Separable and non-selfadjoint boundary-value problems representing the vibration of linearly elastic unidimensional systems are considered. The elastic system is modelled as a continuous distributed-parameter system where singularities in the mass distribution function can be neatly taken into account. Specifically, extending Green's function approach, the free vibration, stability and forced vibration of fixed-free rods with a tip mass and under the action of uniformly distributed non-conservative loads have been investigated analytically.

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doi.org/10.1007/BF00789092
Archive of Applied Mechanics
Department of Mechanical and Aerospace Engineering

Afagh, F, & Lee, J.X. (1995). Vibration of rods with a concentrated mass in the presence of non-conservative forces. Archive of Applied Mechanics, 65(8), 507–521. doi:10.1007/BF00789092