Frequency shifts induced by large deformations in planar phantografic continua

The present article deals with the dynamic behavior of 2D continua representing the homogenized limit of microstructured pantographic systems, i.e., the structures in which two orders of fibers are interconnected by means of pivots. The strain energy density of the continuum model depends on the first and second gradient of the displacement. Numerical simulations on modal analysis are performed and the results are compared with the behavior of an orthotropic lamina of equal mass density. The results show the characteristic features of the dynamic behavior of higher gradient models, and in particular the difference, with respect to classical laminae, in the dependence of the eigenfrequencies on the stiffness.