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JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING, no.4, 2025 (SCI-Expanded)
The axial forced vibration problem of viscoelastic radially graded porous nanorods was examined in this work. Axial harmonic load was either applied as a tip load at the free end or applied as a distributed load along nanorod's length, while the other end of the nanorod was fixed. Governing partial differential equation identifying the problem was derived based on the theory of Eringen's nonlocal elasticity. Kelvin-Voigt viscoelastic model was adopted to express the damped vibration problem of the porous nanorod. Governing equation was solved analytically using the modal analysis technique and the orthogonality properties of the modal coordinate functions. Obtained results were compared with those provided in the open literature, and a very good agreement was attained, which indicated the verification of the proposed study. Then, influences of porosity, viscoelastic damping, nonlocal parameter, dynamic load type and aspect ratio on modal magnification ratio, phase angle and nanorod displacement were determined, which has not been examined before, and thus, forced vibration characteristics of a viscoelastic nanorod including radial porosity were revealed. It was found that viscous damping leads to decrease in modal magnification ratio and shifting behavior in phase angle, and the effect of porosity parameter for elastic modulus and density on vibration frequencies has an inverse effect on modal frequencies, where these effects tend to be significant at higher modes. Results can be useful in mechanical design of small-scale structures possessing porosities in sensing probes and MEMS/NEMS applications.