Parametric eigenvalue analysis for flexible multibody systems

Modal analysis of mechanical systems and structures is a powerful tool for the assessment of vibrational behavior. Dynamical mechanical systems per their intention are used in a vast range of configurations and the vibrational behavior throughout is of interest. Therefore, modal analysis would be necessary at all operating points, which of course would result in great computational effort. To reduce the amount of modal analyses that are needed, an approximation method is introduced here based on Taylor expansion around a single operating point. The parametric modal analysis of this work is based on that introduced by Wittmuess et al. (2016). Using the eigenpair values at an operating point and analytical sensitivity analysis a polynomial expression is derived while the operating position is parameterized together with other variable physical quantities. A two-dof planar robot carrying out a pick-and-place trajectory with a range of payload mass is used to validate this method. This robot is modeled as a flexible multibody system in generalized coordinates using the equivalent rigid link system (ERLS) approach. The approximated results of the eigenpairs are compared with the true results in terms of their values, modal assurance criterion (MAC) and relative error. These values are demonstrated and discussed for the range of trajectory and varying payload.