MS01.3: Reduced-Order Modeling and System Identification

This paper provides the first quantitative characterization of the tang regime in a bell Plate. It gives insight on the design of these resonators to achieve a large quality factor based on finite-element simulations. Experimental results combining ring-down measurements and frequency responses prove that two main resonant modes arise, one being the first bending mode and the other being the (2,0)-mode which has the largest quality factor. We estimate the respective frequency and quality factor of these two modes. We illustrate and quantify the observed nonlinear behavior of the plate. We also prove how the dimensions are critical by studying two different designs, one of which resonates significantly whereas the other one does not resonate at all.

This work presents a model order reduction technique in case when a discrete-time control law is applied to a Lur'e-type system, i.e., to a linear dynamical system with a nonlinear feedback component. It is shown that the Laplace and z-transform of the piecewise-continuous response functions can be determined analytically, which allows model order reduction to be performed on the linear component of the closed control loop. Simulations of a balancing problem verify that the proposed method can accurately model the sampling-related complex vibration phenomena and also the nonlinear characteristics of the system.

The dynamics of the primary Spectral Submanifold (SSM) constructed over the eigenspace spanned by the slowest modes of a dynamical system represent an ideal reduced order model. However, modeling the dynamics of trajectories lying farther away from the primary SSM is difficult if the system exhibits non-normal behavior. In the present work, we address how to apply the primary SSM-based model reduction technique to systems featuring non-orthogonal slow and fast eigenspaces in both linear and nonlinear problems. In particular, the reduced coordinates parametrizing the SSM are found via an oblique projection of the coordinates of the observed space. The projection is constructed minimizing the oscillations of the instantaneous relationship between frequency and amplitude (backbone curves) of decaying trajectories.

While recent designs demand structures more prone to geometric nonlinearity, frictional contact can occur in the interaction between adjacent components. The accuracy and efficiency of the Rubin model order reduction technique enhanced with static modal derivatives are investigated for the vibration analysis of geometrically nonlinear structures with friction contact. This reduced model facilitates the contact treatment by keeping the contact degrees of freedom in generalized coordinates while simulates geometrically nonlinear behavior due to the addition of the static modal derivatives to the reduction basis. The effectiveness of this method is studied by the vibration analysis of a cantilever beam under these nonlinearities. Rubin with free interface modes and their static derivatives is also compared with Craig-Bampton method with fixed interface modes and their static derivatives. The results highlight the good performance of the Enhanced Rubin method. In other words, accurate results are achieved by a small number of modes in the reduced space which leads to low online computation time. Furthermore, the analysis demonstrates the considerable impact of a geometrically nonlinear model on the accurate prediction of contact states.