When modeling flexible robots and structures for control purposes, most often the assumed modes (AMs) method is used to describe the deformation in combination with a floating reference frame formulation. This typically has the benefit of obtaining a low-order, but accurate model of the flexible structure, if the number of modes and AMs are properly chosen. The basis for using this method is, however, that the vibrations (deflections) are time and position independent, i.e., the expression is separable in space and time. This holds for the classic Euler–Bernoulli beam equation, but essentially does not hold for translational links. Hence, special care has to be taken when including flexible translational links. In the current paper, different methods for modeling a hydraulic loader crane with a telescopic arm are investigated and compared using both the finite segment (FS) and AMs method. The translational links are approximated by a single beam, respectively, multiple beam elements, with both one and two modes and using different mode shapes. The models are all validated against experimental data and the comparison is made for different operating scenarios. Based on the results, it is found that in most cases a single beam, low mode order approximation is sufficient to accurately model the mechanical structure and this yields similar results as the FS method.
Infinitely many periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients
