Sharif Digital Repository

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... 

There are experimental observations that show material response in micro-scale is dependent on some other parameters rather than Lame parameters. Strain gradient elasticity has been recently developed to take into account this characteristic of materials response. In strain gradient elasticity, characteristic length parameters enter the constitutive equations through the elastic strain energy density function. The elastic strain energy density function is assumed to be a function of the gradient of strain tensor in addition to the strain tensor. In this way, new material constant (characteristic length parameters) are introduced and entered into the constitutive equations. In recent years,...