Nonlinear vibration of an axially loaded beam carrying multiple mass–spring–damper systems

This paper deals with the nonlinear vibration of a beam subjected to a tensile load and carrying multiple spring–mass–dashpot systems. The nonlinearity is attributable to mid-plane stretching, damping, and spring constant. Explicit expressions are presented for the frequency equations, mode shapes, nonlinear frequency, and modulation equations. The validity of the results is demonstrated via comparison with results in the literature. Parametric studies are conducted on beams with varying boundary conditions to investigate the effect of the location and magnitude of the spring–mass–dashpot system, as well as the role of the tension.