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multiple-nonlinear-regression
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Nanoscale vibrational behavior of single-layered graphene sheets
, Article ASME 2007 International Mechanical Engineering Congress and Exposition, IMECE 2007, 11 November 2007 through 15 November 2007 ; Volume 11 , 2007 , Pages 229-235 ; 079184305X (ISBN) ; Ahmadian, M. T ; Vafai, A ; ASME ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2007
Abstract
Molecular structural mechanics approach is implemented to investigate vibrational behavior of single-layered graphene sheets. By using the atomistic modeling, mode shapes and natural frequencies are obtained. Vibration analysis is performed under different chirality and boundary conditions. Numerical results from the finite element technique are applied to develop empirical equations via a statistical multiple nonlinear regression model. With the proposed empirical equations, fundamental frequencies of single-layered graphene sheets under considered boundary conditions can be predicted within 3 percent accuracy. Copyright © 2007 by ASME
The effect of stiffness on stress intensity factor for a crack in annular disc under constant central torque
, Article International Journal of Damage Mechanics ; Volume 19, Issue 8 , 2010 , Pages 1001-1015 ; 10567895 (ISSN) ; Gowhari Anaraki, A. R ; Hardy, S. J ; Sharif University of Technology
2010
Abstract
The finite element method has been used to predict the stress intensity factors for cracked annular discs under constant central torque. Linear elastic fracture mechanics finite element analyses have been performed and the results are demonstrated in the form of crack configuration factors. To this end, the extensive ranges of crack configuration factors have been employed while considering the effect of disc stiffness. Then, the finite element results are applied to develop equivalent prediction equations using a statistical multiple nonlinear regression model. The accuracy of this model is measured using a multiple coefficient of determination, R2, where 0 ≤R2 ≤1. This coefficient is found...
On the out-of-plane dynamic response of horizontally curved beams resting on elastic foundation traversed by a moving mass
, Article Journal of Sound and Vibration ; Volume 479 , 2020 ; Khaloo, A. R ; Foyouzat, M. A ; Sharif University of Technology
Academic Press
2020
Abstract
In this paper, the dynamic behavior of Horizontally Curved Beams (HCBs) resting on an elastic foundation and subjected to a moving mass is investigated. The governing coupled non-linear differential equations of equilibrium are derived, where Coriolis acceleration, centrifugal force and rotary inertia are incorporated in the problem formulation. In the proposed analytical solution, by employing the transition matrix technique, the governing differential equations of motion are subsequently transformed into a new system of linear ordinary differential equations which can be solved using standard numerical procedures. The accuracy as well as the robustness of the solution is ascertained...