Abstract：Based on uniform Timoshenko nano-beam in viscoelastic medium and taking nonlocal effect, section geometry parameter, piezoelectric effect and flexoelectric effect into consideration, the vibration governing equation of the nonuniform Timoshenko nano-beam in the viscoelastic medium were established, and using perturbation theory, the transfer function method of the structure under typical boundary conditions was presented. The effects of nonlocal parameters, taper coefficient, flexoelectric effect and viscoelastic medium on the vibration characteristics of the nonuniform flexoelectric nano-beam were systematically studied. The results show that increase the taper coefficient can reduce the sensitivity of the natural frequency to nonlocal effect the critical damping coefficient of the structure. The sensitivity of natural frequency to taper can be weakened by increasing nonlocal parameter. Increasing the tangential flexoelectric coefficient f3131 can reduce the sensitivity of the structure to transverse flexoelectric coefficient f3113, while increasing the transverse flexoelectric coefficient f3113 can increase the sensitivity of the structure to transverse flexoelectric coefficient f3131. The research results can provide a theoretical basis for the extension and application of flexoelectric nano-beam in energy harvester.
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