Modeling a fire-rescue turntable ladder as piecewise Euler-Bernoulli beam with a tip mass

The truss structure of the ladder set of a modern fire rescue turntable ladder provides limited stiffness compared to a massive boom and thus is susceptible to oscillations. In this paper, the bending oscillations of this truss structure in the vertical plane shall be modeled and simulated. Distortion and out-of-plane bending are not considered. For the in-plane bending, Euler-Bernoulli beam theory is applied; the model parameters are assumed discontinuous but piecewise constant over the ladder length. The cage at the upper end is accounted for in special boundary conditions. With an appropriately defined inner product, the equations of motion are decomposed in modal coordinates, whereas both damping and gravity effects are included. Suitable parameters to match the identified eigenfrequencies are determined. Comparison of simulation results with measured data shows that this approach allows a good simulation of the oscillatory behavior, including the dominant mode as well as harmonics. An important demand on the proposed approach is to achieve a system description for controller design, taking into account low computational power of the ladder's microcontroller.