Sharif Digital Repository

In this paper, the coupled three-dimensional flexural vibration of micro-rotors is investigated by taking into account the small-scale effects utilizing the strain gradient theory, which is a powerful nonclassical continuum theory in capturing small-scale effects. A micro-rotor consists mainly of a flexible micro-rotating shaft and a disk. With the aid of Hamilton's principle, governing equations of motion are derived and then transformed to the complex form. By implementing the Galerkin's method, a coupled ordinary differential equation is attained for the system. Expressions for the first two natural frequencies of the spinning micro-rotors are obtained with truncated two-term equation.... 

The nonlinear coupled three-dimensional vibrations of microspinning Rayleigh beams are analytically studied utilizing the modified couple stress theory to take into account the small-scale effects. The considered nonlinearity is of geometrical type due to the mid-plane stretching. The rotary inertia and gyroscopic effects are both included in the formulation. Governing equations of motion are derived with the aid of the Hamilton Principle and then transformed into complex form. Then, the Galerkin and multiple scales methods are utilized to solve the nonlinear partial differential equation. Approximate analytical expressions for nonlinear natural frequencies of the spinning beams in forward... 

Based on the micromorphic theory, a novel mathematical formulation for the mechanical modeling of material growth and remodeling processes in finite deformation is developed. These two processes have an important significance in evolution of living tissues. The presented formulation incorporates both the volumetric growth and mass flux phenomena into the modeling with the aid of the micromorphic theory's capability to include internal structures in materials. The balance equation of microinertia is presented which reveals the importance of rearrangement and alteration of microstructure in the micromorphic material growth. Within the framework of material uniformity, the evolution laws are... 

The balance equations for micromorphic materials with mass flux and mass production are determined based on the phenomenon of self-diffusion. In this study, the self-diffusive flux is the flux of mass of a single micromorphic species within itself which is captured by defining the relative macro-element spatial velocity vector and the relative micro-gyration tensor. By use of a binary micromorphic mixture theory, the self-diffusion of a single micromorphic species within itself results in an extra diffusive momentum field, an extra diffusive moment of momentum and their respective non-compliant terms. The concepts of the macro- and micro-mass flux are studied in the framework of the... 

Micro-rotating disks are extensively used in micro-electromechanical systems such as micro-gyroscopes and micro-rotors. Because of the sensitivity of these elements, enough knowledge about the mechanical behavior of these structures is an essential matter for designers and fabricators. The small-scale effects on the in-plane free vibration of such micro-disks present an important aspect of the mechanical behavior of these elements. The small-scale effects on the in-plane free vibration of these micro-disks are investigated in this study using the modified couple stress theory. By using the Hamilton principle, the partial differential equations governing the coupled radial and tangential... 

The way central nervous system manages the excess degrees of freedom to solve kinetic redundancy of musculoskeletal system remains an open question. In this study, we utilise the concept of synergy formation as a simplifying control strategy to find the muscle recruitment based on summation of identified muscle synergies to balance the biomechanical demands (biaxial external torque) during an isometric shoulder task. A numerical optimisation-based shoulder model was used to obtain muscle activation levels when a biaxial external isometric torque is imposed at the shoulder glenohumeral joint. In the numerical simulations, 12 different shoulder torque vectors in the transverse plane are... 

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... 

Selenium, in the form of selenoproteins present in the human body is an important micronutrient in human health. It is involved in immunity, oxidative defense, redox signaling and functioning of thyroid hormones. The narrow line existing between the essential dose satisfying the body needs and its toxic dose raises the question of how selenium cycles in nature. What plants can provide edible selenium? Which soils can provide this element for the plants? How can the presence of selenium in the life cycle be preserved? And what is the role of other biological molecules such as methionine in this cycle? On the other hand, selenium can be toxic in high doses hence, it is important to isolate... 

In this article, a constitutive model in the framework of continuum damage mechanics is proposed to simulate the elastic behavior of concrete in tension and compression states. We assume two parts for Gibbs potential energy function: elastic and damage parts. In order to obtain the elastic-damage constitutive relation with the internal variables, two damage thermodynamic release rates in tension and compression derived from the elastic part of Gibbs potential energy are introduced. Also, two anisotropic damage tensors (tension and compression) are defined which characterize the tensile and compressive behaviors of concrete. Furthermore, two different linear hardening rules for tension and... 

Based on the first-order shear deformation and Donnell's shell theory with von Karman non-linearity, one decoupled stability equation for buckling analysis of functionally graded (FG) and multilayered cylindrical shells with transversely isotropic layers subjected to various cases of combined thermo-mechanical loadings is developed. To this end, the equilibrium equations are uncoupled in terms of the transverse deflection, the force function and a new potential function. Using the adjacent equilibrium method, one decoupled stability equation which is an eighth-order differential equation in terms of transverse deflection is obtained and conveniently solved to present analytical expressions... 

Due to the increase in the number of cancer patients, because of environmental parameters, high stress, low immunity, etc., there is an urgent need to develop cost-effective sensors for early targeted detection of cancerous cells with adequate selectivity and efficiency. Early disease diagnosis is important, as it is necessary to start treatments before disease progression. On the other hand, we need new, more efficient cancer treatment approaches with minimized side effects, more biocompatibility, and easy disposal. Nanobiotechnology is a field that can assist in developing new diagnostic and treatment approaches, specifically in fatal cancers. Herein, a study on the different applications... 

In this paper, a multiplate nonlocal shear model and molecular dynamic simulations are presented to investigate the effects of interlayer shear and nonlocality on the natural frequencies of multilayer graphene sheets (MLGSs). From one aspect in the optimal design of such structures, the interaction between graphene layers, which can significantly vary the static and dynamic behavior due to lack of solidity of layers stack, should be considered. On the other hand, it is requied that the nonlocality phenomenon which has an effective role in the mechanical analysis of nanostructures is taken into account. To this aim, the equation of motion along with corresponding boundary conditions is... 

In this paper, a unified explicit tensorial relation is sought between two stress tensors conjugate to arbitrary and general Hill strains. The approach used for deriving the tensorial relation is based on the eigenprojection method. The result is, indeed, a generalization of the relations that were derived by Farahani and Naghadabadi [1] in 2003 from a component to intrinsic form. The result is unified in the sense that it is valid for all cases of distinct and coalescent principal stretches. Also, in the case of three dimensional Euclidean inner product space, using the derived unified relation, some expressions for the conjugate stress tensors are presented. © Sharif University of... 

We present a perturbation theory for studying the instabilities of non-axisymmetric gaseous discs. We perturb the dynamical equations of self-gravitating fluids in the vicinity of a non-axisymmetric equilibrium, and expand the perturbed physical quantities in terms of a complete basis set and a small non-axisymmetry parameter e. We then derive a linear eigenvalue problem in matrix form, and determine the pattern speed, growth rate and mode shapes of the first three unstable modes. In non-axisymmetric discs, the amplitude and the phase angle of travelling waves are functions of both the radius R and the azimuthal angle φ. This is due to the interaction of different wave components in the... 

In this paper, a multiplate nonlocal shear model and molecular dynamic simulations are presented to investigate the effects of interlayer shear and nonlocality on the natural frequencies of multilayer graphene sheets (MLGSs). From one aspect in the optimal design of such structures, the interaction between graphene layers, which can significantly vary the static and dynamic behavior due to lack of solidity of layers stack, should be considered. On the other hand, it is requied that the nonlocality phenomenon which has an effective role in the mechanical analysis of nanostructures is taken into account. To this aim, the equation of motion along with corresponding boundary conditions is... 

A novel non-classical continuum model for pull-in analysis of multilayer graphene sheets (MLGSs) is developed to consider the effect of shear interaction between layers based on the nonlocal elasticity theory. The equation governing the motion and corresponding boundary conditions of electrostatically actuated MLGSs are obtained based on the nonlocal shear multiplate theory. The Galerkin method along with the first mode shapes for clamped and cantilever MLGSs together with the method of parameter expansion is used to obtain closed-form expressions of the normalized frequency and time history response. In addition, molecular dynamics (MD) simulations are carried out to validate the pull-in... 

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... 

In this paper, a size-dependent formulation is presented for Timoshenko beams made of a functionally graded material (FGM). The formulation is developed on the basis of the modified couple stress theory. The modified couple stress theory is a non-classic continuum theory capable to capture the small-scale size effects in the mechanical behavior of structures. The beam properties are assumed to vary through the thickness of the beam. The governing differential equations of motion are derived for the proposed modified couple-stress FG Timoshenko beam. The generally valid closed-form analytic expressions are obtained for the static response parameters. As case studies, the static and free... 

This paper investigates the deflection and static pull-in voltage of microcantilevers based on the modified couple stress theory, a non-classic continuum theory capable to predict the size effects for structures in micron and sub-micron scales. It is shown that the couple stress theory can remove the gap between the experimental observations and the classical theory based simulations for the static pull-in voltage  

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