• Steel and Composite Structures
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• v.50 no.4
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• pp.403-418
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• 2024

In this paper, vibration and energy absorption characteristics of a nanostructure which is composed of two embedded porous annular/circular nanoplates coupled by a viscoelastic substrate are investigated. The modified couple stress theory (MCST) and the Gurtin-Murdoch theory are applied to take into account the size and the surface effects, respectively. Furthermore, the structural damping effect is probed by the Kelvin-Voigt model and the mathematical model of the problem is developed by a new hyperbolic higher order shear deformation theory. The differential quadrature method (DQM) is employed to obtain the out-of-phase and in-phase frequencies of the structure in order to predict the dynamic response of it. The acquired results reveal that the vibration and energy absorption of the system depends on some factors such as porosity, surface stress effects, material length scale parameter, damping and spring constants of the viscoelastic foundation as well as geometrical parameters of annular/circular nanoplates. A bird's-eye view of the findings in the research paper offers a comprehensive understanding of the vibrational behavior and energy absorption capabilities of annular/circular porous nanoplates. The multidisciplinary approach and the inclusion of porosity make this study valuable for the development of innovative materials and applications in the field of nanoscience and engineering.

• Wind and Structures
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• v.28 no.1
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• pp.49-62
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• 2019

In this paper, an analytical analysis for the study of vibratory behavior and wave propagation of functionally graded plates (FGM) is presented based on a high order shear deformation theory. The manufacture of these plates' defects can appear in the form of porosity. This latter can question and modify the global behavior of such plates. A new shape of the distribution of porosity according to the thickness of the plate was used. The field of displacement of this theory is present of indeterminate integral variables. The modulus of elasticity and the mass density of these plates are assumed to vary according to the thickness of the plate. Equations of motion are derived by the principle of minimization of energies. Analytical solutions of free vibration and wave propagation are obtained for FGM plates simply supported by integrating the analytic dispersion relation. Illustrative examples are given also to show the effects of variation of various parameters such as(porosity parameter, material graduation, thickness-length ratio, porosity distribution) on vibration and wave propagation of FGM plates.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.29-37
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• 2007

This study deals with displacement analysis of anisotropic folded structures with triangular elements and quadrilateral elements. When folded plates are analyzed, triangular elements as well as quadrilateral elements are needed for conveniences of modelling. However, using triangular elements is not a simple problem. A simple formulation is presented which allows a quadrilateral element to degenerate into a triangular element. Therefore it can easily be used for computational simplicity and avoided complexities on mixed use of triangular element and quadrilateral element. In this paper, a high-order shear deformation theory using only Lagrangian interpolation functions and drilling degrees of freedom for folded plates are utilized for more accurate analysis. Especially, various results of anisotropic laminated and folded composite structures with triangular element and quadrilateral element show the structural behavior characteristics of them.

• Advances in nano research
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• v.10 no.4
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• pp.385-395
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• 2021

This research concentrates on the effects of distributions and volume fractions of carbon nanotubes (CNT) on the nonlinear bending behavior of deep cylindrical panels reinforced by functionally graded carbon nanotubes under thermo-mechanical loading, hitherto not reported in the literature. Assuming the effects of shear deformation and moderately high value of the radius-to-side ratio (R/a), based on the first-order shear deformation theory (FSDT) and von Karman type of geometric nonlinearity, the governing system of equations is obtained. The analytical solution of field equations is carried out using the Ritz method together with the Newton-Raphson iterative scheme. The effects of radius-to-side ratio, temperature change, and boundary conditions on the nonlinear response of the functionally graded carbon nanotubes reinforced composite deep cylindrical panel (FG-CNTRC) are investigated. It is concluded that, among the five possible distribution patterns of CNT, FG-V CNTRC deep cylindrical panel is strongest with the highest bending moment and followed by UD, X, O, and Ʌ-ones. Also, considering the present deep cylindrical panel formulation increases the accuracy of the results. Hence, according to the noticeable amount of R/a in FG-CNTRC cylindrical panels, it is mandatory to apply strain-displacement relations of deep cylindrical panels for bending analysis of FG-CNTRC which certainly is desirable for industrial application.

• Steel and Composite Structures
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• v.31 no.3
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• pp.261-276
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• 2019

The study investigates the free vibration of a nano-scale sandwich beam by an extended high order approach, which has not been reported in the existing literature. First-order shear deformation theory for steel skins and so-called high-order sandwich panel theory for the core are applied. Next, the modified couple stress theory is used for both skins and cores. The Hamilton principle is utilized for deriving equations and corresponding boundary conditions. First, in the study the three-mode shapes natural frequencies for various material parameters are investigated. Also, obtained results are evaluated for two types of stiff and soft cores and isotropic, homogenous steel skins. In the research since the governing equations and also the boundary conditions are nonhomogeneous, therefore some closed-form solutions are not applicable. So, to obtain natural frequencies, the boundary conditions are converted to initial conditions called the shooting method as the numerical one. This method is one of the most robust approaches to solve complex equations and boundary conditions. Moreover, three types of simply supported on both sides of the beam (S-S), simply on one side and clamp supported on the other one (S-C) and clamped supported on both sides (C-C) are scrutinized. The parametric study is followed to evaluate the effect of nano-size scale, geometrical configurations for skins, core and material property change for cores as well. Results show that natural frequencies increase by an increase in skins thickness and core Young modulus and a decrease in beam length, core thickness as well. Furthermore, differences between obtained frequencies for soft and stiff cores increase in higher mode shapes; while, the more differences are evaluated for the stiff one.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.491-504
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• 2018

Because of sandwich structures with low weight and high stiffness have much usage in various industries such as civil and aerospace engineering, in this article, buckling and free vibration analyses of coupled micro composite sandwich plates are investigated based on sinusoidal shear deformation (SSDT) and most general strain gradient theories (MGSGT). It is assumed that the sandwich structure rested on an orthotropic elastic foundation and make of four composite face sheets with temperature-dependent material properties that they reinforced by carbon and boron nitride nanotubes and two flexible transversely orthotropic cores. Mathematical formulation is presented using Hamilton's principle and governing equations of motions are derived based on energy approach and applying variation method for simply supported edges under electro-magneto-thermo-mechanical, axial buckling and pre-stresses loadings. In order to predict the effects of various parameters such as material length scale parameter, length to width ratio, length to thickness ratio, thickness of face sheets to core thickness ratio, nanotubes volume fraction, pre-stress load and orthotropic elastic medium on the natural frequencies and critical buckling load of double-bonded micro composite sandwich plates. It is found that orthotropic elastic medium has a special role on the system stability and increasing Winkler and Pasternak constants lead to enhance the natural frequency and critical buckling load of micro plates, while decrease natural frequency and critical buckling load with increasing temperature changes. Also, it is showed that pre-stresses due to help the axial buckling load causes that delay the buckling phenomenon. Moreover, it is concluded that the sandwich structures with orthotropic cores have high stiffness, but because they are not economical, thus it is necessary the sandwich plates reinforce by carbon or boron nitride nanotubes specially, because these nanotubes have important thermal and mechanical properties in comparison of the other reinforcement.

• Journal of Ocean Engineering and Technology
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• v.7 no.2
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• pp.44-56
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• 1993

The purpose of this paper is to analyze the impact response behaviors of glass/epoxy laminated composite plates subjected to the transversely impact of a steel ball. For this purpose, dynamic finite element analysis based on the higher-order shear defomation plate theory is used to compute the contact forces, rebound velocity of a steel ball, and dynamic strain response histories. And low-velocity and high-velocity impact experiments were conducted to compare the results and compute the wave propagation velocities. The results obtained from impact experiments are in good agreement with those of dynamic finite element analysis. Also the wave propagation velocities obtained from high-velocity impact experiments and wave propagation theory agree well, and wave velocities were higher in the smaller radius of steel ball.

• International Journal of High-Rise Buildings
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• v.1 no.4
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• pp.247-254
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• 2012

In order to improve the seismic behaviors of traditional steel-concrete mixed structure, a novel steel concrete mixed structure consisting of steel frames braced with buckling restrained braces (BRBs) and a concrete tube is proposed. Based on several assumptions, the simplified mechanical model of the novel mixed structure is established, and the shear and bending stiffness formulas of the steel frames, BRBs and concrete tube are respectively introduced. The equilibrium differential equation of the novel mixed structure under horizontal load is developed based on the structural elastic theory. The simplified algorithms to determine the lateral displacement and internal forces of the novel mixed structure under the inverted-triangle distributed load, uniformly load and top-concentrated load are then obtained considering several boundary conditions and compatible deformation conditions. The effectiveness of the simplified algorithms is verified by FEM comparison.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.393-406
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• 2023

Smart structures are those structure that could adopt some behavior to prevent instability in their responses. The recognition of stability deterioration has been performed through rigid mathematical formulations in control theory and unpredicted results could not be addressed in control systems since they are able to only work under their predefined condition. On the other hand, incorporating all affecting parameters could result in high computational cost and delay time in the response of the systems. Artificial intelligence (AI) method has shown to be a promising methodology not only in the computer science by at everyday life and in engineering problems. In the present study, we exploit the capabilities of artificial intelligence method to obtain frequency response of a smart structure. In this regard, a comprehensive development of equations is presented using Hamilton' principle and first order shear deformation theory. The equations were solved by numerical methods and the results are used to train an artificial neural network (ANN). It is demonstrated that ANN modeling could provide accurate results in comparison to the numerical solutions and it take less time than numerical solution.

• Structural Engineering and Mechanics
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• v.91 no.3
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• pp.291-300
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• 2024

This paper predicts the combined resonance behavior of the truncated conical shells (TCSs) under transverse and parametric coupled excitation. The motion governing equation is formulated in the framework of high-order shear deformation theory, von Kármán theory and Hamilton principle. The displacements and boundary conditions are characterized by a set of displacement shape functions with double Fourier series. Subsequently, the method of varying amplitude (MVA) is utilized to derive the approximate analytical solution of system response of TCSs. A comparative analysis is conducted to verify the accuracy of the current computational method. Additionally, the interaction mechanism of combined resonance, parametric resonance and primary resonance is examined. And the effect of damping coefficient, the external excitation, initial phase, axial motion speed, temperature variation, humidity variation, material properties and semi-vortex angle on the vibration mechanism are analyzed.