The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

SUMMARYThe main innovation of this paper is determining the dynamic load carrying capacity (DLCC) of a flexible joint manipulator (FJM) using a closed form nonlinear optimal control approach. The proposed method is compared with two closed loop nonlinear methods that are usually applied to robotic systems. As a new idea, DLCC of the manipulator is considered as a criterion to compare how well controllers perform point to point mission for the FJMs. The proposed method is compared with feedback linearization (FL) and robust sliding mode control (SMC) methods to show better performance of proposed nonlinear optimal control approach. An optimal controller is designed by solving a nonlinear partial differential equation named the Hamilton–Jacobi–Bellman (HJB) equation. This equation is complicated to solve exactly for complex dynamics so it is solved numerically using an iterative approximation combined with the Galerkin method. In the FL method, angular position, velocity, acceleration and jerk of links are considered as new states to linearize the dynamic equations. In the case of SMC, the dynamic equations of manipulator are changed to the standard form then the Slotine method is used to design the sliding mode controller. Two simulations are performed for a planar and a spatial Puma manipulator and performances of controllers are compared. Finally an experimental test is done on 6R manipulator and the Stereo vision method is used to determine the position and orientation of the end-effector.

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