• Structural Engineering and Mechanics
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• v.90 no.6
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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.

• Structural Engineering and Mechanics
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• v.27 no.6
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• pp.713-739
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• 2007

Nowadays computers can perform symbolic computations in addition to mere number crunching operations for which they were originally designed. Symbolic computation opens up exciting possibilities in Structural Mechanics and engineering. Classical areas have been increasingly neglected due to the advent of computers as well as general purpose finite element software. But now, classical analysis has reemerged as an attractive computer option due to the capabilities of symbolic computation. The repetitive cycles of simultaneous - equation sets required by the finite element technique can be eliminated by solving a single set in symbolic form, thus generating a truly closed-form solution. This consequently saves in data preparation, storage and execution time. The power of Symbolic computation is demonstrated by six examples by applying symbolic computation 1) to solve coupled shear wall 2) to generate beam element matrices 3) to find the natural frequency of a shear frame using transfer matrix method 4) to find the stresses of a plate subjected to in-plane loading using Levy's approach 5) to draw the influence surface for deflection of an isotropic plate simply supported on all sides 6) to get dynamic equilibrium equations from Lagrange equation. This paper also presents yet another computationally efficient and accurate numerical method which is based on the concept of derivative of a function expressed as a weighted linear sum of the function values at all the mesh points. Again this method is applied to solve the problems of 1) coupled shear wall 2) lateral buckling of thin-walled beams due to moment gradient 3) buckling of a column and 4) static and buckling analysis of circular plates of uniform or non-uniform thickness. The numerical results obtained are compared with those available in existing literature in order to verify their accuracy.

• Structural Engineering and Mechanics
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• v.57 no.1
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• pp.179-200
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• 2016

In this paper the differential transformation method (DTM) is utilized for vibration and buckling analysis of nanotubes in thermal environment while considering the coupled surface and nonlocal effects. The Eringen's nonlocal elasticity theory takes into account the effect of small size while the Gurtin-Murdoch model is used to incorporate the surface effects (SE). The derived governing differential equations are solved by DTM which demonstrated to have high precision and computational efficiency in the vibration analysis of nanobeams. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of thermal loading, small scale and surface effects, mode number, thickness ratio and boundary conditions on the normalized natural frequencies and critical buckling loads of the nanobeams in detail. The results show that the surface effects lead to an increase in natural frequency and critical buckling load of nanotubes. It is explicitly shown that the vibration and buckling of a nanotube is significantly influenced by these effects and the influence of thermal loadings and nonlocal effects are minimal.

• Journal of Korean Tunnelling and Underground Space Association
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• v.6 no.4
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• pp.279-290
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• 2004

The differential quadrature method (DQM) for a system of coupled differential equations governing the elastic stability of thin-walled curved members is presented, and is applied to computation of the eigenvalues of out-of-plane buckling of curved beams subjected to uniformly distributed radial loads including a warping contribution. Critical loads with warping, which were found to be significant, are calculated for a single-span wide-flange beam with various end conditions, opening angles, and stiffness parameters. The results are compared with the exact methods available. New results are given for the case of both ends clamped and clamped-simply supported ends without comparison since no data are available The differential quadrature method gives good accuracy and stability compared with previous theoretical results.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.1 s.256
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• pp.29-39
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• 2007

A second-moment closure is applied to the prediction of a homogeneous turbulent shear flow laden with mono-size particles. The closure is curried out based on a 'two-fluid' methodology in which both carrier and dispersed phases are considered in the Eulerian frame. To reduce the number of coupled differential equations to be solved, Reynolds stress transport equations and algebraic stress models are judiciously combined to obtain the Reynolds stress of carrier and dispersed phases in the mean momentum equation. That is, the Reynolds stress components for carrier and dispersed phases are solved by modelled transport equations, but the fluid-particle velocity covariance tensors are treated by the algebraic models. The present predictions for all the components of Reynolds stresses are compared to the DNS data. Reasonable agreements are observed in all the components, and the effects of the coupling of carrier and dispersed phases are properly captured in every aspects.

• Smart Structures and Systems
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• v.18 no.2
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• pp.335-354
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• 2016

This contribution presents an extended one-dimensional theory for piezoelectric beam-type structures with non-ideal electrodes. For these types of electrodes the equipotential area condition is not satisfied. The main motivation of our research is originated from passive vibration control: when an elastic structure is covered by several piezoelectric patches that are linked via resistances and inductances, vibrational energy is efficiently dissipated if the electric network is properly designed. Assuming infinitely small piezoelectric patches that are connected by an infinite number of electrical, in particular resistive and inductive elements, one obtains the Telegrapher's equation for the voltage across the piezoelectric transducer. Embedding this outcome into the framework of Bernoulli-Euler, the final equations are coupled to the wave equations for the longitudinal motion of a bar and to the partial differential equations for the lateral motion of the beam. We present results for the wave propagation of a longitudinal bar for several types of electrode properties. The frequency spectra are computed (phase angle, wave number, wave speed), which point out the effect of resistive and inductive electrodes on wave characteristics. Our results show that electrical damping due to the resistivity of the electrodes is different from internal (=strain velocity dependent) or external (=velocity dependent) mechanical damping. Finally, results are presented, when the structure is excited by a harmonic single force, yielding that resistive-inductive electrodes are suitable candidates for passive vibration control that might be of great interest for practical applications in the future.

• Proceedings of the Membrane Society of Korea Conference
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• 1999.07a
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• pp.48-51
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• 1999

To investigate numerically the removal behavior of carbon dioxide in a hollow fiber membrane contactor, the system controlling equations were developed including the nonlinear reversible reaction terms. The reversible chemical reactions were incorporated in the system controlling equations, resulting in the coupled nonlinear partial differential equations which could describe either the absorption of the desorption of carbon dioxide. The computer program was coded using the Fortran language and run with a personal computer to find out the effects of the system variables: the pressures of absorbed and desorbed gases, the absorbent flow rate, the concentration of potassium carbonate, the fiber diameter and the length.

• Steel and Composite Structures
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• v.28 no.5
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• pp.589-606
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• 2018

The previous studies reflected the significant effect of neutral-axis position and coupling of in-plane and out-of-plane displacements on behavior of functionally graded (FG) nanobeams. In thin FG beam, this coupling can be eliminated by a proper choice of the reference axis. In shear deformable FG nanobeam, not only this coupling can't be eliminated but also the position of neutral-axis is dependent on through-thickness distribution of shear strain. For the first time, in this paper it is avoided to guess a shear strain shape function and the exact shape function and consequently the exact position of neutral axis for arbitrary gradation of higher order nanobeam are obtained. This paper presents new methodology based on differential transform and collocation methods to solve coupled partial differential equations of motion without any simplifications. Using exact position of neutral axis and higher order beam kinematics as well as satisfying equilibrium equations and traction-free conditions without shear correction factor requirement yields to better results in comparison to the previously published results in literature. The classical rule of mixture and Mori-Tanaka homogenization scheme are considered. The Eringen's nonlocal continuum theory is applied to capture the small scale effects. For the first time, the dependency of exact position of neutral axis on length to thickness ratio is investigated. The effects of small scale, length to thickness ratio, Poisson's ratio, inhomogeneity of materials and various end conditions on vibration and buckling of local and nonlocal FG beams are investigated. Moreover, the effect of axial load on natural frequencies of the first modes is examined. After degeneration of the governing equations, the exact new formulas for homogeneous nanobeams are computed.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.6 s.109
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• pp.501-510
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• 2006

In this paper, the electromagnetic coupling through a slit in a flanged parallel-plate waveguide with a conducting strip is studied. The coupled integro-differential equations for the electric field over the slit and the induced current over the strip are derived and solved by use of the method of moments. The characteristics of some types of maximum coupling phenomena are investigated from the examinations of the variations of the equivalent slit admittance and the coupled power against various parameters such as the location of conducting strip, operating frequency, and strip length.