In this article, the sensitivity and resonant frequency of the atomic force microscope made of functionally graded materials is investigated by couple stress theory (MCST). In MCST, the size effect of the system is taking into account by means of the material length scale parameter. is made of a mixture of metal and ceramic with properties varying through the thickness following a simple In this work, due to the kinematic energy and potential energy of , the governing equations of motion and corresponding boundary conditions are derived on the basis of Hamilton principle by considering Euler-Bernoulli beam theory. Based on the results, it is clear that when the contact stiffness increases, the sensitivity of the system decreases, and resonant frequency increases. Moreover, when the thickness comes approximately close to material length scale parameter, the difference between MCST and classical continuum mechanic becomes significant. Furthermore, in low contact stiffness, increasing the power reduces the sensitivity of , while in high contact stiffness, increasing the power  increases the sensitivity of the system. Results also show that at each value of contact stiffness, as ceramic volume fraction increases the resonant frequency will be increased, too.
 

The present study is an attempt to analyze the yield threshold in a rotating variable-thickness disk made of functionally graded material (FGM) based on the Tresca yield criterion. The analysis was performed based on the small deformation theory and for the plane stress state. The modulus of elasticity, density and yield stress were assumed to be a power function of the radial coordinate. The Poisson’s ratio due to slight variations in engineering materials is assumed constant, and the equilibrium equation governing the rotating disk was solved analytically. In addition to the type of material, the disk cross section profile can affect the distribution of stress fields. The thickness of the disk cross-section varies in the radial direction by a power function. In the present analysis, various states are considered for onset yield and commencement of plastic flow. For evaluation and validation, the results of the study are compared to similar results related to specific states (homogeneous and functionally graded constant-thickness disk) investigated in previous references. The results show that considering variable thickness for disk section has a significant effect on the stress level and the prediction of onset yield point.
 

Structural health monitoring is essential to predict problems and maintain structure integrity which can be effective in prolonging the structure lifetime. The accumulation of failure in the structures causes a severe structural fracture; therefore, the development of damage detection methods for structural fracture is one of the most important points in maintaining the integrity and safety of the structures. In this paper, damage identification in functionally graded (FG) porous circular plates based on modal data and vibration analysis on elastic foundation is carried out. The vibration analysis process is performed based on first-order shear deformation theory and analytical method. Circular plates are widely used in the industry, for example in bower, balconies, screens, halls and swimming pool ceilings. Functionally graded materials are a new type of composite materials and may be characterized by the variation in composition and structure gradually over volume, resulting in desired changes in the characteristics of the material. The porous materials are lightweight, flexible and resistant to tiny cracks, these materials have two phases; their first phase is solid and the second phase is liquid or gas. The proposed method is achieved using modal analysis information extracted from a mathematical code in MAPLE. Based on this method, the plate can be examined with different boundary conditions including clamped, free and simply supported. Power series method has been used to solve the governing equations of circular plate. For the first part of the circular plate, the power series expands around the zero point and for other parts of the plate, the power series expands around the outer radius of its own part. In this study, first of all, the governing equations of circular plates were extracted based on first-order shear deformation theory and displacement functions. Two types of porosity have been used for applying porosity to the plate. Thereafter, the continuity conditions of displacement which generally include 6 items have been applied: continuity of in-plane displacement of the middle layer, continuity of rotation of the transverse surface, continuity of displacement of the plate, continuity of in-plane force, continuity of bending torque and continuity of transverse shear force per unit length. Furthermore, stress resultants in the points of connection have been applied which includes 3 items: in-plane force, bending torque and transverse shear force per unit length. The matrix determinant that is based on boundary and continuity conditions has been calculated to find the natural frequencies of the plate. After that, based on the Newton-Raphson method which is a numerical method for determining the root of a function, the initial natural frequencies of the circular plate were obtained and their modal shapes were plotted. At the end of the process, when the natural frequencies are determined, the unknowns were calculated. To prove the accuracy and efficiency of the proposed method, the natural frequencies obtained from this method were compared with the results presented in other papers. The comparisons have shown that the results obtained through this study had a good agreement with those of other ones and the proposed method could accurately show the damage location.