it will lead to the reduction of structural bearing capacity, durability loss and even structural damage. Boundary condition plays an important role in the research of engineering mechanics. Further discussion on the boundary conditions problems will help to analyze the dynamic and static behavior of structures more accurately. Therefore, in order to understand the dynamic and static behavior of curved beams more comprehensively, this paper mainly studies the nonlinear snap-through buckling and forced vibration characteristics of functionally graded graphene reinforced composites (FG-GPLRCs) curved beams with two different boundary conditions (including clamped-hinged and hinged-hinged) using Euler-Bernoulli beam theory (E-BBT). In addition, the effects of the curved beam radius, the GLPs distributions, number of GLPs layers, the mass fraction of GLPs and elastic foundation parameters on the nonlinear snap-through buckling and forced vibration behavior are discussed respectively.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.4
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• pp.374-383
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• 2011

A numerical model based on a mode method coupling beams and a rectangular plate is proposed to estimate radiation characteristics of an edge-clamped rectangular plate. The radiation efficiency and radiation power in the audio frequency range including the critical frequency can be predicted. The proposed model is rather simple and straightforward and gives reliable results comparing to the previous studies. The estimated radiation characteristics are compared to those of the pinned condition plates and also to those based on the formulae proposed by Maidanik. The radiation efficiency of the clamped plate seems a little higher than that of the pinned plate in the frequency range of corner and edge modes. It is explicitly shown that the power as well as efficiency at high frequencies is not influenced by these edge boundary conditions.

• Smart Structures and Systems
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• v.26 no.3
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• pp.361-371
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• 2020

Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integral-differential equation. The von Kármán geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined.

• Geomechanics and Engineering
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• v.35 no.5
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• pp.465-473
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• 2023

The higher order shear deformable model and an exact analytical method is used for analytical bending analysis of a cylindrical shell subjected to mechanical loads, in this work. The shell is modelled using sinusoidal bivariate shear strain theory, and the static governing equations are derived using changes in virtual work. The eigenvalue-eigenvector method is used to exactly solve the governing equations for a constrained cylindrical shell The proposed kinematic relation decomposes the radial displacement into bending, shearing and stretching functions. The main advantage of the method presented in this work is the study of the effect of clamping constraints on the local stresses at the ends. Stress, strain, and deformation analysis of shells through thickness and length.

• Advances in Computational Design
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• v.5 no.4
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• Geomechanics and Engineering
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• v.16 no.1
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• pp.1-9
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• 2018

In this paper an efficient and simple refined shear deformation theory is presented for the free vibration of Functionally Graded Plates Under Various Boundary Conditions. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. The plates are considered of the type having two opposite sides simply-supported, and the two other sides having combinations of simply-supported, clamped, and free boundary conditions. The mechanical properties of functionally graded material are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived using Hamilton's principle. The results of this theory are compared with those of other shear deformation theories. Various numerical results including the effect of boundary conditions, power-law index, plate aspect ratio, and side-to-thickness ratio on the free vibration of FGM plates are presented.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.1
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• pp.9-20
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• 1999

An accurate method is presented for flexural vibrations of rhombic plates having all combinations of clamped and free edge conditions. The prime focus here is that the analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners having obtuse angles of the rhombic plates. Accurate non-dimensional frequencies and normalized contours of the vibratory transverse displacement are presented for rhombic plates having a large enough obtuse angle of 165$^{\circ}$, so that a significant influence of clamped-free corner stress singularities may be understood.