• Advances in nano research
• /
• v.4 no.2
• /
• pp.65-84
• /
• 2016

This paper investigates the buckling behavior of shear deformable piezoelectric (FGP) nanoscale beams made of functionally graded (FG) materials embedded in Winkler-Pasternak elastic medium and subjected to an electro-magnetic field. Magneto-electro-elastic (MEE) properties of piezoelectric nanobeam are supposed to be graded continuously in the thickness direction based on power-law model. To consider the small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of the embedded piezoelectric nanobeams are obtained. A Navier-type analytical solution is applied to anticipate the accurate buckling response of the FGP nanobeams subjected to electro-magnetic fields. To demonstrate the influences of various parameters such as, magnetic potential, external electric voltage, power-law index, nonlocal parameter, elastic foundation and slenderness ratio on the critical buckling loads of the size-dependent MEE-FG nanobeams, several numerical results are provided. Due to the shortage of same results in the literature, it is expected that the results of the present study will be instrumental for design of size-dependent MEE-FG nanobeams.

• Structural Engineering and Mechanics
• /
• v.70 no.5
• /
• pp.535-549
• /
• 2019

This study aimed to develop a high-order shear deformation theory to predict the free vibration of hybrid cross-ply laminated plates under different boundary conditions. The equations of motion for laminated hybrid rectangular plates are derived and obtained by using Hamilton's principle. The closed-form solutions of anti-symmetric cross-ply and angle-ply laminates are obtained by using Navier's solution. To assess the validity of our method, we used the finite element method. Firstly, the analytical and the numerical implementations were validated for an antisymmetric cross-ply square laminated with available results in the literature. Then, the effects of side-to-thickness ratio, aspect ratio, lamination schemes, and material properties on the fundamental frequencies for different combinations of boundary conditions of hybrid composite plates are investigated. The comparison of the analytical solutions with the corresponding finite element simulations shows the good accuracy of the proposed analytical closed form solution in predicting the fundamental frequencies of hybrid cross-ply laminated plates under different boundary conditions.

• Earthquakes and Structures
• /
• v.24 no.2
• /
• pp.127-140
• /
• 2023

The vibration of microtubule in human cells is the source of electrical field around it and inside cell structure. The induction of electrical field is a direct result of the existence of dipoles on the surface of the microtubules. Measuring the electrical fields could be performed using nano-scale sensors and the data could be transformed to other computers using internet of things (IoT) technology. Processing these data is feasible by artificial intelligence-based methods. However, the first step in analyzing the vibrational behavior is to study the mechanics of microtubules. In this regard, the vibrational behavior of the microtubules is investigated in the present study. A shell model is utilized to represent the microtubules' structure. The displacement field is assumed to obey first order shear deformation theory and classical theory of elasticity for anisotropic homogenous materials is utilized. The governing equations obtained by Hamilton's principle are further solved using analytical method engaging Navier's solution procedure. The results of the analytical solution are used to train, validate and test of the deep neural network. The results of the present study are validated by comparing to other results in the literature. The results indicate that several geometrical and material factors affect the vibrational behavior of microtubules.

• Steel and Composite Structures
• /
• v.52 no.3
• /
• pp.249-271
• /
• 2024

In this scientific work, an analytical solution for the dynamic analysis of cross-ply and angle-ply laminated composite plates is proposed. Due to technical issues during the manufacturing of composite materials, porosities and micro-voids can be produced within the composite material samples, which can carry on to a reduction in the density and strength of the materials. In this research, the laminated composite plates are assumed to have new distributions of porosities over the plate cross-section. The structure is modeled using a simple integral shear deformation theory in which the transverse shear deformation effect is included. The governing equations of motion are obtained employing the principle of Hamilton's. The solution is determined via Navier's approach. The Maple program is used to obtain the numerical results. In the numerical examples, the effects of geometry, ratio, modulus ratio, fiber orientation angle, number of layers and porosity parameter on the natural frequencies of symmetric and anti-symmetric laminated composite plates is presented and discussed in detail. Also, the impacts of the kinds of porosity distribution models on the natural frequencies of symmetric and anti-symmetric laminated composite plates are investigated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1997.04a
• /
• pp.636-642
• /
• 1997

Laminar vortex shedding behind a circular cylinder with and without splitter plates attached to the circular cylinder at low Reynolds numbers are simulated by solving the unsteady incompressible Navier-Strokes equations. The Strouhal number, lift and drag rapidly change with the splitter plate. Far-field noise from the vortex shedding behind the cylinder is computed using the Lighthill acoustic analogy and the Curle's solution for the Lighthill equation. The acoustic source functions are obtained from the computed near-field velocity and pressure. Numerical results show that the volume quadrupole noise is small at low Mach numbers, compared with the surface dipole noise. Also the amplitude and frequency of the acoustic density fluctuations are varied with the length of splitter plates. The scattering effects at the edge of a splitter plate are considered by using the half-plane Green's function.

• Wind and Structures
• /
• v.23 no.1
• /
• pp.59-73
• /
• 2016

In this paper, a hyperbolic shear deformation beam theory is developed for free vibration analysis of functionally graded (FG) sandwich beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded sandwich beam are assumed to vary according to power law distribution of the volume fraction of the constituents. The core layer is still homogeneous and made of an isotropic material. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Illustrative examples are given to show the effects of varying gradients and thickness to length ratios on free vibration of functionally graded sandwich beams.

• Structural Engineering and Mechanics
• /
• v.69 no.6
• /
• pp.637-649
• /
• 2019

In the current research paper, a quasi-3D beam theory is developed for free vibration analysis of functionally graded microbeams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by three functions, power function, symmetric power function and sigmoid law distribution. The modified coupled stress theory is used to incorporate size dependency of micobeam. The equation of motion is derived by using Hamilton's principle, however, Navier type solution method is used to obtain frequencies. Numerical results show the effects of the function distribution, power index and material scale parameter on fundamental frequencies of microbeams. This model provides designers with guidance to select the proper distributions and functions.

• Structural Engineering and Mechanics
• /
• v.77 no.2
• /
• pp.217-229
• /
• 2021

The effect of distribution shape of porosity using a quasi-3D theory for free vibration analysis of FG microbeams is studied analytically in the present paper. The microbeams are simply-supported and nonhomogeneous, with power function variation of Young's modulus along their thickness. The modified coupled stress theory is utilized to consolidate size dependency of microbeam. Both even and uneven distribution shape of porosity are considered and the effective properties of porous FG microbeams are defined by theoretical formula with an additional term of porosity. The equation of motion is obtained through Hamilton's principle, however, Navier type solution method is used to obtain frequencies. The influences played by many parameters are also investigated.

• Advances in concrete construction
• /
• v.15 no.2
• /
• pp.97-114
• /
• 2023

The nonlocal strain gradient theory for the static bending analysis of graphene nanoplatelets (GPLs) reinforced the nanoplate is developed in this paper. The nanoplatelet is exposed to thermo-mechanical loads and is also supposed to stand on an elastic foundation. For computing impressive composite material characteristics, the Halpin-Tsai model is selected for various sectors. The various distributions are propounded including UD, FG-O, and FG-X. The represented equations are acquired based on the virtual work and sinusoidal shear and normal deformation theory (SSNDT). Navier's solution as the analytical method is applied to solve these equations. Furthermore, the effects of GPL weight fraction, temperature parameters, distribution pattern and parameters of the foundation are presented and discussed.

• Advances in nano research
• /
• v.16 no.5
• /
• pp.489-500
• /
• 2024

This paper studies the free vibration analysis of the piezo-magneto-thermo-elastic FG nanobeam submerged in a fluid environment. The problem governed by the partial differential equations is determined by refined higher-order State Space Strain Gradient Theory (SSSGT). Hamilton's principle is applied to discretize the differential equation and transform it into a coupled Euler-Lagrange equation. Furthermore, the equations are solved analytically using Navier's solution technique to form stiffness, damping, and mass matrices. Also, the effects of nonlocal ceramic and metal parts over various parameters such as temperature, Magnetic potential and electric voltage on the free vibration are interpreted graphically. A comparison with existing published findings is performed to showcase the precision of the results.