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#### 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...

#### On free vibration of functionally graded euler-bernoulli beam models based on the non-local theory

, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) ; Volume 12 , 2012 , Pages 169-173 ; 9780791845288 (ISBN) ; Ahmadian, M. T ; Sharif University of Technology
2012

Abstract

In this paper, the governing equations and boundary conditions of a functionally graded Euler-Bernoulli beam are developed based on the non-local theory of elasticity. Afterward, the free vibration is investigated and the effects of the axial load, the non-local parameter and the power index on the natural frequency of a hinged-hinged beam is assessed. The results indicate that the non-local parameter has a decreasing effect on the frequency while the power index has an increasing effect. It is also noted that the effect of the axial load is increasing too

#### An analytical solution for shape-memory-polymer Euler-Bernoulli beams under bending

, Article International Journal of Mechanical Sciences ; Vol. 84, issue , July , 2014 , p. 84-90 ; Mohammadi, H ; Naghdabadi, R ; Sharif University of Technology
Abstract

The purpose of this paper is to present efficient and accurate analytical expressions for deflection of a shape memory polymer (SMP) beam employing Euler-Bernoulli beam theory in a thermomechanical SMP cycle. Material behavior is considered using a recently 3D thermodynamically consistent constitutive model available in literature. In different steps of an SMP thermomechanical cycle, closed form expressions for internal variables variations, stresses and beam curvature distribution are presented. We show that during the cooling process, stored strains evolve to fix the temporary shape and then during the heating process they relax to recover the permanent shape. Effects of applying external...

#### A strain gradient functionally graded Euler-Bernoulli beam formulation

, Article International Journal of Engineering Science ; Volume 52 , 2012 , Pages 65-76 ; 00207225 (ISSN) ; Rahaeifard, M ; Tajalli, S. A ; Ahmadian, M. T ; Sharif University of Technology
2012

Abstract

A size-dependent functionally graded Euler-Bernoulli beam model is developed based on the strain gradient theory, a non-classical theory capable of capturing the size-effect in micro-scaled structures. The governing equation and both classical and non-classical boundary conditions are obtained using variational approach. To develop the new model, the previously used simplifying assumption which considered the length scale parameter to be constant through the thickness is avoided in this work. As a consequence, equivalent length scale parameters are introduced for functionally graded microbeams as functions of the constituents' length scale parameters. Moreover, a generally valid closed-form...

#### Continuum models calibrated with atomistic simulations for the transverse vibrations of silicon nanowires

, Article International Journal of Engineering Science ; Volume 100 , 2016 , Pages 8-24 ; 00207225 (ISSN) ; Afsharmanesh, B ; Tajaddodianfar, F ; Sharif University of Technology
Elsevier Ltd
2016

Abstract

We have conducted Molecular Dynamics (MD) simulations with the Environment-Dependent Interatomic Potential (EDIP) to obtain the natural frequency of ultra-thin Silicon Nanowires (SiNWs) with various crystallographic structures, boundary conditions and dimensions. As expected, results show that the mechanical properties of SiNWs are size-/orientation-dependent. The observed phenomena are ascribed to the surface effects which become dominant due to the large surface-to-volume number of atoms at the investigated range of dimensions. Due to their accuracy, atomistic simulations are widely accepted for the investigations of such nano-scaled systems; however, they suffer from high computational...

#### Free vibration analysis of a beam with an intermediate sliding connection joined by a mass-spring system

, Article JVC/Journal of Vibration and Control ; Volume 22, Issue 4 , 2016 , Pages 955-964 ; 10775463 (ISSN) ; Aftabi Sani, A ; Mofid, M ; Sharif University of Technology
SAGE Publications Inc
2016

Abstract

In the free vibration analysis of beams, the inclusion of an intermediate sliding connection with an attached mass-spring system has not been yet treated. The present paper studies the free vibrations of uniform Euler-Bernoulli beams with an intermediate sliding connection and joined by a mass-spring system. Two different types of beams are considered. The Type 1 is attached with a single-degree-of-freedom mass-spring system and the Type 2 is attached with a two-degree-of-freedom mass-spring system. The ends of both beams are elastically restrained against rotation and translation. First, the eigenvalue problems including differential equations and boundary conditions are introduced. Then,...

#### Mathematical modelingof deflection of a beam: a finite element approach

, Article 2nd International Conference on Environmental and Computer Science, ICECS 20092009 ; Article number 5383533 , 2009 , Pages 161-164 ; 9780769539379 (ISBN) ; Durali, L ; Zareie, S ; International Association of Computer Science; and Information Technology (IACSIT) ; Parvari Rad, F ; Sharif University of Technology
Abstract

Introducing a suitable model for a structure to understand its behavior under different conditions of loading is very important. Mathematical modeling is the simulation of a physical structure or physical process by means of suitable analytical or numerical construct. One of suitable methods for finding deflection of a beam under different forms of loading is Finite Element Method (FEM). In this paper we find deflection of a beam using FEM based on Euler-Bernoulli and Timoshenko theory. © 2009 IEEE

#### A tunable vibration absorber design to suppress chatter in boring manufacturing process

, Article ASME International Mechanical Engineering Congress and Exposition, IMECE 2007, Seattle, WA, 11 November 2007 through 15 November 2007 ; Volume 9 PART C , 2008 , Pages 1943-1950 ; 0791843033 (ISBN); 9780791843031 (ISBN) ; Bakhtiari Nejad, F ; Movahhedi, M. R ; Sharif University of Technology
2008

Abstract

Dynamic vibration absorbers are used to reduce the undesirable vibrations in many applications such as electrical transmission lines, helicopters, gas turbines, engines, bridges and etc. One type of these absorbers is tunable vibration absorber (TVA) which can act as a semi-active controller. In this paper, by applying a (TVA), chatter vibration is suppressed during boring process in which boring bar is modeled as a cantilever Euler-Bernoulli beam. The optimum specifications of absorber such as spring stiffness, absorber mass and its position can be determined by developing an algorithm based upon mode summation method. Finally, using the SIMULINK Toolbox of MATLAB, the analog simulated...

#### Dynamic model of a flying manipulator with two highly flexible links

, Article Applied Mathematical Modelling ; Volume 32, Issue 10 , 2008 , Pages 2117-2132 ; 0307904X (ISSN) ; Khorsandijou, S. M ; Sharif University of Technology
2008

Abstract

Nonlinear dynamic model of a flying manipulator with two revolute joints and two highly flexible links is obtained using Hamilton's principle. Flying base of the manipulator is a rigid body. Stress is treated three dimensionally in the isotropic linearly-elastic links, but the in-plane and out-of-plane warpings of the links' cross-sections are neglected. Although the links' cross-sections undergo negligible elastic orientation, their models are more accurate than a nonlinear 3D Euler-Bernoulli beam. Tension, compression, twisting and spatial deflections of each link are coupled to each other by some nonlinear terms including two new ones. In the issue of flying flexible-link manipulators new...

#### 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...

#### Dynamic behavior and modal control of beams under moving mass

, Article Journal of Sound and Vibration ; Volume 306, Issue 3-5 , 2007 , Pages 712-724 ; 0022460X (ISSN) ; Rahimzadeh Rofooei, F ; Shadnam, M. R ; Sharif University of Technology
Academic Press
2007

Abstract

The constitutive equation of an Euler-Bernoulli beam under the excitation of moving mass is considered. The dynamics of the uncontrolled system is governed by a linear, self-adjoint partial differential equation. A Dirac-delta function is used to describe the position of the moving mass along the beam and its inertial effects. An approximate formulation to the problem is obtained by limiting the inertial effect of the moving mass merely to the vertical component of acceleration. Having defined a "critical velocity" in terms of the fundamental period and span of the beam, it is shown that for smaller velocities, the approximate and exact approaches to the problem almost coincide. Since, the...

#### Strain gradient beam element

, Article Finite Elements in Analysis and Design ; Volume 68 , June , 2013 , Pages 63-75 ; 0168874X (ISSN) ; Asghari, M ; Ahmadian, M. T ; Sharif University of Technology
2013

Abstract

The classical continuum theory is neither able to accurately model the mechanical behavior of micro/nano-scale structures nor capable of justifying the size-dependent behavior observed in these structures; so the non-classical continuum theories such as the strain gradient theory have been emerged and developed. In order to enable the finite element method (FEM) to more accurately deal with the problems in micro/nano-scale structures, a size-dependent Euler-Bernoulli beam element is developed based on the strain gradient theory. Compared to the classical Euler-Bernoulli beam element, the nodal displacement vector of the new Euler-Bernoulli beam element has an additional component, i.e. the...

#### Dynamics of bistable initially curved shallow microbeams: Effects of the electrostatic fringing fields

, Article IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM ; July , 2014 , p. 1279-1283 ; Yazdiو M. H ; Pishkenariو H. N ; Sharif University of Technology
Abstract

Effects of fringing electrostatic fields on the behavior of a double clamped initially curved microbeam are investigated. Galerkin's decomposition method is applied on the governing Euler-Bernoulli equation with distributed electrostatic force to obtain the lumped-parameter model of the system. The resulting single degree of freedom model is obtained with the Palmer's formula as a model for the fringing field effects. To derive an applied form of the fringing field effect in lumped model, we have used Genetic Algorithms as an optimization method. Then using the lumped model, we have investigated the system nonlinear dynamics. Comparison of the obtained bifurcation diagrams with the...

#### Vibration of Euler Bernoulli and Timoshenko beams in large overall motion on flying support using finite element method

, Article Scientia Iranica ; Volume 19, Issue 4 , 2012 , Pages 1105-1116 ; 10263098 (ISSN) ; Kakavand, F ; Sharif University of Technology
Elsevier
2012

Abstract

The equations of motion for a beam on a flying support for EulerBernoulli and Timoshenko Beam Theories is derived. In modeling and attempting to have an accurate model at high speeds, a stretch variable instead of conventional axial deformation is used. For a planar rotating beam and a spatial rotating beam, equations of motion are lineralized and verified. Finite element and Newmark direct integration methods are employed for numerical simulations

#### Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains

, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Volume 226, Issue 5 , 2012 , Pages 1225-1236 ; 09544062 (ISSN) ; Zohoor, H ; Yoon, Y. J ; Sharif University of Technology
2012

Abstract

Using Hamilton's principle, exact equations of motion for non-linear planar and spatial Euler-Bernoulli beams are derived. In the existing non-linear Euler-Bernoulli beam formulations, some elastic terms are dropped by differentiation from the incomplete Green-Lagrange strain tensor followed by negligible elastic deformations of cross-sectional frame. On the other hand, in this article, the exact strain field concerning considerable elastic deformations of cross-sectional frame is used as a source in differentiations. As a result, the achieved closed-form equations are exact and more accurate than formerly reported equations in the literature. Moreover, the applicable dynamic model of...

#### Vibration of a microbeam under ultra-short-pulsed laser excitation considering momentum and heating effect

, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE), 12 November 2010 through 18 November 2010, Vancouver, BC ; Volume 10 , 2010 , Pages 195-200 ; 9780791844472 (ISBN) ; Vaghasloo, Y. A ; Ahmadian, M. T ; Moheimani, R ; Sharif University of Technology
2010

Abstract

In this study, vibration of a microbeam excited by an ultrashort- pulsed laser considering the momentum and heating effect of the laser beam is investigated. When the laser impacts the microbeam, portion of the photons is absorbed by the beam and their energy will be transformed into heat while the others are reflected. The momentum change of the absorbed and reflected laser photons is considered and modeled as a distributed force on the beam. The absorbed thermal energy yields non-uniform thermal stress causing the beam to vibrate. According to short duration of laser pulse, the non-Fourier conduction equation which takes into account the finite propagation speed of thermal energy, is...

#### Enhanced nonlinear 3D Euler-Bernoulli beam with flying support

, Article Nonlinear Dynamics ; Volume 51, Issue 1-2 , 2008 , Pages 217-230 ; 0924090X (ISSN) ; Khorsandijou, S. M ; Sharif University of Technology
2008

Abstract

Using Hamilton's principle the coupled nonlinear partial differential motion equations of a flying 3D Euler-Bernoulli beam are derived. Stress is treated three dimensionally regardless of in-plane and out-of-plane warpings of cross-section. Tension, compression, twisting, and spatial deflections are nonlinearly coupled to each other. The flying support of the beam has three translational and three rotational degrees of freedom. The beam is made of a linearly elastic isotropic material and is dynamically modeled much more accurately than a nonlinear 3D Euler-Bernoulli beam. The accuracy is caused by two new elastic terms that are lost in the conventional nonlinear 3D Euler-Bernoulli beam...

#### On the resolution of existing discontinuities in the dynamic responses of an Euler-Bernoulli beam subjected to the moving mass

, Article 8th Biennial ASME Conference on Engineering Systems Design and Analysis, ESDA2006, Torino, 4 July 2006 through 7 July 2006 ; Volume 2006 , 2006 ; 0791837793 (ISBN); 9780791837795 (ISBN) ; Saeedi, K ; Sharif University of Technology
American Society of Mechanical Engineers
2006

Abstract

The dynamic response of a one-dimensional distributed parameter system subjected to a moving mass with constant speed is investigated. An Euler-Bernoulli beam with the uniform cross-section and finite length with specified boundary support conditions is assumed. In this paper, rather a new method based on the time dependent series expansion for calculating the bending moment and the shear force due to motion of the mass is suggested. Governing differential equations of the motion are derived and solved. The accuracy of the numerical results primarily is verified and further the rapid convergence of this new technique was illustrated over other existing methods. Finally, it is shown that a...

#### On the stability of rotating pipes conveying fluid in annular liquid medium

, Article Journal of Sound and Vibration ; Volume 494 , 2021 ; 0022460X (ISSN) ; Dehghani Firouz-abadi, R ; Rahmanian, M ; Sharif University of Technology
Academic Press
2021

Abstract

This study provides a stability analysis of flexible rotating pipes taking into account the simultaneous effects of internal and external fluid loading. Using the Euler-Bernoulli beam assumptions, governing equations for flexural vibrations of rotating pipes are obtained. The internal flow characteristics and the double gyroscopic effect are taken into account when deriving the structural equations coupled with the internal flow. External fluid loading is determined by a special linearization of the Navier-Stokes equations. Considering the circular wall of the pipe as an impermeable boundary to the flow, fluid-induced forcing functions are obtained and then applied to the structural...

#### On the stability of rotating pipes conveying fluid in annular liquid medium

, Article Journal of Sound and Vibration ; Volume 494 , 2021 ; 0022460X (ISSN) ; Dehghani Firouz-abadi, R ; Rahmanian, M ; Sharif University of Technology
Academic Press
2021

Abstract

This study provides a stability analysis of flexible rotating pipes taking into account the simultaneous effects of internal and external fluid loading. Using the Euler-Bernoulli beam assumptions, governing equations for flexural vibrations of rotating pipes are obtained. The internal flow characteristics and the double gyroscopic effect are taken into account when deriving the structural equations coupled with the internal flow. External fluid loading is determined by a special linearization of the Navier-Stokes equations. Considering the circular wall of the pipe as an impermeable boundary to the flow, fluid-induced forcing functions are obtained and then applied to the structural...