Search for: closed-form-analytical-solutions
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    Torsion of strain gradient bars

    , Article International Journal of Engineering Science ; Volume 49, Issue 9 , September , 2011 , Pages 856-866 ; 00207225 (ISSN) Kahrobaiyan, M. H ; 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  

    On the nonlinear dynamics of trolling-mode AFM: analytical solution using multiple time scales method

    , Article Journal of Sound and Vibration ; Volume 423 , 9 June , 2018 , Pages 263-286 ; 0022460X (ISSN) Sajjadi, M. R ; Nejat Pishkenari, H ; Vossoughi, G ; Sharif University of Technology
    Academic Press  2018
    Trolling mode atomic force microscopy (TR-AFM) has resolved many imaging problems by a considerable reduction of the liquid-resonator interaction forces in liquid environments. The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method. Based on the developed analytical solution, the frequency-response curves of the resonator operation in air and liquid (for different penetration length of the nanoneedle) are obtained. The closed-form analytical solution and the frequency-response curves are validated by the... 

    A modified gaussian moment closure method for nonlinear stochastic differential equations

    , Article Nonlinear Dynamics ; Volume 89, Issue 4 , 2017 , Pages 2609-2620 ; 0924090X (ISSN) Makarem, H ; Pishkenari, H. N ; Vossoughi, G. R ; Sharif University of Technology
    There are many physical phenomena in engineering applications that are mostly modeled as stochastic differential equations. Sensor noise and environmental disturbance are two main sources of randomness. Determination of a closed-form analytical solution for the dynamical systems under random excitation is significantly useful for further investigations of these systems. Linear systems with stochastic excitation obey simple classified rules, leading to straightforward procedures for derivation of their analytical solutions. However, it is not the case for nonlinear systems with stochastic excitation, where no comprehensive method has been developed to be applicable to all such systems. This... 

    Nonlinear mechanics of soft composites: hyperelastic characterization of white matter tissue components

    , Article Biomechanics and Modeling in Mechanobiology ; Volume 19, Issue 3 , 2020 , Pages 1143-1153 Yousefsani, S. A ; Shamloo, A ; Farahmand, F ; Sharif University of Technology
    Springer  2020
    This paper presents a bi-directional closed-form analytical solution, in the framework of nonlinear soft composites mechanics, for top-down hyperelastic characterization of brain white matter tissue components, based on the directional homogenized responses of the tissue in the axial and transverse directions. The white matter is considered as a transversely isotropic neo-Hookean composite made of unidirectional distribution of axonal fibers within the extracellular matrix. First, two homogenization formulations are derived for the homogenized axial and transverse shear moduli of the tissue, based on definition of the strain energy density function. Next, the rule of mixtures 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) Asghari, M ; Kahrobaiyan, M. H ; Rahaeifard, M ; Ahmadian, M. T ; Sharif University of Technology
    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...