Abstract
In this paper, the in-plane vibration of a curved beam is investigated. The elastic waves in the curved beam are divided into four regions. Considering the moment of inertia and shear effect of the curved beam, the characteristic curve for wavenumber versus frequency is depicted based on the in-plane vibration equation. Then the amplitude ratio and the phase of the radial wave, the tangential wave and the angle will also be analyzed. Additionally, a sinusoidal phononic crystal curved beam is constructed based on the solution of the wave for the beam. The transfer matrix of in plane vibration for the crystal curved beam is derived theoretically. Combining Bloch theory, the energy band of the phononic crystal curved beam is also calculated. Furthermore, by applying boundary conditions, transmissibility curves of the radial and tangential waves are obtained. Finally, finite element simulations are carried out to verify the theoretical results.
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