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R. Heuer, G. El Chabaan:
"On Nonlinear Vibrations of Bimodular Beam Structures";
in: "Dynamics and Control of Advanced Structures and Machines", H. Irschik, M. Krommer et al. (ed.); Springer Nature, 2021, (invited), ISBN: 978-3-030-79324-1, 61 - 71.

The paper is concerned with the modeling and numerical solution of the
dynamic response of the Bernoulli-Euler beams rigid in shear due to time-variant
excitation. The beams are assumed to be homogeneous and show classical boundary
conditions. However, they are composed of a bimodular material, thus behaving differently
in tension and compression. Generally, bimodular beams can be modeled as
effective two-layer laminates. However, their neutral axis depends on the curvature´s
sign. Thus, the equations of motion for flexural oscillations are developed by defining
an effective composite layered structure with a discontinuous natural beam axis.
The position of the natural axis follows from a (highly) nonlinear equation that is
dependent on both the geometry of the cross-section and the elastic material properties.
After an appropriate transformation, all calculations are formulated respecting
an independent reference axis of the bimodular beam structure. Within a numerical
study, structures of various cross-sections are considered showing the influence of
the bimodular material on the dynamic response. When considering mode shape
expansion, beams can be analyzed numerically by means of a modified Newmark
method.

Bimodular material, beam structures, nonlinear vibrations

https://publik.tuwien.ac.at/files/publik_302524.pdf