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In this paper, a new type of lightweight metastructure for vibration isolation in small devices is investigated. The metastructure contains periodical repeated units of stiff structure-absorber type. On the basic stiff structure, which is excited with the periodical force, a mass-spring absorber is connected. Mass of the basic structure is neglected. The unit represents a two-degree-of-freedom system described with a differential and an algebraic equation. As the elastic property of the structure and of the spring is nonlinear, both of equations are strongly nonlinear. A new mathematical procedure for solving the problem is developed. The method applies the Ateb function (inverse Beta function), which is the exact solution of the equation with polynomial nonlinearity. For vibration elimination in the resonant region, the ‘effective stiffness’ parameter is introduced. The effective stiffness parameter is required to have a negative value. It is obtained that the region of negative effective stiffness depends on the order and coefficient of nonlinearity. The frequency gap is wider for higher values of order and coefficient of nonlinearity and moves to higher frequencies. Parameters of unit for vibration isolation in a wide range of frequencies are calculated. The obtained results are tested on the one-dimensional lattice. It is proved that the result in negative effective stiffness of the unit corresponds to the lattice. The continuous structure has very good vibration isolation performance and has great potential in the vibration isolation applications for small-scale equipment. Better isolation properties are achieved for high vibration excitation frequency. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.