Nonlinear dynamics of traveling beam with longitudinally varying axial tension and variable velocity under parametric and internal resonances

In this investigation, the nonlinear dynamics of an axially accelerating viscoelastic beam on a pully mounting system have been analyzed. The axial tension is modeled as function traveling velocity, support stiffness parameter well spatial coordinate. Geometric cubic nonlinearity in equation motion due to elongation neutral axis beam. integro-partial differential associated with simply supported end conditions solved analytically by adopting direct perturbation method multiple time scales. As result, set complex variable modulation equations generated, which governs amplitude and phase. This modulated numerically explore influence upon stability bifurcation has not addressed existing literature. Apart from this, impact fluctuating velocity component, coefficient, longitudinal parameter, internal parametric frequency detuning parameters analysis studied, revealing significant dynamic characteristics system. fourth-order Runge–Kutta applied find solution displays stable periodic, quasi-periodic, mixed-mode responses along unstable chaotic behavior for specific parameters. results obtained through analytical–numerical approach may help design operation moving