Band gap and modal interaction analysis of metastructures with high-static- low-dynamic stiffness with multiple scales

Resumo

In this work, we explore the dynamical response of metastructures with high-static-low-dynamic stiff-
ness (HSLDS) characteristics, with focus on the vibration attenuation performance through band gaps and band

stops. A metastructure consists fundamentally of identical components, the cells, connected in a way that charac-
teristics of mass, stiffness, and or damping are spatially repeated. Metastructures present interesting characteristics

for vibration attenuation that are not found in classical structures. These characteristics have been explored for

automotive and aerospace applications, among others, as structures with low mass are paramount for these indus-
tries, and keeping low vibration levels in a wide frequency range is also desirable. One unit cell with three degrees

of freedom is used, with an axial harmonic force applied at the rightmost element. The dynamical response of the
linear metastructure is found by mechanical impedance and transmissibility methods. The cell dynamical response
of the nonlinear metastructure is found using the method of multiple scales (MMS), and the response is compared
to the fourth-order Runge-Kutta method (RK). The influence of the mass ratio between the elements of the cell and
number of cells in the complete structure are analysed in the frequency response of the metastructure.