Amin Kimiaeifar

Vibrational analysis of curved single-walled carbon nanotube on a Pasternak elastic foundation

Continuum mechanics and an elastic beam model were employed in the nonlinear force vibrational analysis of an embedded, curved, single-walled carbon nanotube. The analysis considered the effects of the curvature or waviness and midplane stretching of the nanotube on the nonlinear frequency. By utilizing Hes Energy Balance Method (HEBM), the relationships of the nonlinear amplitude and frequency were expressed for a curved, single-walled carbon nanotube. The amplitude frequency response curves of the nonlinear free vibration were obtained for a curved, single-walled carbon nanotube embedded in a Pasternak elastic foundation. Finally, the influence of the amplitude of the waviness, midplane stretching nonlinearity, shear foundation modulus, surrounding elastic medium, radius, and length of the curved carbon nanotube on the amplitude frequency response characteristics are discussed. As a result, the combination effects of waviness and stretching nonlinearity on the nonlinear frequency of the curved SWCNT with a small outer radius were larger than the straight one.

An analytical solution for the Marangoni mixed convection boundary layer flow

Abstract In this article, an analytical solution for a Marangoni mixed convection boundary layer flow is presented. A similarity transform reduces the Navier—Stokes equations to a set of non-linear ordinary differential equations, which are solved analytically by means of the homotopy analysis method (HAM). The results obtained in this study are compared with the numerical results released in the literature. A close agreement of the two sets of results indicates the accuracy of the HAM. The method can obtain an expression that is acceptable for all values of effective parameters and is also able to control the convergence of the solution. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on the HAM.

HOMOTOPY ANALYSIS AND DIFFERENTIAL QUADRATURE SOLUTION OF THE PROBLEM OF FREE-CONVECTIVE MAGNETOHYDRODYNAMIC FLOW OVER A STRETCHING SHEET WITH THE HALL EFFECT AND MASS TRANSFER TAKEN INTO ACCOUNT

This paper presents an analytical solution of the problem of free-convective magnetohydrodynamic flow over a stretched sheet with the Hall effect and mass transfer taken into account. A similarity transform reduces the Navier-Stokes, energy, Ohm law, and mass-transfer equations to a system of nonlinear ordinary differential equations. The governing equations are solved analytically using an analytical method for solving nonlinear problems, namely, the homotopy analysis method. The results are compared with the results of a promising numerical method of differential quadrature developed by the authors. It is shown that there is very good agreement between analytical results and those obtained by the differential quadrature method. The differential quadrature method was validated, and the effects of non-dimensional parameters on the velocity, temperature and concentration profiles were studied.

Series solution for heat transfer of continuous stretching sheet immersed in a micropolar fluid in the existence of radiation

Purpose – The purpose of this paper is to study a two‐dimensional steady convective flow of a micropolar fluid over a stretching sheet in the presence of radiation with constant temperature.Design/methodology/approach – The corresponding momentum, microrotation and energy equations are analytically solved using homotopy analysis method (HAM).Findings – To validate the method, investigate the accuracy and convergence of the results, a comparison with existing numerical and experimental results is done for several cases. Finally, by using the obtained analytical solution, for the skin‐friction coefficient and the local Nusselt number as well as the temperature, velocity and angular velocity, profiles are obtained for different values of the constant parameters, such as Prandtl number, material, boundary and radiation parameter.Originality/value – In this paper, a series solution is presented for the first time.

On Approximate Analytical Solutions of Nonlinear Vibrations of Inextensible Beams using Parameter-Expansion Method

In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which is valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed.

Large deflection analysis of cantilever beam under end point and distributed loads

Although the deflection of beams has been studied for decades, the solutions were either linearized (i.e. small deflection) or based on elliptic integrals or functions (large deflection). The latter one includes the geometric nonlinearity but calculation of the deflection along the beam length requires numerical solution of simultaneous equations which is a significant drawback for optimization or reliability analysis. This paper is motivated to overcome these shortcomings by presenting an analytical solution for the large deflection analysis of a cantilever beam under free end point and uniform distributed loads. Direct nonlinear solution by use of homotopy analysis method was implemented to drive the semi-exact solution of trajectory position of any point along the beam length. For the purpose of comparison, the deflections were calculated and compared to those of finite element method which was taken as reference. It was found that the proposed solution is very accurate, efficient, and convenient for the discussed problem and can be applied to a large class of practical problems.

Application of the homotopy analysis method to determine the analytical limit state functions and reliability index for large deflection of a cantilever beam subjected to static co-planar loading

In this paper, the Homotopy Analysis Method (HAM) is applied to obtain the limit state function, probability of failure and reliability index based on all stochastic and deterministic variables for a cantilever beam subjected to co-planar loading for the first time. First, it is established that a few iterations in the series expansion are sufficient to obtain highly accurate results and a substantial convergence region. After showing the effectiveness of HAM, two limit state functions are introduced as the maximum deflection in the y direction and maximum allowable stress, respectively. Then the first order reliability method (FORM) is employed to obtain reliability index, and omission sensitivity factor analytically. It is shown that HAM is a promising tool to obtain limit state function, probability of failure and reliability index analytically for nonlinear problems. Finally, a sensitivity analysis is done to show that which parameters could be considered deterministic or stochastic variables.

A Closed Form Solution for Nonlinear Oscillators Frequencies Using Amplitude-Frequency Formulation

Many nonlinear systems in industry including oscillators can be simulated as a mass-spring system. In reality, all kinds of oscillators are nonlinear due to the nonlinear nature of springs. Due to this nonlinearity, most of the studies on oscillation systems are numerically carried out while an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude-Frequency Formulation (AFF) approach is applied to analyze some periodic problems arising in classical dynamics. Results are compared with another approximate analytical technique called Energy Balance Method developed by the authors (EBM) and also numerical solutions. Close agreement of the obtained results reveal the accuracy of the employed method for several practical problems in engineering.

HAM and DQM solutions for slip flow over a flat plate in the presence of constant heat flux

Abstract In this paper, an analytical solution for boundary layer flow over a flat plate with slip flow and constant heat flux surface condition has been presented for the first time. The Navier–Stokes and energy equations are reduced by a similarity transform in order for a set of nonlinear ordinary differential equations to be formed. Then, governing equations will be solved analytically by using a kind of analytic technique for nonlinear problems which has been named the homotopy analysis method (HAM). The obtained results of this study have been compared with the results of differential quadrature method (DQM) as a promising numerical method. Very good agreement has been shown between analytical results and those obtained by DQ. Finally, effects of the Prandtl number and rarefaction parameter K on velocity and temperature profiles are investigated.

Effects of using smart fluid in lubrication on skirt‐liner friction

Purpose – The purpose of this paper is to present, for the first time, a mathematical model for a piston skirt in mixed lubrication with respect to applying a smart fluid in lubrication. In this way, the smart fluid, as a lubricant with controlled variable viscosity, is proposed and applied to minimize the power loss in the interaction between liner and skirt.Design/methodology/approach – Based on signal processing, the relationships between viscosity of lubricant and the friction loss, the hydrodynamic and contact friction force consequently are found, as part of an effective approach to acquire the function of variable viscosity.Findings – It is shown that hydrodynamics and contact friction forces can be controlled and minimized by using the variable viscosity signal with the optimized viscosity signal technique.Originality/value – In this paper, a mathematical model for a piston skirt in mixed lubrication with respect to applying a smart fluid in lubrication is presented for the first time.