Flexural Vibration Analysis and Improvement of Wave Filtering Capability of Periodic Pipes

Abstract

This article examines the propagation properties of flexural wave in periodic pipelines. In order to realize the effect of boundary condition on stopbands, a pipe with two types of periodic supports is investigated: (i) pipe on translational and rotational springs, and (ii) pipe on simple supports restraint with rotational springs. Initially, the dispersion relationships for the corresponding homogeneous pipe with different boundary conditions are derived in the context of Bloch-Floquet theory of periodic structures. Successively, the accuracy of resulting band structures is verified based on the vibration transmission spectrum computed by finite element models. In the examined frequency range, both Bragg and resonance type of stopbands are evolved in the pipe with first kind of supports while in second case only Bragg type stopbands are emerged. The waves corresponding to frequency range other than stopbands indicate passbands and they can freely propagate through the pipe. Hence, in order to control a specific passband, a single-degree-of-freedom resonator is employed at the center of each span of the pipe. The width and position of stopband due to resonator depend upon the mass and stiffness properties of the resonator. Therefore, the stopbands properties can be tuned by means of properly adjusting parameters of the resonator. The dispersion relations provided herein are promising to realize the characteristics of flexural waves and to design the resonator for the similar periodic structures with different boundary conditions.