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In this work, nonlinear vibration and frequency response analysis of a double-walled piezoelectric nanoresonator based on a cylindrical nanoshell is performed using the Gurtin–Murdoch surface/interface theory. The piezoelectric nanoresonator is simultaneously subjected to the visco-Pasternak medium and nonlinear van der Waals and electrostatic forces. It is found that the electrostatic and piezoelectric voltages, length to radius ratio, nanoresonator gap width, linear and nonlinear van der Waals coefficients and other parameters can effectively change the flexural rigidity of the system, which in turn affects the nonlinear frequency response. Also, increasing or decreasing of some parameters leads to increase or decrease in the resonance amplitude, resonant frequency, instability of the system, nonlinear behavior and bandwidth.

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SUMMARYThis paper presents a new algorithm to find the singularity-free cylindrical workspace of parallel manipulators. Because of the limited workspace of parallel manipulators cluttered with different types of singularities, a simple and robust technique to determine continuous singularity-free zones in the workspace of parallel manipulators is required. Here, the largest singularity-free cylinder within the workspace for any prescribed orientation ranging around a reference orientation angle of moving platform is determined. To this end, Particle Swarm Optimization is utilized to find the closest point on the singularity surface to the axis of the cylinder. By implementing the algorithm on 3-RPR planar parallel manipulator, the results show that this algorithm improves the efficiency and leads to significantly larger singularity-free workspace than those reported earlier.