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Modal analysis is an often-used method for the solution of dynamical problems in engineering practice. In the case of continuous systems and discretization methods (e.g., FEM) with a large number of degrees of freedom, the reduced modal analysis is used, where only a selected number of modes are applied, while the higher modes are neglected. A piecewise linear elastic structure has state-dependent stiffness and as such, state-dependent vibration modes. During the dynamic modal analysis of such systems, one has to switch between the modes. During the switch a part of the kinetic and potential energy is transferring into modes, which are neglected in the reduced modal analysis. Thus, using the reduced modal analysis for the numerical calculation of the dynamic behavior of piecewise linear elastic structures introduces the modal truncation damping. In this paper, we present on a continuous system, how this modal truncation damping can be characterized, what are the upper and lower limits of that damping and how the characteristics of the free vibration of a piecewise linear elastic structure can be predicted.

Modal truncation damping in reduced modal analysis of piecewise linear continuum structures