Abstract:
This paper presents an exact method for maximizing the natural frequencies of functionally graded material (FGM) bars in axial motion. To satisfy the economic feasibility requirements, the total structural mass is maintained at a constant value equal to that of a defined baseline design. The composition of the material of construction is optimized by defining the spatial distribution of volume fractions of the material constituents using either continuous or discrete distributions along the bar length. The major aim is to tailor the material distribution in the axial direction so as to maximize the frequencies and place them at their target values to avoid the occurrence of large amplitudes of vibration without the penalty of increasing structural mass. The resulting optimization problem has been formulated as a nonlinear mathematical programming problem solved by invoking the MatLab optimization toolbox routines, which implement the method of feasible directions interacting with the associated eigenvalue problem routines. As a case study, a bar with Fixed-Fixed boundary condition has been thoroughly investigated. It was shown that the use of material grading concept can be promising in maximizing the natural frequencies and producing efficient economical designs having optimal stiffness and mass distributions as compared with their corresponding baseline designs.