This article deals with analyzing nonlinear free vibrations of nonlocal two-phase piezo-magnetic beam with geometric imperfection rested on viscoelastic substrate. The two-phase piezo-magnetic material is based on a composition of piezoelectric and magnetic constituents with desirable percentages. An assumption is that the nanobeam is rested in an initial position due to geometric imperfection. In addition, the equilibrium equations of nanobeam with piezo-magnetic properties are derived utilizing Hamilton’s principle and the von Kármán geometric nonlinearity. Then, an exact solution based on the Jacobi elliptic functions has been provided to obtain nonlinear vibration frequency. It is found that nonlinear vibration behavior of the nanobeam is dependent on the magnitude of induced electric voltage, magnetic field intensity, geometric imperfection, and viscoelastic substrate parameters.
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