• Advances in nano research
• /
• v.13 no.5
• /
• pp.465-474
• /
• 2022

Based on the nonlocal strain gradient (NSG) theory and considering the influence of moment of inertia, the governing equations of motion of porous functionally graded (FG) nanoplates with four edges clamped are established; The Galerkin method is applied to eliminate the spatial variables of the partial differential equation, and the partial differential governing equation is transformed into an ordinary differential equation with time variables. By satisfying the boundary conditions and solving the characteristic equation, the dispersion relations of the porous FG strain gradient nanoplates with four edges fixed are obtained. It is found that when the wave number is very small, the influences of nonlocal parameters and strain gradient parameters on the dispersion relation is very small. However, when the wave number is large, it has a great influence on the group velocity and phase velocity. The nonlocal parameter represents the effect of stiffness softening, and the strain gradient parameter represents the effect of stiffness strengthening. In addition, we also study the influence of power law index parameter and porosity on guided wave propagation.

• Geomechanics and Engineering
• /
• v.35 no.6
• /
• pp.637-646
• /
• 2023

At present, the research on wave propagation in graphene platelet reinforced composite plates focuses on the propagation behavior of bulk waves, in which the effect of boundary condition is ignored, there is no literature report on propagation behaviors of guided waves in graphene platelet reinforced metal foams (GPLRMF) plates. In fact, wave propagation is affected by boundary conditions, so it is necessary to study the propagation characteristics of guided waves. The aim of this paper is to solve this problem. The effective performance of the material was calculated using the mixing law. Equations of motion of GPLRMF plate is derived by using Hamilton's principle. Then, the eigenvalue method is used to obtain the expressions of bending wave, shear wave and longitudinal wave, and the degradation verification is carried out. Finally, the effects of graphene platelets (GPLs) volume fraction, elastic foundation, porosity coefficient, GPLs distribution types and porosity distribution types on the dispersion relations are studied. We find that these factors play an important role in the propagation characteristics and phase velocity of guided waves.

• Computers and Concrete
• /
• v.33 no.3
• /
• pp.241-250
• /
• 2024

This article investigates the thermal and post-buckling problems of graphene platelets reinforced metal foams (GPLRMF) beams with initial geometric imperfection. Three distribution forms of graphene platelet (GPLs) and foam are employed. This article utilizes the mixing law Halpin Tsai model to estimate the physical parameters of materials. Considering three different boundary conditions, we used the Euler beam theory to establish the governing equations. Afterwards, the Galerkin method is applied to discretize these equations. The correctness of this article is verified through data analysis and comparison with the existing articles. The influences of geometric imperfection, GPL distribution modes, boundary conditions, GPLs weight fraction, foam distribution pattern and foam coefficient on thermal post-buckling are analyzed. The results indicate that, perfect GPLRMF beams do not undergo bifurcation buckling before reaching a certain temperature, and the critical buckling temperature is the highest when both ends are fixed. At the same time, the structural stiffness of the beam under the GPL-A model is the highest, and the buckling response of the beam under the Foam-II mode is the lowest, and the presence of GPLs can effectively improve the buckling strength.

• Nuclear Engineering and Technology
• /
• v.55 no.11
• /
• pp.4295-4306
• /
• 2023

The vibration of fuel rods in axial flow is a universally recognized issue within both engineering and academic communities due to its significant importance in ensuring structural safety. This paper aims to thoroughly investigate the stability and nonlinear vibration of a fuel rod subjected to axial flow in a newly designed high temperature gas cooled reactor. Considering the possible presence of thermal expansion and large deformation in practical scenarios, the thermal effect and geometric nonlinearity are modeled using the von Karman equation. By applying Hamilton's principle, we derive the comprehensive governing equation for this fluid-structure interaction system, which incorporates the quadratic nonlinear stiffness. To establish a connection between the fluid and structure aspects, we utilize the Galerkin method to solve the perturbation potential function, while employing mode expansion techniques associated with the structural analysis. Following convergence and validation analyses, we examine the stability of the structure under various conditions in detail, and also investigate the bifurcation behavior concerning the buckling amplitude and flow velocity. The findings from this research enhance the understanding of the underlying physics governing fuel rod behavior in axial flow under severe yet practical conditions, while providing valuable guidance for reactor design.

• Advances in nano research
• /
• v.17 no.1
• /
• pp.61-73
• /
• 2024

This paper presents nonlinear vibration analysis of a composite cylindrical shell. The core of the shell is made of functionally graded (FG) porous materials and layers is fabricated of carbon nanotubes (CNTs) reinforced nanocomposites. To increase the accuracy of results, neutral surface position is considered. First-order shear deformation theory is used as displacement field to derive the basic relations of equation motions. In addition, von-Karman nonlinear strains are employed to account geometric nonlinearity and to enhance the results' precision, the exact position of the neutral surface is considered. To governing the partial equations of motion, the Hamilton's principle is used. To reduce the equation motions into a nonlinear motion equation, the Galerkin's approach is employed. After that the nonlinear motion equation is solved by multiple scales method. Effect of various parameters such as volume fraction and distribution of CNTs along the thickness directions, different patterns and efficiency coefficients of porous materials, geometric characteristics and initial conditions on nonlinear to linear ratio of frequency is investigated.

• Structural Engineering and Mechanics
• /
• v.92 no.2
• /
• pp.163-172
• /
• 2024

This paper intends to analyze the nonlinear forced vibrations of functionally graded material (FGM) beams with initial geometrical defects in hygro-thermal ambiences. For this purpose, we assume that the correlation properties of the material alter along the thickness direction in succession and the surface of the beam is subjected to humid and thermal loads. Based on the Euler Bernoulli beam theory and geometrical non-linearity, we use the Hamiltonian principle to formulate a theoretical model with consideration of the hygrothermal effects. Galerkin's technique has been proposed for the control equations of discrete systems. The non-linear primary resonances are acquired by applying the modified Lindstedt-Poincare method (MLP). Verify the reliability of the data obtained through comparison with literature. The non-linear resonance response is reflected by amplitude-frequency response curves. The numerical results indicate that the resonances of FGM beams include three non-linear characteristics, namely hard springs, soft springs and soft-hard spring types. The response modalities of the structure may transform between those non-linear characteristics when material properties, spring coefficients, geometric defect values, temperature-humidity loads and even the external stimulus generate variations.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.37 no.3
• /
• pp.229-235
• /
• 2013

To investigate the effect of the flexible artery wall on the blood flow, three-dimensional numerical simulations were carried out for analyzing the time-dependent incompressible flows of Newtonian fluids constrained by a flexible wall. The Navier-Stokes equations for fluid flow were solved using the P2P1 Galerkin finite element method, and mesh movement was achieved using an arbitrary Lagrangian-Eulerian formulation. The Newmark method was employed for solving the dynamic equilibrium equations for the deformation of a linear elastic solid. To avoid complexity due to the necessity of additional mechanical constraints, we used a combined formulation that includes both the fluid and structure equations of motion to produce a single coupled variational equation. The results showed that the flexibility of the carotid wall significantly affects flow phenomena during the pulse cycle. The flow field was also found to be strongly influenced by the bifurcation angle.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.22 no.10
• /
• pp.1005-1011
• /
• 2011

In this paper, we present a marching-on-in-degree(MOD) finite difference method(FDM) based on the Helmholtz wave equation for analyzing transient electromagnetic responses in a general dispersive media. The two issues related to the finite difference approximation of the time derivatives and the time consuming convolution operations are handled analytically using the properties of the Laguerre functions. The basic idea here is that we fit the transient nature of the fields, the flux densities, the permittivity with a finite sum of orthogonal Laguerre functions. Through this novel approach, not only the time variable can be decoupled analytically from the temporal variations but also the final computational form of the equations is transformed from finite difference time-domain(FDTD) to a finite difference formulation through a Galerkin testing. Representative numerical examples are presented for transient wave propagation in general Debye, Drude, and Lorentz dispersive medium.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.25 no.12
• /
• pp.866-873
• /
• 2015

The transverse vibration of the deploying beam from rigid hub was analyzed by simulation and experiment. The linear governing equation of the deploying beam was obtained using the Euler-Bernoulli beam theory. To discretize the governing equation, the Galerkin method was used. After transforming the governing equation into the weak form, the weak form was discretized. The discretized equation was expressed by the matrix-vector form, and then the Newmark method was applied to simulate. To consider the damping effect of the beam, we conducted the modal test with various beam length. The mass proportional damping was selected by the relation of the first and second damping ratio. The proportional damping coefficient was calculated using the acquired natural frequency and damping ratio through the modal test. The experiment was set up to measure the transverse vibration of the deploying beam. The fixed beam at the carriage of the linear actuator was moved by moving the carriage. The transverse vibration of the deploying beam was observed by the Eulerian description near the hub. The deploying or retraction motion of the beam had the constant velocity and the velocity profile with acceleration and deceleration. We compared the transverse vibration results by the simulation and experiment. The observed response by the Eulerian description were analyzed.

• Wind and Structures
• /
• v.15 no.6
• /
• pp.481-494
• /
• 2012

The greenhouse type metal structures are increasingly used in modern construction of livestock farms because they are less laborious to construct and they provide a more favorable microclimate for the growth of animals compared to conventional livestock structures. A key stress factor for metal structures is the wind. The external pressure coefficient ($c_{pe}$) is used for the calculation of the wind effect on the structures. A high pressure coefficient value leads to an increase of the construction weight and subsequently to an increase in the construction cost. The EC1 in conjunction with EN 13031-1:2001, which is specialized for greenhouses, gives values for this coefficient. This value must satisfy two requirements: the safety of the structure and a reduced construction cost. In this paper, the Navier - Stokes and continuity equations are solved numerically with the finite element method (Galerkin Method) in order to simulate the two dimensional, incompressible, viscous air flow over the vaulted roofs of single span and twin-span with eaves livestock greenhouses' structures, with a height of 4.5 meters and with length of span of 9.6 and 14 m. The simulation was carried out in a wind tunnel. The numerical results of pressure coefficients, as well as, the distribution of them are presented and compared with data from Eurocodes for wind actions (EC1, EN 13031-1:2001). The results of the numerical experiment were close to the values given by the Eurocodes mainly on the leeward area of the roof while on the windward area a further segmentation is suggested.