Order reduction of structural dynamic systems with static piecewise linear nonlinearities |
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Authors: | Eric A Butcher Rongdong Lu |
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Institution: | (1) Department of Mechanical Engineering, University of Alaska Fairbanks, Fairbanks, AK 99775–5905, USA |
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Abstract: | A technique for order reduction of dynamic systems in structural form with static piecewise linear nonlinearities is presented.
By utilizing two methods which approximate the nonlinear normal mode (NNM) frequencies and mode shapes, reduced-order models
are constructed which more accurately represent the dynamics of the full model than do reduced models obtained via standard
linear transformations. One method builds a reduced-order model which is dependent on the amplitude (initial conditions) while
the other method results in an amplitude-independent reduced model. The two techniques are first applied to reduce two-degree-of-freedom
undamped systems with clearance, deadzone, bang-bang, and saturation stiffness nonlinearities to single-mode reduced models
which are compared by direct numerical simulation with the full models. It is then shown via a damped four-degree-of-freedom
system with two deadzone nonlinearities that one of the proposed techniques allows for reduction to multi-mode reduced models
and can accommodate multiple nonsmooth static nonlinearities with several surfaces of discontinuity. The advantages of the
proposed methods include obtaining a reduced-order model which is signal-independent (doesn’t require direct integration of
the full model), uses a subset of the original physical coordinates, retains the form of the nonsmooth nonlinearities, and
closely tracks the actual NNMs of the full model. |
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Keywords: | Piecewise linear nonlinearities Order reduction Nonlinear normal modes |
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