Negative effective mass in the mass-in-mass subsystem with cubic nonlinearity, by Livija Cveticanin (University of Novi Sad)

Jan. 25, 2017
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DENORMS Action’s Workshop “Modelling of high performance acoustic structures Porous media, metamaterials and sonic crystals”, Rome, 24-25th January 2017

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Session on Use of metamaterials in other fields of Physics and metamaterials exposed to multiple physical phenomena

Speaker: Livija Cveticanin (University of Novi Sad)


In this paper based on the dynamics of the mass-in-mass system with cubic nonlinearity the acoustic metamaterial with negative effective mass is suggested. The excitation is assumed in the form of the Jacobi elliptic function. Mathematical model of the motion is a system of two coupled strong nonlinear and nonhomogeneous second order differential equations. Particular solution to the system is obtained. The analytical solution of the problem is based on the simple and double integral of the cosine Jacobi function. Conditions for elimination of the motion of the mass 1 by connection of the nonlinear dynamic absorber (mass - spring system) are defined. In the consideration the effective mass ratio is introduced in the nonlinear mass-in-mass system. Negative effective mass ratio gives the absorption of vibrations with certain frequencies. The advantage of the nonlinear subunit in comparison to the linear one is that the frequency gap is significantly wider. Nevertheless, it has to be mentioned that the amplitude of vibration differs from zero for a small value. In the paper the analytical results are compared with numerical one and are in agreement.