Morphing beam dynamics under moving force and moving moment with inertia effects

Morphing structures are re-configurable structures that can change its geometry to perform multiple functions in multiple operating conditions. Morphing beam structures have considerable applications in industrial robots, morphing aircraft, deployable space structures, etc. In this study, dynamic modelling and analysis of a telescopic type morphing beam, modelled as moving load problem with inertia effects, is performed. The moving loads are assumed to travel along the length of the beam, from fixed to free end and free to fixed end. The material and geometric parameters of the beam are assumed to be constant. The Rayleigh beam theory is used to model the beam, taking into account the rotating inertia effects. Dirac Delta function is used to model the moving loads in the governing equation. A hybrid analytical and numerical approach that couples eigenfunction expansions and Laplace transformation, along with the Crank–Nicholson numerical scheme, is developed to solve the coupled differential equations. The number of oscillations per unit travel time of the moving load and the Dynamic Amplification Factor (DAF) of the beam’s tip response are used to quantify the dynamic effects. Numerical results are investigated for the various non-dimensionalized speeds defined in terms of the moving loads’ critical speed. Numerical result shows that loads moving at low speeds have a more pronounced impact on the dynamic response compared to high speeds. Moving moment induces significant oscillatory behaviour for both (Fixed-free and Free-fixed) boundary conditions. In contrast, the moving mass induces oscillation only when it travels from free-end to fixed-end.