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Guided Wave Propagation Showing Frequency Trapping in Periodic Structure

Sourav Banerjee (University of South Carolina)

Mechanics and Dynamics of Periodic Structures

Wed 3:10 - 4:30

Salomon 101

Structures with non-planar boundaries are frequently encountered in engineering structures and are almost neglected in wave propagation simulation. Periodically corrugated boundaries are found in the surfaces formed by the friction stir welding, reinforcement steel bars have rectangular periodic grating. Engineers create periodic trenches around buildings to create desired seismic band gaps. In addition to many such applications, health monitoring of structures with periodic geometry requires detailed understanding of the elastic wave propagation in periodic media because crack initiation creates acoustic waves that propagate through the periodic geometry of the structure. These acoustic signals can be detected at remote locations and correctly interpreted only if the mechanics of elastic wave propagation through such periodic structures is well understood. With this application in mind it is conceptualized that any geometrical surfaces can be represented as superposition of multiple sinusoidal surfaces in the frequency domain. A theoretical model is presented to simulate the wave propagation in sinusoidally corrugated cylindrical wave guide. Wave function expansion method is employed to formulate the stress and displacement potentials with all possible travelling wave combination under the Bloch-wave frame work. Using Helmholtz decomposition, the potentials are substituted in to the stress and displacement functions and further substituted in to the governing differential equation. Traction free boundary conditions (BC) are enforced for guided wave propagation and the BC equations are integrated over the period of corrugation after multiplying the orthogonal eigen modes. Eigen solution was obtained and the dispersion curves are presented in this presentation, which shows clear indication of stop bands, frequency trapping and negative group velocity in the structure as a function of corrugation depth and period.