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timoshenko-beam-theory
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Analytical determination of shear correction factor for Timoshenko beam model
, Article Steel and Composite Structures ; Volume 29, Issue 4 , 2018 , Pages 483-491 ; 12299367 (ISSN) ; Faghidian, S. A ; Shodja, H. M ; Sharif University of Technology
Techno Press
2018
Abstract
Timoshenko beam model is widely exploited in the literature to examine the mechanical behavior of stubby beam-like components. Timoshenko beam theory is well-known to require the shear correction factor in order to recognize the non-uniform shear distribution at a section. While a variety of shear correction factors are appeared in the literature so far, there is still no consensus on the most appropriate form of the shear correction factor. The Saint-Venant's flexure problem is first revisited in the frame work of the classical theory of elasticity and a highly accurate approximate closed-form solution is presented employing the extended Kantorovich method. The resulted approximate solution...
Free vibration analysis of cross-ply layered composite beams with finite length on elastic foundation
, Article International Journal of Computational Methods ; Volume 5, Issue 1 , 2008 , Pages 21-36 ; 02198762 (ISSN) ; Kargarnovin, M. H ; Ahmadian, M. T ; Sharif University of Technology
2008
Abstract
In this paper, free vibration analysis of cross-ply layered composite beams (LCB) with finite length and rectangular cross-section rested on an elastic foundation is investigated by finite element method. Based on the Timoshenko beam theory which includes the shear deformation and rotary inertia, the stiffness and mass matrices of a LCB are obtained using the energy method. Then, the natural frequencies are calculated by employing eigenvalue technique. The obtained results are verified against existing data in the literatures for a LCB with no foundation and uniform cross-section. Good agreements are observed between these cases. In the same way, the natural frequencies of a specific case,...
A study of gyroscopic effects on stability of high speed milling
, Article 2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005, Orlando, FL, 5 November 2005 through 11 November 2005 ; Volume 16-1 , 2005 , Pages 659-665 ; 0791842231 (ISBN); 9780791842232 (ISBN); 0791842231 (ISBN); 9780791842232 (ISBN) ; Mosaddegh, P ; Sharif University of Technology
2005
Abstract
Dynamic stability of machine tools during operations is dependent on many parameters including the spindle speed. In high and ultra high speed machining, the gyroscopic on the spindle dynamics becomes more pronounced and can affect the borders of stability of the rotating system. In this paper, a finite element based model of spindle, tool holder and cutting tool based on Timoshenko beam theory is used to obtain the dynamic response of the system when gyroscopic terms are included. An iterative scheme is used to update the speed dependent frequency response of the system for obtaining system stability characteristics. It is shown that the gyroscopic effect reduces the critical depth of cut...
Development, modeling and deflection analysis of hybrid micro actuator with integrated thermal and piezoelectric actuation
, Article Meccanica ; Volume 48, Issue 5 , 2013 , Pages 1081-1091 ; 00256455 (ISSN) ; Zohoor, H ; Kargarnovin, M. H ; Sharif University of Technology
2013
Abstract
Micro actuators are irreplaceable part of motion control in minimized systems. The current study presents an analytical model for a new Hybrid Thermo Piezoelectric micro actuator based on the combination of piezoelectric and thermal actuation mechanisms. The micro actuator structure is a double PZT cantilever beam consisting of two arms with different lengths. The presented micro actuator uses the structure of electrothermal micro actuator in which polysilicon material is replaced by PZT. Also the voltage and poling directions are considered in the lengthwise of PZT beams. As a result, the piezoelectric actuation mechanism is based on d33 strain coefficient. The tip deflection of micro...
Dynamic error analysis of gantry type coordinate measuring machines
, Article Scientia Iranica ; Volume 14, Issue 3 , 2007 , Pages 278-290 ; 10263098 (ISSN) ; Vossoughi, G. R ; Ramezani, S ; Sharif University of Technology
Sharif University of Technology
2007
Abstract
Coordinate Measuring Machines (CMMs) are designed for precision inspection of complex industrial products. The mechanical accuracy of CMMs depends on both static and dynamic sources of error. In automated CMMs, one of the dynamic error sources is vibration of the probe, due to inertia forces resulting from parts acceleration and deceleration. Modeling of a gantry type CMM, based on the Timoshenko beam theory with moving mass effects, is developed and the dynamic errors of the probe resulting from the acceleration and deceleration of moving parts, are calculated. Findings from analytical solution and dynamic modeling software indicate high accuracy and good agreement between the results. ©...
Size dependent vibrations of micro-end mill incorporating strain gradient elasticity theory
, Article Journal of Sound and Vibration ; Volume 332, Issue 15 , 2013 , Pages 3922-3944 ; 0022460X (ISSN) ; Movahhedy, M. R ; Akbari, J ; Sharif University of Technology
2013
Abstract
In this paper, a size-dependent formulation is presented for vibration analysis of micro-end mill tool. The formulation is developed based on the strain gradient elasticity theory in order to enhance the modeling capability of micro-size structures. Due to stubby geometry of micro-tool, the shear deformation and rotary inertia effects are considered in the derivation of equations. Hence, based on the strain gradient Timoshenko beam theory, the extended Hamilton's principle is used to formulate a detailed dynamical model of the rotating micro-tool. The dynamical model includes a set of partial differential equations with gyroscopic coupling produced due to the spindle rotation. The governing...
Implementation of microplane model into three-dimensional beam element for shape memory alloys
, Article International Journal of Applied Mechanics ; Volume 7, Issue 6 , December , 2015 ; 17588251 (ISSN) ; Arghavani, J ; Naghdabadi, R ; Sohrabpour, S ; Sharif University of Technology
World Scientific Publishing Co. Pte Ltd
2015
Abstract
In this study, a three-dimensional (3D) beam element based on Timoshenko beam theory is introduced for shape memory alloys (SMAs). Employing the microplane approach, we use a 3D SMA constitutive model extended from a 1D model proposed by Brinson. The SMA model is implemented into a user-defined subroutine (UMAT) in the nonlinear finite element software ABAQUS/Standard. Results of numerical examples show reasonable agreement with experimental data in proportional and non-proportional loadings. Furthermore, several applications (staple, spring, structure) are simulated and the results are compared with those of continuum elements. According to the results, the 3D SMA beam element can be used...
Effect of size dependency on in-plane vibration of circular micro-rings
, Article Scientia Iranica ; Volume 24, Issue 4 , 2017 , Pages 1996-2008 ; 10263098 (ISSN) ; Ahmadian, M. T ; Rahaeifard, M ; Sharif University of Technology
Sharif University of Technology
2017
Abstract
In this paper, based on the modified couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The findings are compared with classical beam...
Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam
, Article Applied Physics A: Materials Science and Processing ; Volume 123, Issue 1 , 2017 ; 09478396 (ISSN) ; Mirjavadi, S. S ; Shafiei, N ; Hamouda, A. M. S ; Sharif University of Technology
Springer Verlag
2017
Abstract
The free vibration analysis of rotating axially functionally graded nanobeams under an in-plane nonlinear thermal loading is provided for the first time in this paper. The formulations are based on Timoshenko beam theory through Hamilton’s principle. The small-scale effect has been considered using the nonlocal Eringen’s elasticity theory. Then, the governing equations are solved by generalized differential quadrature method. It is supposed that the thermal distribution is considered as nonlinear, material properties are temperature dependent, and the power-law form is the basis of the variation of the material properties through the axial of beam. Free vibration frequencies obtained are...
Global sensitivity analysis of backside coating parameters on dynamic response of AM-AFM
, Article Mechanika ; Volume 23, Issue 2 , 2017 , Pages 282-290 ; 13921207 (ISSN) ; Zohoor, H ; Habibnejad Korayem, M ; Sharif University of Technology
Kauno Technologijos Universitetas
2017
Abstract
Influence of backside coating parameters on dynamic response of AM-AFM is modeled. Timoshenko based beam model is used and the general nonlinear interaction force is enclosed. The coupled ODEs of motion are achieved. The mode shapes are determined for coated cantilever and the natural frequency of each mode is validated with experimental results. It is showed a shorter cantilever with tip mass have better accuracy and inelastic and massless assumptions are not proper choice for modelling of the coating. The assumed mode method is used to determine time response of system for faraway and scanning condition of AM-AFM. Amplitude of response is calculated by FFT of time domain. Sensitivity...
Effect of axially graded constraining layer on the free vibration properties of three layered sandwich beams with magnetorheological fluid core
, Article Composite Structures ; Volume 255 , 2021 ; 02638223 (ISSN) ; Asgari, M ; Haddadpour, H ; Sharif University of Technology
Elsevier Ltd
2021
Abstract
The free linear vibration of an adaptive sandwich beam consisting of a frequency and field-dependent magnetorheological fluid core and an axially functionally graded constraining layer is investigated. The Euler-Bernoulli and Timoshenko beam theories are utilized for defining the longitudinal and lateral deformation of the sandwich beam. The Rayleigh-Ritz method is used to derive the frequency-dependent eigenvalue problem through the kinetic and strain energy expressions of the sandwich beam. In order to deal with the frequency dependency of the core, the approached complex eigenmodes method is implemented. The validity of the formulation and solution method is confirmed through comparison...
Vibration analysis of axially loaded bridges traversed by accelerating vehicles with passenger dynamics
, Article Proceedings of the 7th Biennial Conference on Engineering Systems Design and Analysis - 2004, Manchester, 19 July 2004 through 22 July 2004 ; Volume 2 , 2004 , Pages 275-280 ; 0791841731 (ISBN); 9780791841730 (ISBN) ; Mehdigholi, H ; Esmailzadeh, E ; Sharif University of Technology
2004
Abstract
An investigation into the dynamics of vehicle-passenger-structure-induced vibration of suspension bridges traversed by accelerating vehicles is carried out. The vehicle including the driver and passengers is modeled as a half-car planer model with six degrees-of-freedom. In addition, the stiffness of compliant bushings at the connecting points of the shock absorbers to the body is considered. The bridge is assumed to obey the Timoshenko beam theory with axial load and arbitrary conventional boundary conditions. The roughness of the bridge is assumed as a differentiable function of location. Due to continuously moving the location of the variable loads on the bridge, and in the presence of...
Optimal design of two-dimensional porosity distribution in shear deformable functionally graded porous beams for stability analysis
, Article Thin-Walled Structures ; Volume 120 , 2017 , Pages 81-90 ; 02638231 (ISSN) ; Arghavani, J ; Sharif University of Technology
Abstract
In the present study, considering two-dimensional porosity distribution through a functionally graded porous (FGP) beam, its optimal distributions are obtained. A multi-objective optimization problem is defined to maximize critical buckling load and minimize mass of the beam, simultaneously. To this end, Timoshenko beam theory is employed and equilibrium equations for two-dimensional functionally graded porous (2D-FGP) beam are derived. For the solution, we present generalized differential quadrature method (GDQM) and consider two symmetric boundary conditions (Clamped-Clamped and Hinged-Hinged). Solving generalized eigenvalue problem, critical buckling load for 2D-FGP beam is then obtained....
An analytical approach for the free vibration analysis of generally laminated composite beams with shear effect and rotary inertia
, Article International Journal of Mechanical Sciences ; Volume 65, Issue 1 , December , 2012 , Pages 97-104 ; 00207403 (ISSN) ; Abedi, M ; Kargarnovin, M. H ; Ahmadian, M. T ; Sharif University of Technology
2012
Abstract
In this paper, the free vibration analysis of generally laminated composite beam (LCB) based on Timoshenko beam theory are presented using the method of Lagrange multipliers where in the free vibration problem is posed as a constrained variational problem. The effect of material couplings (bending-tension, bending-twist, and tension-twist couplings) with the effects of shear deformation, rotary inertia and Poisson's effect are taken into account. Analytical expression for the natural frequencies and mode shapes are presented. The calculated natural frequencies are verified against some available results in the literature and very good agreement is observed. Furthermore, the effects of some...
Vibration analysis of a new type of compliant mechanism with flexible-link, using perturbation theory
, Article Mathematical Problems in Engineering ; Volume 2012 , February , 2012 ; 1024123X (ISSN) ; Zohoor, H ; Kargarnovin, M. H ; Sharif University of Technology
2012
Abstract
Vibration analysis of a new type of compliant parallel mechanism with flexible intermediate links is investigated. The application of the Timoshenko beam theory to the mathematical modeling of the intermediate flexible link is described, and the equations of motion of the flexible links are obtained by using Lagrange's equation of motion. The equations of motion are obtained in the form of a set of ordinary differential equations by using assumed mode method theory. The governing differential equations of motion are solved using perturbation method. The assumed mode shapes and frequencies are to be obtained based on clamped-clamped boundary conditions. Comparing perturbation method with...
Investigation of the effects of process damping on chatter instability in micro end milling
, Article Procedia CIRP ; Volume 1, Issue 1 , 2012 , Pages 156-161 ; 22128271 (ISSN) ; Movahhedy, M. R ; Akbari, J ; Sharif University of Technology
2012
Abstract
In this paper, chatter instability of micro end mill tools is studied by taking into account the process damping effect. The actual geometry of the micro tool including shank, taper part and fluted section is considered in the analysis. Timoshenko beam theory is utilized to consider the shear deformation and rotary inertia effects due to short and thick beam-type structures of each parts of the micro tool. The extended Hamilton's Principle is used to formulate a detailed dynamical model of the rotating micro end mill. The governing equations are solved by assumed mode model expansion. An exact dynamic stiffness method is developed to investigate modal characteristics of the tool including...
Nonlinear vibration of rectangular atomic force microscope cantilevers by considering the Hertzian contact theory
, Article Canadian Journal of Physics ; Volume 88, Issue 5 , 2010 , Pages 333-348 ; 00084204 (ISSN) ; Zohoor, H ; Sharif University of Technology
Abstract
The nonlinear flexural vibration for a rectangular atomic force microscope cantilever is investigated by using Timoshenko beam theory. In this paper, the normal and tangential tip-sample interaction forces are found from a Hertzian contact model and the effects of the contact position, normal and lateral contact stiffness, tip height, thickness of the beam, and the angle between the cantilever and the sample surface on the nonlinear frequency to linear frequency ratio are studied. The differential quadrature method is employed to solve the nonlinear differential equations of motion. The results show that softening behavior is seen for most cases and by increasing the normal contact...
Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale timoshenko beam
, Article JVC/Journal of Vibration and Control ; Volume 24, Issue 18 , 2018 , Pages 4211-4225 ; 10775463 (ISSN) ; Mohasel Afshari, B ; Shafiei, N ; Rabby, S ; Kazemi, M ; Sharif University of Technology
Abstract
This work is aimed to present analysis on the thermal vibrational behavior of two-dimensional functionally graded porous microbeams based on Timoshenko beam theory. According to the power law function, the material composition and so the material properties are varying along thickness and axis of the microbeam. The governing equations are derived on the basis of the couple stress theory and the generalized differential quadrature method is used to solve the equations. The temperature gradient is considered to be uniform and nonuniform across the thickness of the microbeam. The results are presented to show the effect of temperature change, porosity, functionally graded and axially...
Post-buckling optimization of two-dimensional functionally graded porous beams
, Article International Journal of Mechanics and Materials in Design ; Volume 15, Issue 4 , 2019 , Pages 801-815 ; 15691713 (ISSN) ; Arghavani, J ; Maboudi, G ; Sharif University of Technology
Springer Netherlands
2019
Abstract
In the present study, an attempt is made to present the governing equations on the post-buckling of two-dimensional (2D) FGP beams and propose appropriate optimization procedure to achieve optimal post-buckling behavior and mass. To this end, Timoshenko beam theory, Von-Karman nonlinear relations, virtual work principle, and generalized differential quadrature method are considered to derive and solve governing equations and associated boundary condition (Hinged–Hinged) for an unknown 2D porosity distribution. Proposed method is validated using the papers in the literature. The optimization procedure including defining porosity distributions (interpolations), post-buckling function and...
Investigation of the size effects in Timoshenko beams based on the couple stress theory
, Article Archive of Applied Mechanics ; Volume 81, Issue 7 , July , 2011 , Pages 863-874 ; 09391533 (ISSN) ; Kahrobaiyan, M. H ; Rahaeifard, M ; Ahmadian, M. T ; Sharif University of Technology
2011
Abstract
In this paper, a size-dependent Timoshenko beam is developed on the basis of the couple stress theory. The couple stress theory is a non-classic continuum theory capable of capturing the small-scale size effects on the mechanical behavior of structures, while the classical continuum theory is unable to predict the mechanical behavior accurately when the characteristic size of structures is close to the material length scale parameter. The governing differential equations of motion are derived for the couple-stress Timoshenko beam using the principles of linear and angular momentum. Then, the general form of boundary conditions and generally valid closed-form analytical solutions are obtained...