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This paper presents research on a new type of energy harvester consisting of two parts – the classical tristable system based on a flexible beam and permanent magnets, supplemented by the second part: an additional nonlinear support made of ethylene propylene diene monomer (EPDM). This support is used to amplify the vibration amplitude. As part of this work, laboratory tests on the EPDM material are performed to determine the strain curve. Then, finite element modeling (FEM) software is applied to determine the characteristics of the designed three shapes of the amplifiers and the efficiency of energy harvesting from the vibrations is tested based on the developed dimensionless model. The results are presented with regard to the effective value of the voltage induced on the piezoelectric electrodes and the efficiency factor that compares the tristable energy harvester with the structure developed in this paper. The obtained results allow for the conclusion that the average values of harvested energy over the entire frequency range ω characterize the system, in which the amplifier is two to six times more effective than the system without it. The best results are achieved for a solution based on a full cross-section. Moreover, the introduction of a nonlinear mechanical amplifier caused the classic system based on a magnetic section to obtain the so-called broadband effect over a wide spectrum of frequencies.