In this work, the two-temperature dual-phase-lag theorem has been used to present an analytical mathematical model for calculating the vibration in a viscothermoelastic nano-resonator. The governing equations have been derived when a simply supported nano-resonator is exposed to a ramp-type thermal load and static pre-stress. The governing equations have been solved by using a direct method and obtained the solution in the Laplace transform domain where the inversions of the Laplace transform have been calculated by using the Tzou approximation method. The increments of the dynamic and conductive temperatures, volumetric deformation, and stress regarding the resonator length for various cases of temperature type, static-pre-stress, and viscothermoelastic properties with different values of ramping heat parameter have been presented in figures and studied. The parameter of the two-temperature model, static pre-stress, ramp-type heat parameter, and viscothermoelastic parameter has a significant impact on all functions studied. The ramping time parameter may be utilized to change the thermal and mechanical properties of the nano-resonator.
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