• Smart Structures and Systems
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• 제16권1호
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• pp.141-162
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• 2015

The magneto-rheological visco-elastomer (MRVE) is used as a smart core to control the stochastic micro-vibration of a sandwich plate with supported mass. The micro-vibration response of the sandwich plate with MRVE core and supported mass under stochastic support motion excitations is studied and compared to evaluate the vibration suppression capability. The effects of the supported mass and localized magnetic field on the stochastic micro-vibration response of the MRVE sandwich plate are taken into account. The dynamic characteristics of the MRVE core in micro-vibration are described by a non-homogeneous complex modulus dependent on vibration frequency and controllable by applied magnetic fields. The partial differential equations for the coupled transverse and longitudinal motions of the MRVE sandwich plate with supported mass are derived from the dynamic equilibrium, constitutive and geometric relations. The simplified ordinary differential equations are obtained for the transverse vibration of the MRVE sandwich plate under localized magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of sandwich plates with supported mass is developed based on the Galerkin method and random vibration theory. The expressions of frequency-response functions, response power spectral densities and root-mean-square velocity responses of the plate in terms of the one-third octave frequency band are obtained for micro-vibration evaluation. Finally, numerical results are given to illustrate the large response reduction capacity of the MRVE sandwich plate with supported mass under stochastic support motion excitations, and the influences of MRVE parameters, supported mass and localized magnetic field placement on the micro-vibration response.

• Steel and Composite Structures
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• 제25권3호
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• pp.337-346
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• 2017

Sandwich shells made of composite materials are the main focus on recent literature parallel to the requirements of industry. They are commonly chosen for the modern engineering applications which require moderate strength to weight ratio without dependence on conventional manufacturing techniques. The investigations on hyperbolic paraboloidal formed sandwich composite shells are limited in the literature contrary to shells that have a number of studies, consisting of doubly curved surfaces, arbitrary boundaries and laminations. Because of the lack of contributive data in the literature, the aim of this study is to present the effects of curvature on hyperbolic paraboloidal formed, layered sandwich composite surfaces that have arbitrary boundary conditions. Analytical solution methodology for the analyses of stresses and deformations is based on Third Order Shear Deformation Theory (TSDT). Double Fourier series, which are specialized for boundary discontinuity, are used to solve highly coupled linear partial differential equations. Numerical solutions showing the effects of shell geometry are presented to provide benchmark results.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2001년도 추계학술발표대회 논문집
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• pp.191-194
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• 2001

A partially coupled thermo-piezoelectric-mechanical triangular finite element model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied mechanical load, temperature change load, electric field load is developed. The governing differential equations are obtained by applying the principle of free energy and variational techniques. A higher order zigzag theory displacement field is employed to accurately capture the transverse shear and normal effects in laminated composite plates of arbitrary thickness. Nonconforming shape functions by Specht are employed in the transverse displacement variables. Numerical examples demonstrate the accuracy and efficiency of the proposed triangular plate element.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권1호
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• pp.17-35
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• 2016

In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin's Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.

• Structural Engineering and Mechanics
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• 제58권6호
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• pp.1001-1020
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• 2016

The study is to investigate the free vibration of antisymmetric angle-ply conical shells having non-uniform sinusoidal thickness variation. The arbitrarily varying thickness is considered in the axial direction of the shell. The vibrational behavior of shear deformable conical shells is analyzed for three different support conditions. The coupled differential equations in terms displacement and rotational functions are obtained. These displacement and rotational functions are invariantly approximated using cubic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration characteristic of the shells is examined for cone angle, aspect ratio, sinusoidal thickness variation, layer number, stacking sequence, and boundary conditions.

• Steel and Composite Structures
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• 제20권5호
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• pp.1087-1102
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• 2016

The paper proposes to characterize the free vibration behaviour of non-uniform cylindrical shells using spline approximation under first order shear deformation theory. The system of coupled differential equations in terms of displacement and rotational functions are obtained. These functions are approximated by cubic splines. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector which are spline coefficients. Four and two layered cylindrical shells consisting of two different lamination materials and plies comprising of same as well as different materials under two different boundary conditions are analyzed. The effect of length parameter, circumferential node number, material properties, ply orientation, number of lay ups, and coefficients of thickness variations on the frequency parameter is investigated.

• Steel and Composite Structures
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• 제20권5호
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• pp.1043-1066
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• 2016

A new analytical solution based on a third order shear deformation theory for the problem of static analysis of cross-ply doubly-curved shells is presented. The boundary-discontinuous generalized double Fourier series method is used to solve highly coupled linear partial differential equations with the mixed type simply supported boundary conditions prescribed on the edges. The complementary boundary constraints are introduced through boundary discontinuities generated by the selected boundary conditions for the derivation of the complementary solution. The numerical accuracy of the solution is compared by studying the comparisons of deflections, stresses and moments of symmetric and anti-symmetric laminated shells with finite element results using commercially available software under uniformly distributed load. Results are in good agreement with finite element counterparts. Additional results of the symmetric and anti-symmetric laminated and sandwich shells under single point load at the center and pressure load, are presented to provide data for the unsolved boundary conditions, benchmark comparisons and verifications.

• Structural Engineering and Mechanics
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• 제31권3호
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• pp.277-296
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• 2009

The paper investigates the dynamic behaviour of stiffened panels. The coupled differential equations for eccentric stiffening configuration are first derived. Then a semi-analytical procedure for dynamic analysis of stiffened panels is presented. Unlike finite element or finite strip methods, where the plate is discretized into a set of elements or strips, the plate in this procedure is treated as a single element. The potential energy of the structure is first expressed in terms generalized functions that describe the longitudinal and transverse displacement profiles. The resulting non-linear strain energy functions are then transformed into unconstrained optimization problem in which mathematical programming techniques are employed to determine the magnitude of the lowest natural frequency and the associated mode shape for pre-selected plate/stiffener geometric parameters. The described procedure is verified with other numerical methods for several stiffened panels. Results are then presented showing the variation of the natural frequency with plate/stiffener geometric parameters for various stiffening configurations.

• 소성∙가공
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• 제14권3호
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• pp.215-223
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• 2005

A numerical analysis program is developed by FDM scheme for the prediction of microstructural transformation during heat treatment of steels. In this study, multi-phase model was used fur description of diffusional austenite transformations in low-alloy hypoeutectoid steels during cooling after austenitization. A fundamental property of the model consisting of coupled differential equations is that by taking into account the rate of austenite grain growth, it permits the prediction of the progress of ferrite, pearlite, and bainite transformations simultaneously during quenching and estimate the amount of martensite also by using K-M eq. In order to simulate the microstructural evolution during tempering process, another Avrami-type eq. was adopted and method for vickers hardness prediction was also proposed. To verify the developed program, the calculated results are compared with experimental ones of casting product. Based on these results, newly designed heat treatment process is proposed and it was proved to be effective for industry.

• Coupled systems mechanics
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• 제9권1호
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• pp.63-75
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• 2020

Transport is the central ingredient of all numerical schemes for hyperbolic partial differential equations and in particular for hydrodynamics. Transport has thus been extensively studied in many of its features and for numerous specific applications. In more than one dimension, it is most commonly plagued by a major artifact: mesh imprinting. Though mesh imprinting is generally inevitable, its anisotropy can be modulated and is thus amenable to significant reduction. In the present work we introduce a new definition of stencils by taking into account second nearest neighbors (across cell corners) and call the resulting strategy "co-mesh approach". The modified equation is used to study numerical dissipation and tune enlarged stencils in order to minimize transport anisotropy.