Sharif Digital Repository

Based on the modified couple stress and Mindlin plate theories, a Levy type solution is presented for bending and vibration analysis of rectangular isotropic micro plates with simple supports at opposite edges and different boundary conditions at the other two ones. Modified couple stress theory is taken into account to capture the size effect and the governing equations are derived using Hamilton's principle, and solved by Levy solution and space-state method. The results are verified with the existing ones in the literature. As a benchmark, additional tables for vertical deflections and free vibrations of plate with various boundary conditions are presented  

In this thesis, static and dynamic analysis of nano beams based on second strain gradient theory is presented. Due to their small sizes, nano electro mechanical devices (NEMS) hold tremendous promise for novel, versatile and very sensitive devices for different applications ranging from actuators, transducers and also mass, force, light and frequency detectors. Therefore accurate modeling and analysis of such devices has an important role in their design and performance improvement. Neglecting the size effect, traditional theory of elasticity can not be suitable to predict mechanical behavior of these systems and so, it should be used non-classical theories which include size dependency... 

Vibration analysis of micro-structures has been a major topic in recent years. Among them micro-plates play an important role in micro- and nano-electromechanical systems (MEMS and NEMS), e.g. micropumps, micromirrors, and microresonators. Some experimental observations revealed the size-dependent mechanical behavior in micro-scaled structures. Because of the incapability of the classical continuum theory to interpret the experimentally-detected small-scale effects in mechanical behavior of micro-scaled systems, non-classical theories should be used to deal with micron and sub-micron structures. Couple stress theory is one of the non-classical theories with only one length scale parameter. A... 

In this research, a new Kirchhoff plate model based on the modified couple stress theory has been utilized to derive the corresponding closed-form expression for the buckling load. Moreover, a numerical mesh-less method, Reproducing Kernel Particle Method (RKPM), in combination with Corrected Collocation Method (CCM) has been employed to model the nano-plate and calculate its buckling load in the framework of the modified couple stress theory. To this end, two kinds of nano-plates have been modeled, the square nano-plates with all edges simply supported 1) in the presence of the nano-void and 2) without the nano-void. It should be noted that the analytical and numerical solutions for the... 

In this project, a size-dependent formulation is presented for mechanical analyses of inhomogeneous micro-plates based on the modified couple stress theory. The modified couple stress theory as a non-classical continuum theory has the ability to consider the small size effects in the mechanical behavior of the structures.The material properties are supposed arbitrarily to vary through the thickness of the plate. The governing differential equations of motion are derived for functionally graded plates utilizing variational approach. Based on the derived formulation, the static and free-vibration behaviors as well as buckling analysis of a rectangular functionally graded micro-plate are... 

One of the extensively used, yet complex, structures in the industry is pre-twisted Micro/Nano beams. Studying their mechanical behavior helps to have a broader view of them. In this present study, explores and analyzes the behavior of a pre-twisted Micro/Nano beam with a quadrangular/rectangular cross-section using the strain gradient theory and modified couple stress theory. Using the calculus of variations and the Hamiltonian principle the elastodynamics governing partial differential equations of transverse deflection of the pre-twisted Micro/Nano beam with hinged-hinged boundary conditions are derived. Then the mechanical behavior of the pre-twisted Micro/Nano beam in static mode and... 

Micro-Structures, especially cylindrical shells, has been widely used in different high tech industries, that this extreme usage emphasis, analyze of the vibration behavior of these structures. For gain an appropriate characteristics for a known purpose we can stiffen cylindrical shells with some rings that lids to improvement in mechanical properties of them. With advent of new materials, such as Functionally Graded Materials (FGM) and unique properties of these materials investigation of vibration behavior and characteristics of micro cylinders which has been made of FGM can be very important and essential. By using FGM materials many mechanical characteristics of these structures can be... 

Due to the features like small dimensions, low manufacturing cost and low power consumption, micro-electromechanical systems (MEMS) are widely utilized in engineering applications. Many experimental investigations have indicated that the mechanical behavior of constructive microelements of these systems isn’t predictable by classical continuum theory. Therefore, to analyze the behavior of microelements, the non-classical continuum theories which can capture size effects should be utilized. On the other hand, various experimental observations have confirmed that thermoelastic damping (TED) is a dominant source of energy dissipation in microelements, in contrast to the non-small parts and... 

Incapability of the classical continuum mechanics theory to justify the experimental observations of the mechanical response of the small-scale structures and parts motivated the researchers to pursue the introduction and utilization of the non-classical continuum theories for analysis and design of such structures and parts. In this paper, utilizing the modified couple stress theory and the strain gradient theory as well-known and powerful non-classical continuum theories, the mechanical response, including the displacement and stress fields, for micro-rotating disks with angular acceleration is investigated. The governing differential equations of motion and the corresponding boundary...