• Interaction and multiscale mechanics
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• v.5 no.1
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• pp.13-26
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• 2012

In this paper, the wave propagation in a generalized thermo elastic plate embedded in an elastic medium (Winkler model) is studied based on the Lord-Schulman (LS) and Green-Lindsay (GL) generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations that include the interaction between the plate and foundation are obtained by the traction free boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency and attenuation coefficient are plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries. The wave characteristics are found to be more stable and realistic in the presence of thermal relaxation times and the foundation parameter. A comparison of the results for the case with no thermal effects shows well agreement with those by the membrane theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.1
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• pp.1-15
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• 2013

In this paper the three dimensional wave propagation in a homogeneous isotropic thermo elastic cylindrical panel embedded in an elastic medium (Winkler model) is investigated in the context of the L-S (Lord-Shulman) theory of generalized thermo elasticity. The analysis is carried out by introducing three displacement functions so that the equations of motion are uncoupled and simplified. A Bessel function solution with complex arguments is then directly used for the case of complex Eigen values. This type of study is important for design of structures in atomic reactors, steam turbines, wave loading on submarine, the impact loading due to superfast train and jets and other devices operating at elevated temperature. In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a zinc material with the support of MATLAB.

• Structural Engineering and Mechanics
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• v.82 no.4
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• pp.459-467
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• 2022

We investigated the influence of variable thermal conductivity on waves propagating through the elastic medium. Infinitesimal deformation results in generation of thermal signal, and is analyzed by using dual phase lag heat (DPL) conduction model. The medium considered is homogenous, isotropic and bounded by thermal shock. The elastic waves propagating through the medium are considered to be harmonic in nature, and expressions for the physical variables are obtained accordingly. Analytically, we obtained the expressions for displacement components, temperature, micro-temperature component and stresses. The theoretical results obtained are computed graphically for the particular medium by using MATLAB.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.171-180
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• 2017

Static and dynamic instability of a viscoelastic carbon nanotube (CNT) embedded on a thermo-elastic foundation are investigated, in this research. The CNT is modeled based on Euler-Bernoulli beam (EBB) and nonlocal small scale elasticity theory is utilized to analyze the structure. Governing equations of the system are derived using Hamilton's principle and differential quadrature (DQ) method is applied to solve the partial differential equations. The effects of variable axial load and diverse boundary conditions on static/vibration instability are studied. To verify the result of the DQ method, the Galerkin weighted residual approach is used for the instability analysis. It is observed appropriate agreement for results of two different solution methods and satisfactory accuracy with those obtained in prior studies. The results of this work could be useful for engineers and designers in order to produce and design nano/micro structures in thermo-elastic medium.

• Advances in nano research
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• v.17 no.3
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• pp.197-211
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• 2024

This work investigates the thermo-mechanical vibration frequencies of an embedded composite nano-beam restrained with elastic springs at both ends. Composite nanobeam consists of a matrix and short fibers as reinforcement elements placed inside the matrix. An approach based on Fourier sine series and Stokes' transform is adopted to present a general solution that can examine the elastic boundary conditions of the short-fiber-reinforced nanobeam considered with the Halpin-Tsai model. In addition to the elastic medium effect considered by the Winkler model, the size effect is also considered on the basis of nonlocal strain gradient theory. After creating an eigenvalue problem that includes all the mentioned parameters, this problem is solved to examine the effects of fiber and matrix properties, size parameters, Winkler stiffness and temperature change. The numerical results obtained at the end of the study show that increasing the rigidity of the Winkler foundation, the ratio of fiber length to diameter and the ratio of fiber Young's modulus to matrix Young's modulus increase the frequencies. However, thermal loads acting in the positive direction and an increase in the ratio of fiber mass density to matrix mass density lead to a decrease in frequencies. In this study, it is clear from the eigenvalue solution calculating the frequencies of thermally loaded embbeded short-fiber-reinforced nanobeams that changing the stiffness of the deformable springs provides frequency control while keeping the other properties of the nanobeam constant.

• Structural Engineering and Mechanics
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• v.73 no.5
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• pp.565-584
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• 2020

The nonlinear thermo-electro-elastic buckling behavior of viscoelastic nanoplates under magnetic field is investigated based on nonlocal elasticity theory. Employing nonlinear strain-displacement relations, the geometrical nonlinearity is modeled while governing equations are derived through Hamilton's principle and they are solved applying semi-analytical generalized differential quadrature (GDQ) method. Eringen's nonlocal elasticity theory considers the effect of small size, which enables the present model to become effective in the analysis and design of nano-sensors and nano actuators. Based on Kelvin-Voigt model, the influence of the viscoelastic coefficient is also discussed. It is demonstrated that the GDQ method has high precision and computational efficiency in the buckling analysis of viscoelastic nanoplates. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as electric voltage, small scale effects, elastomeric medium, magnetic field, temperature effects, the viscidity and aspect ratio of the nanoplate on its nonlinear buckling characteristics. It is explicitly shown that the thermo-electro-elastic nonlinear buckling behavior of viscoelastic nanoplates is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of viscoelastic nanoplates as fundamental elements in nanoelectromechanical systems.

• Advances in aircraft and spacecraft science
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• v.7 no.1
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• pp.41-52
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• 2020

The effect of relaxation times is studied on plane waves propagating through semiconductor half-space medium by using the eigen value approach. The bounding surface of the half-space is subjected to a heat flux with an exponentially decaying pulse and taken to be traction free. Solution of the field variables are obtained in the form of series for a general semiconductor medium. For numerical values, Silicon is considered as a semiconducting material. The results are represented graphically to assess the influences of the thermal relaxations times on the plasma, thermal, and elastic waves.

• Structural Engineering and Mechanics
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• v.29 no.6
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• pp.673-687
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• 2008

In this paper, a thermo-viscoelastic problem in an infinite isotropic medium in two dimensions in the presence of a point heat source is considered. The fundamental equations of the problems of generalized thermoelasticity including heat sources in a thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace-Fourier transform domain for a two dimensional problem. These equations have been solved by the eigenvalue approach. The results have been compared to those available in the existing literature. The graphs have been drawn for different cases.

• Structural Engineering and Mechanics
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• v.58 no.5
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• pp.931-947
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• 2016

The effects of nanotechnology and smartness on the buckling reduction of pipes are the main contributions of present work. For this ends, the pipe is simulated with classical piezoelectric polymeric cylindrical shell reinforced by armchair double walled boron nitride nanotubes (DWBNNTs), The structure is subjected to combined electro-thermo-mechanical loads. The surrounding elastic foundation is modeled with a novel model namely as orthotropic nonhomogeneous Pasternak medium. Using representative volume element (RVE) based on micromechanical modeling, mechanical, electrical and thermal characteristics of the equivalent composite are determined. Employing nonlinear strains-displacements and stress-strain relations as well as the charge equation for coupling of electrical and mechanical fields, the governing equations are derived based on Hamilton's principal. Based on differential quadrature method (DQM), the buckling load of pipe is calculated. The influences of electrical and thermal loads, geometrical parameters of shell, elastic foundation, orientation angle and volume percent of DWBNNTs in polymer are investigated on the buckling of pipe. Results showed that the generated ${\Phi}$ improved sensor and actuator applications in several process industries, because it increases the stability of structure. Furthermore, using nanotechnology in reinforcing the pipe, the buckling load of structure increases.

• Structural Engineering and Mechanics
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• v.53 no.2
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• pp.277-296
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• 2015

The objective of this paper is to investigate the surface waves in fibre-reinforced anisotropic thermoelastic medium subjected to gravity field. The theory of generalized surface waves has firstly developed and then it has been employed to investigate particular cases of waves, viz., Stoneley waves, Rayleigh waves and Love waves. The analytical expressions for displacement components, force stress and temperature distribution are obtained in the physical domain by using the harmonic vibrations. The wave velocity equations have been obtained in different cases. The numerical results are given and presented graphically in Green-Lindsay and Lord-Shulman theory of thermoelasticity. Comparison was made with the results obtained in the presence and absence of gravity, anisotropy, relaxation times and parameters for fibrereinforced of the material medium. The results indicate that the effect of gravity, anisotropy, relaxation times and parameters for fibre-reinforced of the material medium are very pronounced.