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• Theoretical model of the double tumbler is built to derive the equation of motion. • The eigenmodes of double tumblers are synchronous and bidirectional swings. • Motion of double tumblers is periodic or quasi-periodic under various excitations. • Two adjacent resonance peaks shows great potential for broadband absorbers. The oscillation mechanism of tumblers differs from traditional mass-spring-dampers. This work studies the complicated dynamic behaviors of a double tumbler on a curved surface. The theoretical model of the double tumbler is established, and the equations of motion based on the Lagrange equation are derived. The effects of the geometric parameters on the dynamic responses are analyzed numerically. The experiment is also conducted to validate the theoretical model of double tumblers. The results show that two eigenmodes of the double tumbler are the synchronous and bidirectional swings, respectively. Due to the amplification effect of double tumblers on the dynamic responses, the amplitudes of the inner tumbler are larger than that of the outer tumbler. The resonance peaks and the peak frequencies of the swing angles can be changed significantly by adjusting geometric parameters. In addition, the double tumblers can exhibit periodic and quasi-periodic oscillations with the increase in the excitation amplitude. The unique dynamic characteristics of the double tumblers show great potential for the design and application of low-frequency devices, such as absorbers and energy harvesters. [ABSTRACT FROM AUTHOR]