Impact of model reduction on frequency responses of linear and geometric nonlinear finite element models

Analyzing the behavior of mechanical structures with regard to periodic excitations is an important tool in structural mechanics. Complex structures are typically assembled of multiple components. Thus, the transfer function of an individual component, from one mounting point to another, naturally plays an important role in the overall system behavior. In industrial applications a single component can possess several hundred thousands to millions of degrees of freedom, rendering the calculation of its frequency response functions a challenging task. When reaching geometric nonlinear behavior due to high excitation levels, such as for lightweight structures, analyses have to be extended to nonlinear frequency response functions. Those are calculated using the shooting method (time-domain) or harmonic balancing (frequency-domain) in combination with a continuation algorithm. The numerical effort for calculation increases drastically with respect to the number of degrees of freedom and excitation levels of interest. Model reduction aims for resolving this burden. The model is reduced by projecting the equations of motion onto a lower-order subspace, spanned by a reduction basis ideally covering the main dynamics. Thus, a low-order model can be utilized as approximation for the original high-order one. In model reduction of geometric nonlinear systems, the evaluation of the nonlinear internal restoring forces has to be accelerated additionally through hyper reduction. This work focuses on model reduction of linear and geometric nonlinear mechanical systems concerning a good approximation of the input-output behavior. It starts with reviewing classical model reduction methods for linear mechanical systems and arrives at an approach for systematic extension of the bases for the reduction of geometric nonlinear mechanical systems. The impact of the projection step, meaning the specific choice of reduction basis, is analyzed based on (nonlinear) frequency response functions for various examples.     «

Analyzing the behavior of mechanical structures with regard to periodic excitations is an important tool in structural mechanics. Complex structures are typically assembled of multiple components. Thus, the transfer function of an individual component, from one mounting point to another, naturally plays an important role in the overall system behavior. In industrial applications a single component can possess several hundred thousands to millions of degrees of freedom, rendering the calculation...     »