• Composites Research
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• v.12 no.4
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• pp.25-32
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• 1999

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures, with irregular cross sections and with arbitrary boundary conditions was developed and reported by Kim, D. H. in 1974. In this paper, the result of application of this method to the special orthotropic plates on elastic foundation with free boundaries is presented. Such plates represent the concrete highway slab and hybrid composite pavement on bridges. Any method may be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purpose, in this paper. The influence of the modulus of the foundation and the aspect ratio of the plate on the natural frequency is thoroughly studied. The effect of neglecting the mass of the plates on the natural frequency, as the ratio of the point mass/masses to the plate mass increases, is also studied, in deep.

• Geomechanics and Engineering
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• v.13 no.6
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• pp.1027-1044
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• 2017

Membrane penetration is the most important factor influencing the measurement of volume change for triaxial consolidated-drained shear test for coarse-grained soil. The effective pressure p, average particle size $d_{50}$, thickness $t_m$ and elastic modulus $E_m$ of membrane, contact area between membrane and soil $A_m$ as well as the initial void ratio e are the major factors influencing membrane penetration. According to the membrane deformation model given by Kramer and Sivaneswaran, an analytical solution of the membrane penetration considering the initial void ratio is deduced using the energy conservation law. The basic equations from theory of plates and shells and the elastic mechanics are employed during the derivation. To verify the presented solution, isotropic consolidation tests of a coarse-grained soil are performed by using the method of embedding different diameter of iron rods in the triaxial samples, and volume changes due to membrane penetration are obtained. The predictions from presented solution and previous analytical solutions are compared with the test results. It is found that the prediction from presented analytical solution agrees well with the test results.

• Nuclear Engineering and Technology
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• v.53 no.11
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• pp.3816-3823
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• 2021

The mechanical features evaluated theoretically using Makishima-Mackenzie's model for glasses xBaO-(50-x) PbO-50P₂O₅ where x = 0, 5, 10, 15, 20, 30, 40, and 50 mol%. Wherefore, the elastic characteristics; Young's, bulk, shear, and longitudinal modulus calculated. The obtained result showed an increase in the calculated values of elastic moduli with the replacement of the PbO by BaO contents. Moreover, the Poisson ratio, micro-hardness, and the softening temperature calculated for the investigated glasses. Besides, gamma and neutron shielding ability evaluated for the barium doped lead phosphate glasses. Monte Caro code (MCNP-5) and the Phy-X/PSD program applied to estimate the mass attenuation coefficient of the studied glasses. The decrease in the PbO ratio has a negative effect on the MAC. The highest MAC decreased from 65.896 cm²/g to 32.711 cm²/g at 0.015 MeV for BPP0 and BPP7, respectively. The calculated values of EBF and EABF showed that replacement of PbO with BaO contents in the studied BPP glasses helps to reduce the number of photons accumulated inside the studied BPP glasses.

• Journal of the Korean institute of surface engineering
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• v.54 no.3
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• pp.139-143
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• 2021

Cr-Al-N coatings were deposited onto WC-Co substrates using a cathodic arc evaporation (CAE) system. CAE technique is recognized to be a very useful process for hard coatings because it has many advantages such as high packing density and good adhesion to metallic substrates. In this study, the influence of deposition temperature as a key process parameter on film growth behavior and mechanical properties of Cr-Al-N coatings were systematically investigated and correlated with microstructural changes. From various analyses, the Cr-Al-N coatings prepared at deposition temperature of 450℃ in the CAE process showed excellent mechanical properties with higher deposition rate. The Cr-Al-N coatings with deposition temperature around 450℃ exhibited the highest hardness of about 35 GPa and elastic modulus of 442 GPa. The resistance to elastic strain to failure (H/E ratio) and the index of plastic deformation (H³/E² ratio) were also good values of 0.079 and 0.221 GPa, respectively, at the deposition temperature of 450℃. Based on the XRD, SEM and TEM analyses, the Cr-Al-N coatings exhibited a dense columnar structure with f.c.c. (Cr,Al)N multi-oriented phases in which crystallites showed irregular shapes (50~100nm in size) with many edge dislocations and lattice mismatches.

• Steel and Composite Structures
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• v.30 no.1
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• pp.13-29
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• 2019

This work presents the buckling investigation of functionally graded plates resting on two parameter elastic foundations by using a new hyperbolic plate theory. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only four unknowns and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. The governing equations are derived using Hamilton's principle and solved using Navier's steps. The validation of the proposed theoretical model is performed to demonstrate the efficacy of the model. The effects of various parameters like the Winkler and Pasternak modulus coefficients, inhomogeneity parameter, aspect ratio and thickness ratio on the behaviour of the functionally graded plates are studied. It can be concluded that the present theory is not only accurate but also simple in predicting the critical buckling loads of functionally graded plates on elastic foundation.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.471-502
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• 2016

This paper presents the dynamic instability analysis of un-damped elastically supported piezoelectric functionally graded (FG) beams subjected to in-plane static and dynamic periodic thermomechanical loadings with uncertain system properties. The elastic foundation model is assumed as one parameter Pasternak foundation with Winkler cubic nonlinearity. The piezoelectric FG beam is subjected to non-uniform temperature distribution with temperature dependent material properties. The Young's modulus and Poison's ratio of ceramic, metal and piezoelectric, density of respective ceramic and metal, volume fraction exponent and foundation parameters are taken as uncertain system properties. The basic nonlinear formulation of the beam is based on higher order shear deformation theory (HSDT) with von-Karman strain kinematics. The governing deterministic static and dynamic random instability equation and regions is solved by Bolotin's approach with Newmark's time integration method combined with first order perturbation technique (FOPT). Typical numerical results in terms of the mean and standard deviation of dynamic instability analysis are presented to examine the effect of slenderness ratios, volume fraction exponents, foundation parameters, amplitude ratios, temperature increments and position of piezoelectric layers by changing the random system properties. The correctness of the present stochastic model is examined by comparing the results with direct Monte Caro simulation (MCS).

• Composites Research
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• v.18 no.2
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• pp.30-37
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• 2005

In this paper, geometrically non-linear finite element analyses were performed to study the mechanical behavior of the material system of the envelope of stratospheric airships. The microstructure of the load-bearing plain weave layer was identified and modeled. The Updated Lagrangian formulation was employed to consider the geometric non-linearity as well as the induced structural non-linearity for the fiber tows. The stress-strain behavior was predicted and the effective elastic modulus was calculated by numerical experiments. It was found the non-linear stress-strain curves were largely different from those by linear analysis. And non-linear elastic moduli were much higher than linear elastic moduli. The difference was more distinguishable when the tow waviness ratio was smaller.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.6
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• pp.122-129
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• 2000

The purpose of this study is to investigate both the fundamental and some higher natural frequencies and mode shapes of compressive members resting on the linear elastic foundation. The model of compressive member is based on the classical Bernoulli-Euler beam theory. The differential equation governing free vibrations of such members subjected to an axial load is derived and solved numerically for calculating the natural frequencies and mode shapes. The Improved Euler method is used to integrate the differential equation and the Determinant Search method combined with the Regula-Falsi method to determine the natural frequencies, respectively. In numerical examples, the hinged-hinged, hinged-clamped, clamped-hinged and clamped-clamped end constraints are considered. The convergence analysis is conducted for determining the available step size in the Improved Euler method. The validation of theories developed herein is also conducted by comparing the numerical results between this study and SAP 90. The non-dimensional frequency parameters are presented as the non-dimensional system parameters: section ratio, modulus parameter and load parameter. Also typical mode shapes are presented.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.327-334
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• 1998

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and toll.or structures, with irregular cross sections and with arbitrary boundary conditions was developed and reported by Kim, D. H. in 1974. In this paper, the result of application of this method to the special orthotropic plates with free edges supported on elastic foundation and with a pair of opposite edges under axial forces is presented. Such plates represent the concrete highway slab and hybrid composite pavement of bridges. The reinforced concrete slab can be assumed as a special orthotropic plate, as a close approximation. The highway slab is supported on elastic foundation, with free boundaries. Sometimes, the pair of edges perpendicular to the traffic direction may be subject to the axial forces. The plate is subject to the concentrated load/loads, in the form of traffic loads, or the test equipments. Any method nay be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purpose, in this paper. The influence of the modulus of the foundation, the aspect ratio of the plate, and the magnitudes of the axial forces and the concentrated attached mass on the plate, on the natural frequency is thoroughly studied.

• Structural Engineering and Mechanics
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• v.70 no.6
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• pp.737-750
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• 2019

This paper investigates the static and dynamic behaviors of imperfect single walled carbon nanotube (SWCNT) modeled as a beam structure by using energy-equivalent model (EEM), for the first time. Based on EEM Young's modulus and Poisson's ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The equation governed the motion of curved CNTs is a nonlinear integropartial-differential equation. It is derived in terms of only the lateral displacement. The nonlinear integro-differential equation that governs the buckling of CNT is numerically solved using the differential integral quadrature method (DIQM) and Newton's method. The linear vibration problem around the static configurations is discretized using DIQM and then is solved as a linear eigenvalue problem. Numerical results are depicted to illustrate the influence of chirality angle and imperfection amplitude on static response, buckling load and dynamic behaviors of armchair and zigzag CNTs. Both, clamped-clamped (C-C) and simply supported (SS-SS) boundary conditions are examined. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.