Abstract
Based on the governing differential equation of out-of-plane curved beam, the wave propagation behavior, free vibration, and transmission properties are presented theoretically in this paper. Firstly, harmonic wave solutions are given to investigate the dispersion relation between frequency and wave number, cut-off frequency, displacement, amplitude ratio, and phase diagram. The frequency spectrum results are obtained to verify the work by Kang and Lee. Furthermore, natural frequencies of the single and composite curved beam are calculated through solving the characteristic equation in the case of free-free, clamped-clamped, and free-clamped boundaries. Finally, the transfer matrices of the out-of-plane curved beam are derived by combining the continuity between the different interfaces. The transmissibility curves of the single and composite curved beam are compared to find the vibration attention band. This work will be valuable to extend the study of the out-of-plane vibration of curved beams.
Highlights
Curved beams are widely used in many built-up structures and arch structures because of their valuable engineering applications
Huang investigated the free vibration of rotating thin rings using the wave approach. e harmonic wave solutions, frequency spectra, displacement amplitude ratio, and cut-off frequencies are analyzed theoretically [2]
Wu proposed a new approach for free vibration analysis of arches with the effects of shear deformation and rotary inertia considered
Summary
Curved beams are widely used in many built-up structures and arch structures because of their valuable engineering applications. Wu proposed a new approach for free vibration analysis of arches with the effects of shear deformation and rotary inertia considered He calculated the natural frequencies for the clamped-clamped and free-free boundaries [11]. To obtain the natural frequencies and mode shapes of curved beams with hinged-hinged, hinged-clamped, and clamped-clamped boundaries, Lee derived the differential equations governing out-of-plane free vibrations of the elastic curved beams with variable curvature. Wang investigated the inplane vibration of a curved beam by considering the moment of inertia and shear effect He obtained the dispersion relation of wave number and frequency and analyzed the radial and tangential coupled band gaps of a periodic curved beam [16].
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