• Steel and Composite Structures
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• v.18 no.1
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• pp.187-212
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• 2015

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

• Steel and Composite Structures
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• v.19 no.6
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• pp.1421-1447
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• 2015

In this paper, the effect of material-temperature dependent on the wave propagation of a cantilever beam composed of functionally graded material (FGM) under the effect of an impact force is investigated. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. Material properties of the beam are temperature-dependent and change in the thickness direction. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Euler-Bernoulli beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain and frequency domain by using Newmark average acceleration method. In order to establish the accuracy of the present formulation and results, the comparison study is performed with the published results available in the literature. Good agreement is observed. In the study, the effects of material distributions and temperature rising on the wave propagation of the FGM beam are investigated in detail.

• Structural Engineering and Mechanics
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• v.86 no.1
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• pp.1-16
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• 2023

The free vibration of temperature-dependent functionally graded plates (FGPs) resting on a viscoelastic foundation is investigated in this paper using a newly developed simple first-order shear deformation theory (FSDT). Unlike other first order shear deformation (FSDT) theories, the proposed model contains only four variables' unknowns in which the transverse shear stress and strain follow a parabolic distribution along the plates' thickness, and they vanish at the top and bottom surfaces of the plate by considering a new shape function. For this reason, the present theory requires no shear correction factor. Linear steady-state thermal loads and power-law material properties are supposed to be graded across the plate's thickness. Uniform, linear, non-linear, and sinusoidal thermal rises are applied at the two surfaces for simply supported FGP. Hamilton's principle and Navier's approach are utilized to develop motion equations and analytical solutions. The developed theory shows progress in predicting the frequencies of temperature-dependent FGP. Numerical research is conducted to explain the effect of the power law index, temperature fields, and damping coefficient on the dynamic behavior of temperature-dependent FGPs. It can be concluded that the equation and transformation of the proposed model are as simple as the FSDT.

• Wind and Structures
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• v.26 no.4
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• pp.205-214
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• 2018

In this paper, the thermo-mechanical buckling characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form and the material properties are assumed to be temperature-dependent. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal governing equations are derived based on Timoshenko beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate critical buckling temperature results of the FG nanobeams as compared to some cases in the literature. 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 material distribution profile, small scale effects and aspect ratio on the critical buckling temperature of the FG nanobeams in detail. It is explicitly shown that the thermal buckling of a FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

• Electrical & Electronic Materials
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• v.8 no.2
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• pp.151-157
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• 1995

Frequency-dependent electrical properties of $C_{22}$-Quinolinium(TCNQ) LB films were investigated in a frequency range of 10[Hz]-13[MHz] along a perpendicular direction. The films were heat-treated to understand an electrodynamic response in a temperature range of 20-240[.deg. C]. Frequencydependent dielectric constants show that there are two characteristic dispersions; one is a dispersion occuring near 1[MHz] coming from the orientational polarization of the molecules and the other one is an interfacial polarization effect below 1[kHz] or so when the annealing temperature is above 80 [.deg. C]. The overall frequency-dependent dielectric constant is higher near 80[.deg. C]. It may be due to a softness of the alkyl chains. Several other methods were employed to identify the internal structure change of the films. DSC(differential scanning calorimetry) data of the $C_{22}$-Quinolinium(TCNQ) molecules shows that there is an endothermic process near 110[.deg. C] and a weak exothermic process near 180[.deg. C]. While the endothermic process is related to a disordering of the alkyl chains, the exothermic process seems to be due to a chemical structure change of the TCNQ molecules. Thickness measurement by ellipsometry shows that there is a thickness drop near 100[.deg. C], and the thickness above 120[.deg. C] becomes around 20[%] of the room-temperature value.lue.

• Advances in aircraft and spacecraft science
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• v.6 no.3
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• pp.207-223
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• 2019

Current investigation deals with the thermal stability characteristics of carbon nanotube reinforced composite beams (CNTRC) on elastic foundation and subjected to external uniform temperature rise loading. The single-walled carbon nanotubes (SWCNTs) are supposed to have a distribution as being uniform or functionally graded form. The material properties of the matrix as well as reinforcements are presumed to be temperature dependent and evaluated through the extended rule of mixture which incorporates efficiency parameters to capture the size dependency of the nanocomposite properties. The governing differential equations are achieved based on the minimum total potential energy principle and Euler-Bernoulli beam model. The obtained results are checked with the available data in the literature. Numerical results are supplied to examine the effects of numerous parameters including length to thickness ratio, elastic foundations, temperature change, and nanotube volume fraction on the thermal stability behaviors of FG-CNT beams.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.5
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• pp.673-679
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• 2001

The objective of this work is to estimate the temperature dependent thermal properties of the APC-2 composite using a inverse parameter estimation technique. The present inverse method features the estimation of the thermal conductivity and the volumetric heat capacity, which are dependent on the temperature inside the composite. Furthermore, the thermal conductivity is directionally dependent because of the aniosotropy of the composite. An on-line temperature measurement system with a suitable method of heating is built. A composite slab is fabricated using thermoplastic prepreg for the investigation. The corresponding computer code for evaluating the thermal properties inversely using the temperature reading transmitted from the measurement system is developed. The parameterized form is used for the rapid and stable estimation. The modified Newtons method is adopted for the solution technique of the inverse analysis. The estimated results are compared with the measured data from a previous study for the verification.

• Food Science and Biotechnology
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• v.14 no.3
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• pp.413-415
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• 2005

Time-dependent flow properties of commercial kochujang (hot pepper-soybean paste) were evaluated at various shear rates (5, 15, 25, and $35\;sec^{-1}$) and temperatures (5, 15, and $25^{\circ}C$). Flow properties of all samples showed thixotropic behaviors, which were qualitatively evaluated and quantitatively described by the Weltman, Hahn, and Figoni and Shoemaker models. Time-dependent flow properties of kochujang were found to vary over the range of the shear rate and temperature investigated. Time-dependent models of Weltman and Hahn were suitable ($R^2=0.923-0.987$) for commercial kochujang.

• Structural Engineering and Mechanics
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• v.68 no.3
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• pp.313-323
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• 2018

A numerical study is performed to investigate the impacts of thermal loading on the vibration and buckling of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical shells. Thermo-mechanical properties of constituents are considered to be temperature-dependent. Considering the shear deformation theory, the energy functional is derived, and applying the variational differential quadrature (VDQ) method, the mass and stiffness matrices are obtained. The shear correction factors are accurately calculated by matching the shear strain energy obtained from an exact three-dimensional distribution of the transverse shear stresses and shear strain energy related to the first-order shear deformation theory. Numerical results reveal that considering temperature-dependent material properties plays an important role in predicting the thermally induced vibration of FG-CNTRC conical shells, and neglecting this effect leads to considerable overestimation of the stiffness of the structure.

• Steel and Composite Structures
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• v.27 no.6
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• pp.777-788
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• 2018

An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.