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Application of elastically supported single-walled carbon nanotubes for sensing arbitrarily attached nano-objects
, Article Current Applied Physics ; Volume 13, Issue 1 , 2013 , Pages 107-120 ; 15671739 (ISSN) ; Ghaffari, H ; Mehri, B ; Sharif University of Technology
Abstract
The potential application of SWCNTs as mass nanosensors is examined for a wide range of boundary conditions. The SWCNT is modeled via nonlocal Rayleigh, Timoshenko, and higher-order beam theories. The added nano-objects are considered as rigid solids, which are attached to the SWCNT. The mass weight and rotary inertial effects of such nanoparticles are appropriately incorporated into the nonlocal equations of motion of each model. The discrete governing equation pertinent to each model is obtained using an effective meshless technique. The key factor in design of a mass nanosensor is to determine the amount of frequency shift due to the added nanoparticles. Through an inclusive parametric...
Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method
, Article Acta Mechanica Sinica/Lixue Xuebao ; Volume 26, Issue 5 , October , 2010 , Pages 721-733 ; 05677718 (ISSN) ; Nikkhoo, A ; Mehri, B ; Sharif University of Technology
Abstract
Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method (GMLSM) and then, discrete equations of motion based on Lagrange's equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between...
Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories
, Article Journal of Sound and Vibration ; Volume 329, Issue 11 , May , 2010 , Pages 2241-2264 ; 0022460X (ISSN) ; Mehri, B ; Sharif University of Technology
2010
Abstract
Dynamic analysis of nanotube structures under excitation of a moving nanoparticle is carried out using nonlocal continuum theory of Eringen. To this end, the nanotube structure is modeled by an equivalent continuum structure (ECS) according to the nonlocal Euler-Bernoulli, Timoshenko and higher order beam theories. The nondimensional equations of motion of the nonlocal beams acted upon by a moving nanoparticle are then established. Analytical solutions of the problem are presented for simply supported boundary conditions. The explicit expressions of the critical velocities of the nonlocal beams are derived. Furthermore, the capabilities of various nonlocal beam models in predicting the...
Prediction capabilities of classical and shear deformable beam models excited by a moving mass
, Article Journal of Sound and Vibration ; Volume 320, Issue 3 , 2009 , Pages 632-648 ; 0022460X (ISSN) ; Nikkhoo, A ; Mehri, B ; Sharif University of Technology
2009
Abstract
In this paper, a comprehensive assessment of design parameters for various beam theories subjected to a moving mass is investigated under different boundary conditions. The design parameters are adopted as the maximum dynamic deflection and bending moment of the beam. To this end, discrete equations of motion for classical Euler-Bernoulli, Timoshenko and higher-order beams under a moving mass are derived based on Hamilton's principle. The reproducing kernel particle method (RKPM) and extended Newmark-β method are utilized for spatial and time discretization of the problem, correspondingly. The design parameter spectra in terms of the beam slenderness, mass weight and velocity of the moving...
Parametric analyses of multispan viscoelastic shear deformable beams under excitation of a moving mass
, Article Journal of Vibration and Acoustics, Transactions of the ASME ; Volume 131, Issue 5 , 2009 , Pages 0510091-05100912 ; 10489002 (ISSN) ; Nikkhoo, A ; Mehri, B ; Sharif University of Technology
2009
Abstract
This paper presents a numerical parametric study on design parameters of multispan viscoelastic shear deformable beams subjected to a moving mass via generalized moving least squares method (GMLSM). For utilizing Lagrange's equations, the unknown parameters of the problem are stated in terms of GMLSM shape functions and the generalized Newmark-β scheme is applied for solving the discrete equations of motion in time domain. The effects of moving mass weight and velocity, material relaxation rate, slenderness, and span number of the beam on the design parameters and possibility of mass separation from the base beam are scrutinized in some detail. The results reveal that for low values of beam...
Dynamic response of euler-Bernoulli, Timoshenko and higher-Order beams under a moving mass via RKPM
, Article 7th European Conference on Structural Dynamics, EURODYN 2008, 7 July 2008 through 9 July 2008 ; 2008 ; 9780854328826 (ISBN) ; Kiani, K ; Mehri, B ; Sharif University of Technology
University of Southampton, Institute of Sound Vibration and Research
2008
Abstract
Discrete motion equations of an Euler-Bernoulli, Timoshenko and higher-order beams under a moving mass are derived for different boundary conditions. To this end, the reproducing kernel particle method (RKPM) has been utilized for spatial discretization, beside the extension of Newmark-β method for time discretization of the beams motion equations. The effects of significant parameters such as the beam's slenderness and velocity of the moving mass on the maximum deflection and bending moment of different beams are studied in some details. The results indicate the existence of a critical beam's slenderness mostly as a function of beam's boundary conditions, in which for slenderness lower than...
On the existence of positive solution for second-order multi-points boundary value problems
, Article Journal of Computational and Applied Mathematics ; Volume 193, Issue 1 , 2006 , Pages 269-276 ; 03770427 (ISSN) ; Mehri, B ; Sharif University of Technology
2006
Abstract
Here we are concerned with the existence of positive solution for autonomous and nonautonomous second-order systems with multi-points boundary conditions. For nonautonomous systems we use the Schauder's fixed point theorem in a suitable Banach space, while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree. In order to verify the obtained results, we have considered some definite systems to verify the results numerically. © 2005 Elsevier B.V. All rights reserved
The best approximation of some rational functions in uniform norm
, Article Applied Numerical Mathematics ; Volume 55, Issue 2 , 2005 , Pages 204-214 ; 01689274 (ISSN) ; Mehri, B ; Sharif University of Technology
2005
Abstract
Here we are concerned with the best approximation by polynomials to rational functions in the uniform norm. We give some new theorems about the best approximation of 1/(1+x) and 1/(x-a) where a>1. Finally we extend this problem to that of computing the best approximation of the Chebyshev expansion in uniform norm and give some results and conjectures about this. © 2005 IMACS. Published by Elsevier B.V. All rights reserved
A non-homogeneous Hill's equation
, Article Applied Mathematics and Computation ; Volume 167, Issue 1 , 2005 , Pages 68-75 ; 00963003 (ISSN) ; Mehri, B ; Sharif University of Technology
2005
Abstract
The existence of periodic solutions for a forced Hill's equation is proved. The proof is then extended to the case of a non-homogeneous matrix valued Hill's equation. Under the stated conditions, using Lyapunov's criteria [Proc. AMS 13 (1962) 601; Hill's Equation, Interscience Publishers, New York, 1966] some results on the stability oh Hill's equation are obtained. © 2004 Elsevier Inc. All rights reserved
Response of a suspended cable to narrow-band random excitation with peaked P.S.D
, Article Mathematical and Computer Modelling ; Volume 41, Issue 11-12 , 2005 , Pages 1203-1212 ; 08957177 (ISSN) ; Mehri, B ; Younesian, D ; Sharif University of Technology
2005
Abstract
The response of a suspended cables subjected to narrow-band random excitations with two types of peaked P.S.D. is formulated and analyzed. Banach fixed-point theorem is used for eigenfunction analysis of the differential-integral equations of motion for the first time in this paper. Fredholm approach also is used in the free vibration analysis of the suspended cable and then using Galerkin mode approximation method, power spectral density, and root mean square of the response are computed for two practical types of excitation. All of the calculated results converted to dimensionless quantities make their usage easier in vibration analysis of some practical cases such as vibration of moving...
In-plane and out-of-plane waves in nanoplates immersed in bidirectional magnetic fields
, Article Structural Engineering and Mechanics ; Volume 61, Issue 1 , 2017 , Pages 65-76 ; 12254568 (ISSN) ; Gharebaghi, S. A ; Mehri, B ; Sharif University of Technology
Techno Press
2017
Abstract
Prediction of the characteristics of both in-plane and out-of-plane elastic waves within conducting nanoplates in the presence of bidirectionally in-plane magnetic fields is of interest. Using Lorentz's formulas and nonlocal continuum theory of Eringen, the nonlocal elastic version of the equations of motion is obtained. The frequencies as well as the corresponding phase and group velocities pertinent to the in-plane and out-of-plane waves are analytically evaluated. The roles of the strength of in-plane magnetic field, wavenumber, wave direction, nanoplate's thickness, and small-scale parameter on characteristics of waves are discussed. The obtained results show that the in-plane...
Dynamics of nonlinear plates under moving loads
, Article Mechanics Research Communications ; Volume 28, Issue 4 , 2001 , Pages 453-461 ; 00936413 (ISSN) ; Rofooei, F. R ; Mehri, B ; Sharif University of Technology
2001
Abstract
The governing differential equation of the Duffing's oscillator with time varying coefficients is addressed. It is shown that the response of a flexible nonlinear plate can be simulated by such equation. Existence of the periodic behavior that is the most important regular solution is illustrated using Banach's fixed-point theorem
A new orthonormal polynomial series expansion method in vibration analysis of thin beams with non-uniform thickness
, Article Applied Mathematical Modelling ; Volume 37, Issue 18-19 , 2013 , Pages 8543-8556 ; 0307904X (ISSN) ; Nikkhoo, A ; Vaseghi Amiri, J ; Mehri, B ; Sharif University of Technology
2013
Abstract
In this article, OPSEM (Orthonormal Polynomial Series Expansion Method) is developed as a new computational approach for the evaluation of thin beams of variable thickness transverse vibration. Capability of the OPSEM in assessing the free vibration frequencies and mode shapes of an Euler-Bernoulli beam with varying thickness is discussed. Multispan continuous beams with various classical boundary conditions are included. Contribution of BOPs (Basic Orthonormal Polynomials) in capturing the beam vibrations is also illustrated in numerical examples to give a quantitative measure of convergence rate. Furthermore, OPSEM is adopted for the forced vibration of a thin beam caused by a moving mass....
Green's function for uniform Euler-Bernoulli beams at resonant condition: Introduction of Fredholm Alternative Theorem
, Article Applied Mathematical Modelling ; Volume 39, Issue 12 , 2015 , Pages 3366-3379 ; 0307904X (ISSN) ; Aftabi Sani, A ; Mehri, B ; Mofid, M ; Sharif University of Technology
Elsevier Inc
2015
Abstract
This paper deals with the dynamic analysis of Euler-Bernoulli beams at the resonant condition. The governing partial differential equation of the problem is converted into an ordinary differential equation by applying the well-known Fourier transform. The solution develops a Green's function method which involves establishing the Green's function of the problem, applying the pertinent boundary conditions of the beam. Due to the special conditions of the resonant situation, a significant obstacle arises during the derivation of the Green's function. In order to overcome this hurdle, however, the Fredholm Alternative Theorem is employed; and it is shown that the modified Green's function of...
Periodicity in the response of nonlinear plate, under moving mass
, Article Thin-Walled Structures ; Volume 40, Issue 3 , 2002 , Pages 283-295 ; 02638231 (ISSN) ; Rahimzadeh Rofooei, F ; Mofid, M ; Mehri, B ; Sharif University of Technology
2002
Abstract
The dynamics of nonlinear thin plates under influence of relatively heavy moving masses is considered. By expansion of the solution as a series of mode functions, the governing equations of motion are reduced to an ordinary differential equation for time development of vibration amplitude, which is Duffing's oscillator with time varying coefficients. Through the application of Banach's fixed-point theorem, the periodic solutions are predicted. The method presented in this paper is general so that the response of plate to moving force systems can also be considered. © 2002 Published by Elsevier Science Ltd