Search for: free-vibration-behavior
Article JVC/Journal of Vibration and Control ; Volume 19, Issue 11 , 2013 , Pages 1614-1632 ; 10775463 (ISSN) ; Taati, E ; Sharif University of Technology
In this paper, a size-dependent formulation is presented for mechanical analyses of inhomogeneous micro-plates based on the modified couple stress theory. The plate properties can arbitrarily vary through the thickness. The governing differential equations of motion are derived for functionally graded (FG) plates with arbitrary shapes utilizing a variational approach. Moreover, the boundary conditions are provided at smooth parts of the plate periphery and also at the sharp corners of the periphery. Utilizing the derived formulation, the free-vibration behavior as well as the static response of a rectangular FG micro-plate is investigated
Article Acta Mechanica ; Volume 223, Issue 6 , 2012 , Pages 1233-1249 ; 00015970 (ISSN) ; Kahrobaiyan, M. H ; Nikfar, M ; Ahmadian, M. T ; Sharif University of Technology
The geometrically nonlinear governing differential equations of motion and the corresponding boundary conditions are derived for the mechanical analysis of Timoshenko microbeams with large deflections, based on the strain gradient theory. The variational approach is employed to achieve the formulation. Hinged-hinged beams are considered as an important practical case, and their nonlinear static and free-vibration behaviors are investigated based on the derived formulation
Article International Journal of Engineering Science ; Volume 49, Issue 9 , September , 2011 , Pages 856-866 ; 00207225 (ISSN) ; Tajalli, S. A ; Movahhedy, M. R ; Akbari, J ; Ahmadian, M. T ; Sharif University of Technology
The governing differential equation and both classical and non-classical boundary conditions of strain gradient bars are derived using variational approach. A closed-form analytical solution is obtained for static torsion and the characteristic equation, which gives the natural frequencies, is derived and analytically solved for the free torsional vibrations of the strain gradient microbars. A fixed-fixed microbar is considered as a specific case to investigate the torsional size-dependent static and free-vibration behavior of strain gradient microbars. The results of the current model are compared to those of the modified couple stress and classical theories
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
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...
Article International Journal of Engineering Science ; Volume 91 , June , 2015 , Pages 63-75 ; 00207225 (ISSN) ; Asghari, M ; Vatankhah, R ; Sharif University of Technology
Elsevier Ltd 2015
The geometrically nonlinear governing differential equation of motion and corresponding boundary conditions of small-scale Euler-Bernoulli beams are achieved using the second strain gradient theory. This theory is a non-classical continuum theory capable of capturing the size effects. The appearance of many higher-order material constants in the formulation can certify that it appropriately assesses the behavior of extremely small-scale structures. A hinged-hinged beam is chosen as an example to lay out the nonlinear size-dependent static bending and free vibration behaviors of the derived formulation. The results of the new model are compared with the previously obtained results based on...
Article International Journal of Engineering Science ; Volume 48, Issue 12 , 2010 , Pages 1749-1761 ; 00207225 (ISSN) ; Kahrobaiyan, M. H ; Ahmadian, M. T ; Sharif University of Technology
This paper presents a nonlinear size-dependent Timoshenko beam model based on the modified couple stress theory, a non-classical continuum theory capable of capturing the size effects. The nonlinear behavior of the new model is due to the present of induced mid-plane stretching, a prevalent phenomenon in beams with two immovable supports. The Hamilton principle is employed to determine the governing partial differential equations as well as the boundary conditions. A hinged-hinged beam is chosen as an example to delineate the nonlinear size-dependent static and free-vibration behaviors of the derived formulation. The solution for the static bending is obtained numerically. The solution for...
Optimal material tailoring of functionally graded porous beams for buckling and free vibration behaviors, Article Mechanics Research Communications ; Volume 88 , 2018 , Pages 19-24 ; 00936413 (ISSN) ; Arghavani, J ; Sharif University of Technology
Elsevier Ltd 2018
In this paper, assuming porosity varies only along thickness direction, its optimal distributions in functionally graded porous (FGP) beams are tailored. Two multi-objective optimization problems are defined. In the first one, critical buckling load and mass are optimized simultaneously while in the second one, we concentrate on simultaneous optimization of mass and fundamental frequency. Employing Timoshenko beam theory, we present governing equations for a FGP beam. For the solution, we use Ritz method and propose appropriate trial functions according to the boundary conditions (Hinged-Hinged, Clamped-Clamped, Clamped-Hinged and Clamped-Free). Since the porosity distribution along...
Analytical and molecular dynamics simulation approaches to study behavior of multilayer graphene-based nanoresonators incorporating interlayer shear effect, Article Applied Physics A: Materials Science and Processing ; Volume 124, Issue 2 , 2018 ; 09478396 (ISSN) ; Asghari, M ; Sharif University of Technology
Springer Verlag 2018
Analytical and molecular dynamics simulation approaches are used in this paper to study free-vibration behavior of multilayer graphene-based nanoresonators considering interlayer shear effect. According to experimental observations, the weak interlayer van der Waals interaction cannot maintain the integrity of carbon atoms in the adjacent layers. Hence, it is vital that the interlayer shear effect is taken into account to design and analyze multilayer graphene-based nanoresonators. The differential equation of motion and the general form of boundary conditions are first derived for multilayer graphene sheets with rectangular shape using the Hamilton’s principle. Then, by pursuing an...
Article Applied Mathematical Modelling ; Volume 79 , 2020 , Pages 341-361 ; Rahnama, H ; Sharif University of Technology
Elsevier Inc 2020
Based on the first order shear deformation theory, free vibration behavior of functionally graded (FG) annular sector plates integrated with piezoelectric layers is investigated. The distribution of electric potential along the thickness direction of piezoelectric layers which is assumed to be a combination of linear and sinusoidal functions, satisfies both open and closed circuit electrical boundary conditions. Through a reformulation of governing equations and harmonic motion assumption, a novel decoupling method is suggested to transform the six second order coupled partial differential equations of motion into two eighth order and fourth order equations. A Fourier series method is then...