• Advances in nano research
• /
• v.8 no.1
• /
• pp.13-24
• /
• 2020

In this paper, for the first time based on the nonlocal strain gradient theory the effect of size dependency in torsional vibration of bi-direction functionally graded (FG) nonlinear nano-cone is study. The material properties were assumed to vary according to the arbitrary function in radial and axial directions. The Navier equation and boundary conditions of the size-dependent bidirectional FG nonlinear nano-cone were derived by Hamilton's principle. These equations were solved by employing the generalized differential quadrature method (GDQM). The presented model can turn into the classical model if the material length scale parameters are taken to be zero. The effects of some parameters, such as inhomogeneity constant, cross-sectional area parameter and small-scale parameters, were studied. As an essential result of this study can be stated that an FG nano-cone model based on the nonlocal elasticity theory behaves softer and based on the strain gradient theory behaves harder.

• Structural Engineering and Mechanics
• /
• v.72 no.2
• /
• pp.229-244
• /
• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• Kyungpook Mathematical Journal
• /
• v.61 no.4
• /
• pp.831-843
• /
• 2021

In this paper we look at the three dimensional stagnation point flow problem over a rough rotating disk. We study the theoretical behaviour of the stagnation point flow, or forced flow, in the presence of a slip factor in which convective instability stationary modes appear. We make a numerical investigation of the effects of slip on the behaviour of the flow components of the stagnation point flow where the disk is rough. We provide, for the first time in the literature, a complete convective instability analysis and an energy analysis. Suitable similarity transformations are used to reduce the Navier-Stokes equations and the continuity equation into a system of highly non-linear coupled ordinary differential equations, and these are solved numerically subject to suitable boundary conditions using the bvp4c function of MATLAB. The convective instability analysis and the energy analysis are performed using the Chebyshev spectral method in order to obtain the neutral curves and the energy bars. We observe that the roughness of the disk has a destabilising effect on both Type-I and Type-II instability modes. The results obtained will be prominently treated as benchmarks for our future studies on stagnation flow.

• Steel and Composite Structures
• /
• v.43 no.1
• /
• pp.117-127
• /
• 2022

This study investigates the wave propagation in porous functionally graded (FG) sandwich plates subjected to hygrothermal environments. A new simple three-unknown first-ordershear deformation theory (FSDT) incorporating an integral term is utilized in this paper. Only three unknowns are used to formulate the governing differential equation by applying the Hamilton principle. The FG layer of the sandwich plate is modeled using the power-law function with evenly distributed porosities to represent the defects of the manufacturing process. The plate is subjected to nonlinear hygrothermal changes across the thickness. The effects of the power-law exponent, core to thickness ratios, porosity volume, and the relations between volume fraction and wave properties of porous FG plate under the hygrothermal environment are investigated. The results showed that the waves' phase velocities increase linearly with the waves number in the FGM plate. The porosity of the FG materials plate has a noticeable impact on the phase velocity when considering the high ratios of the core layer. It has a negligible effect on small core layers. Finally, it is observed that changing temperatures and moistures do not influence the relationship between the power law and the phase velocity.

• Structural Engineering and Mechanics
• /
• v.85 no.6
• /
• pp.729-742
• /
• 2023

It is a recent attraction to the mechanical scientists to investigate state of wave propagation, buckling and vibration in the sport balls to observe the importance of different parameters on the performance of the players and the quality of game. Therefore, in the present study, we aim to investigate the wave propagation in handball game ball in term of mass of the ball and geometrical parameters wit incorporation of the viscoelastic effects of the ball material into account. In this regard, the ball is modeled using thick shell structure and classical elasticity models is utilized to obtain the equation of motion via Hamilton's principle. The displacement field of the ball model is obtained using first order shear deformation theory. The resultant equations are solved with the aid of generalized differential quadrature method. The results show that mass of the ball and viscoelastic coefficient have considerable influence on the state of wave propagation in the ball shell structure.

• Structural Engineering and Mechanics
• /
• v.85 no.6
• /
• pp.717-728
• /
• 2023

The effect of temperature dependent material properties on the free vibration of FG porous beams is investigated in the present paper. A quasi-3D shear deformation solution is used involves only three unknown function. The mechanical properties which are considered to be temperature-dependent as well as the porosity distributions are assumed to gradually change along the thickness direction according to defined law. The beam is supposed to be simply supported and lying on variable elastic foundation. The differential equation system governing the free vibration behavior of porous beams is derived based on the Hamilton principle. Navier's method for simply supported systems is then used to determine and compute the frequencies of FG porous beam. The results of the present formulation are validated by comparing with those available literatures. Finally, the effects of several parameters such as porosity distribution and the parameters of variable elastic foundation on the free vibration behavior of temperature-dependent FG beams are presented and discussed in detail.

• Steel and Composite Structures
• /
• v.51 no.4
• /
• pp.363-375
• /
• 2024

Within the optimization field, addressing the intricate posed by fluidic pressure loads on functionally graded structures with frequency-related designs is a kind of complex design challenges. This paper thus introduces an innovative density-based topology optimization strategy for frequency-constraint functionally graded structures incorporating Darcy's law and a drainage term. It ensures consistent treatment of design-dependent fluidic pressure loads to frequency-related structures that dynamically adjust their direction and location throughout the design evolution. The porosity of each finite element, coupled with its drainage term, is intricately linked to its density variable through a Heaviside function, ensuring a seamless transition between solid and void phases. A design-specific pressure field is established by employing Darcy's law, and the associated partial differential equation is solved using finite element analysis. Subsequently, this pressure field is utilized to ascertain consistent nodal loads, enabling an efficient evaluation of load sensitivities through the adjoint-variable method. Moreover, this novel approach incorporates load-dependent structures, frequency constraints, functionally graded material models, and polygonal meshes, expanding its applicability and flexibility to a broader range of engineering scenarios. The proposed methodology's effectiveness and robustness are demonstrated through numerical examples, including fluidic pressure-loaded frequency-constraint structures undergoing small deformations, where compliance is minimized for structures optimized within specified resource constraints.

• Journal of Auto-vehicle Safety Association
• /
• v.16 no.2
• /
• pp.51-59
• /
• 2024

This study presents a method for health monitoring of rotating objects for mobility based on multiple recursive least squares(RLS) algorithms. The performance degradation of the rotating objects causes low handing / low driving performances and even fatal accidents. Therefore, health monitoring algorithm of rotating objects is one of the important technologies for mobility fail-safe and maintenance areas. In order for health monitoring of rotating objects, four recursive least squares algorithms with forgetting factor were designed in this study. The health monitoring algorithm proposed in this study consists of two steps such as uncertainty estimation and parameter changes estimation. In order to improve estimation accuracy, time delay function was applied to the estimated signals based on the first order differential equation and forgetting factors used for the RLS were reasonably tuned. The health monitoring algorithm was constructed in Matlab/Simulink environment and simulation-based performance evaluation was conducted using DC motor model. The evaluation results showed that the proposed algorithm estimates the actual parameter differences reasonably using velocity and current information.

• 한국신재생에너지학회:학술대회논문집
• /
• 2009.06a
• /
• pp.373-373
• /
• 2009

Relative humidity, membrane conductivity and water activity are critical parameters of polymer electrolyte membrane fuel cells (PEMFC) for high performance and reliability. These parameters are closely related with temperature. Moreover, the ideal values of these parameters are not always identical along the channels. Therefore, the cooling channel design and its operating condition should be well optimized along the all location of the channels. In the present study, we have performed a numerical investigation on the effects of cooling channels on performance of a PEMFC. Three-dimensional Navier-Stokes equations are solved with the energy equation including heat generated by the electrochemical reactions in the fuel cell. The present numerical model includes the gas diffusion layers (GDL) and serpentine channels for both anode and cathode gas flows, as well as cooling channels. To accurately predict the water transport across the membrane, the distribution of water content in the membrane is calculated by solving a nonlinear differential equation with a nonlinear coefficient, i.e., the water diffusivity which is a function of water content as well as temperature. Main emphasis is placed on the heat transfer between the solid bipolar plate and coolant flow. The present results show that local current density is affected by cooling channels due to the change of the oxygen concentration and the membrane conductivity as well as the water content. It is also found that the relative humidity is influenced by the generated water and the gas temperature and thus it affects the distribution of fuel concentration and the conductivity of the membrane, ultimately fuel cell performance. Unit-cell experiments are also carried out to validate the numerical models. The performance curves between the models and experiments show reasonable results.

• Structural Engineering and Mechanics
• /
• v.71 no.6
• /
• pp.627-641
• /
• 2019

The paper focuses on bending analysis of the functionally graded (FG) plates with arbitrary shapes and boundary conditions. The material property of FG plates is modelled by using the power law distribution. Based on the first order shear deformation plate theory (FSDT), the governing equations as well as boundary conditions are formulated and obtained by using the principle of virtual work. The coupled Boundary Element-Radial Basis Function (BE-RBF) method is established to solve the complex FG plates. The proposed methodology is developed by applying the concept of the analog equation method (AEM). According to the AEM, the original governing differential equations are replaced by three Poisson equations with fictitious sources under the same boundary conditions. Then, the fictitious sources are established by the application of a technique based on the boundary element method and approximated by using the radial basis functions. The solution of the actual problem is attained from the known integral representations of the potential problem. Therefore, the kernels of the boundary integral equations are conveniently evaluated and readily determined, so that the complex FG plates can be easily computed. The reliability of the proposed method is evaluated by comparing the present results with those from analytical solutions. The effects of the power index, the length to thickness ratio and the modulus ratio on the bending responses are investigated. Finally, many interesting features and results obtained from the analysis of the FG plates with arbitrary shapes and boundary conditions are demonstrated.