• Interaction and multiscale mechanics
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• v.6 no.1
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• pp.1-14
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• 2013

The aim of this paper is to study the propagation of torsional surface waves in non-homogeneous isotropic layer of finite thickness placed over a homogeneous viscoelastic half-space, when both density and rigidity of the non-homogeneous medium are assumed to vary exponentially with depth. The frequency equations are obtained by using simple method of separation of variables. Further, it is seen that when viscoelastic parameter and non-homogeneity parameter is neglected, the dispersion equation gives the dispersion equations of Love waves in homogeneous, elastic and isotropic layer placed over homogeneous viscoelastic medium. The problem has been solved numerically and the effects of various inhomogeneities of the medium on torsional waves have been illustrated graphically.

• Geomechanics and Engineering
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• v.16 no.2
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• pp.169-176
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• 2018

An attempt has been made here to study the propagation of SH-type surface waves in an elastic medium, which is initially stressed and heterogeneous and has a point source inside the medium. The upper portion of the composite medium is a sandy layer. It is situated on an initially stressed heterogeneous half-space, whose density, rigidity and internal friction are function of depth. The analysis has been carried out by using Fourier transform and Green's function approach. The phase velocity has been investigated for several particular situations. It has been shown that the results of the study agree with those the case of Love wave propagation in a homogeneous medium in the absence of the sandy layer, when the initial stress is absent. In order to illustrate the validity of the analysis presented here, the derived analytical expression has been computed numerically, by considering an illustrative example and the variances of the concerned physical variables have been presented graphically. It is observed that the velocity of shear wave is amply influenced by the initial stress and heterogeneity parameters and the presence of the sandy layer. The study has an important bearing on investigations of different problems in the earth's interior and also in seismological studies.

• Wind and Structures
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• v.19 no.4
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• pp.443-465
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• 2014

Hyperbolic thin-shell cooling towers have complicated vibration modes, and are very sensitive to the effects of group towers and wind-induced vibrations. Traditional aero-elastic models of cooling towers are usually designed based on the method of stiffness simulation by continuous medium thin shell materials. However, the method has some shortages in actual engineering applications, so the so-called "equivalent beam-net design method" of aero-elastic models of cooling towers is proposed in the paper and an aero-elastic model with a proportion of 1: 200 based on the method above with integrated pressure measurements and vibration measurements has been designed and carried out in TJ-3 wind tunnel of Tongji university. According to the wind tunnel test, this paper discusses the impacts of self-excited force effect on the surface wind pressure of a large-scale cooling tower and the results show that the impact of self-excited force on the distribution characteristics of average surface wind pressure is very small, but the impact on the form of distribution and numerical value of fluctuating wind pressure is relatively large. Combing with the Complete Quadratic Combination method (hereafter referred to as CQC method), the paper further studies the numerical sizes and distribution characteristics of background components, resonant components, cross-term components and total fluctuating wind-induced vibration responses of some typical nodes which indicate that the resonance response is dominant in the fluctuating wind-induced vibration response and cross-term components are not negligible for wind-induced vibration responses of super-large cooling towers.

• Geomechanics and Engineering
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• v.31 no.1
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• pp.99-112
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• 2022

The present study examines the natural frequencies (NFs) of perfect/imperfect functionally graded sandwich beams (P/IP-FGSBs), which are composed of a porous core constructed of functionally graded materials (FGMs) and a homogenous isotropic metal and ceramic face sheets resting on elastic foundations. To accomplish this, the material properties of the FGSBs are assumed to vary continuously along the thickness direction as a function of the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction represented using four distinct types of porosity distribution models. Additionally, to characterize the reaction of the two-parameter elastic foundation to the Perfect/Imperfect (P/IP) FGSBs, the medium is assumed to be linear, homogeneous, and isotropic, and it is described using the Winkler-Pasternak model. Furthermore, the kinematic relationship of the P/IP-FGSBs resting on the Winkler-Pasternak elastic foundations (WPEFs) is described using trigonometric shear deformation theory (TrSDT), and the equations of motion are constructed using Hamilton's principle. A closed-form solution is developed for the free vibration analysis of P/IP-FGSBs resting on the WPEFs under four distinct boundary conditions (BCs). To validate the new formulation, extensive comparisons with existing data are made. A detailed investigation is carried out for the effects of the foundation coefficients, mode numbers (MNs), porosity volume fraction, power-law index, span to depth ratio, porosity distribution patterns (PDPs), skin core skin thickness ratios (SCSTR), and BCs on the values of the NFs of the P/IP-FGSBs.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.737-748
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• 2018

The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.9 s.114
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• pp.949-957
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• 2006

In this Paper, reduction of noise and vibration in ship cabins by using floating floor is studied. Two theoretical models are presented and predicted insertion losses of floating floor are compared to experimental results, where measurements have been done in mock-up built for simulating typical ship cabin structures. In ships, mineral wool is usually used as the impact absorbing materials. The first model (M-S-Plate Model) is that upper plate and mineral wool are assumed as a one-dimensional mass-spring system, which is in turn attached to the simply supported elastic floor. The second model (Wave-Plate Model) is that mineral wool is assumed as an elastic medium for wave propagation. The comparisons show that M-S-Plate model is in good agreement with experimental results when density of mineral wool is 140K, and fiber direction is horizontal. For higher density and vertical fiber direction, Wave-Plate model shows good agreements with measurements. It is found that including the elastic behavior of the floor is essential in improving accuracy of the prediction for low frequency ranges below $100{sim}200Hz$.

• Advances in nano research
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• v.4 no.3
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• pp.229-249
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• 2016

In this paper, buckling characteristics of nonhomogeneous functionally graded (FG) nanobeams embedded on elastic foundations are investigated based on third order shear deformation (Reddy) without using shear correction factors. Third-order shear deformation beam theory accounts for shear deformation effects by a parabolic variation of all displacements through the thickness, and verifies the stress-free boundary conditions on the top and bottom surfaces of the FG nanobeam. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam in deformation, which acts in tension as well as in compression. The material properties of FG nanobeam are supposed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. Nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. Comparison between results of the present work and those available in literature shows the accuracy of this method. The obtained results are presented for the buckling analysis of the FG nanobeams such as the effects of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Structural Engineering and Mechanics
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• v.28 no.3
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• pp.295-316
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• 2008

In the present paper a mechanical model to predict the compressive response of high strength short concrete columns with square cross-section confined by transverse steel is presented. The model allows one to estimate the equivalent confinement pressures exercised by transverse steel during the loading process taking into account of the interaction of the stirrups with the inner core both in the plane of the stirrups and in the space between two successive stirrups. The lateral pressure distributions at hoop levels are obtained by using a simple model of elastic beam on elastic medium simulating the interaction between stirrups and concrete core, including yielding of steel stirrups and damage of concrete core by means of the variation in the elastic modulus and in the Poisson's coefficient. Complete stress-strain curves in compression of confined concrete core are obtained considering the variation of the axial forces in the leg of the stirrup during the loading process. The model was compared with some others presented in the literature and it was validated on the basis of the existing experimental data. Finally, it was shown that the model allows one to include the main parameters governing the confinement problems of high strength concrete members such as: - the strength of plain concrete and its brittleness; - the diameter, the pitch and the yielding stress of the stirrups; - the diameter and the yielding stress of longitudinal bars; - the side of the member, etc.

• Structural Engineering and Mechanics
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• v.74 no.2
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• pp.297-311
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• 2020

The main purpose of this study is to analyze the effects of external pressure on the vibration and buckling of functionally graded (FG) spherical panels resting of elastic medium. The material characteristics of the FG sphere continuously vary through the thickness direction based on the power-law rule. In accordance with first-order shear deformation shell theory and by the use of Ritz formulation the governing equations are presented. In this regard, the beam functions are applied in two-dimensions for different sets of boundary supports. The Winkler and Pasternak models of elastic foundations are also taken into account. In order to show the validity and applicability of the presented formulation, various comparison studies are given. Furthermore, a diverse range of numerical results is reported to check the impacts of geometrical and material parameters along with external pressure on the vibration and buckling analysis of FG spherical panels.

• Steel and Composite Structures
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• v.24 no.6
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• pp.711-726
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• 2017

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded (FG) nanocomposite sandwich plates resting on Pasternak foundation are presented. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. To determine the effect of CNT agglomeration on the elastic properties of CNT-reinforced composites, a two-parameter micromechanical model of agglomeration is employed. In this research work, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented straight CNTs. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated FG nanocomposite plates are investigated. It is shown that the natural frequencies of structure are seriously affected by the influence of CNTs agglomeration. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated plates.