Plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading

Free plane wave propagation in infinitely long periodic elastic structures with and without heavy fluid loading is considered. The structures comprise continuous elements of two different types connected in an alternating sequence. In the absence of fluid loading, an exact solution which describes wave motion in each unboundedly extended element is obtained analytically as a superposition of all propagating and evanescent waves, continuity conditions at the interfaces between elements are formulated and standard Floquet theory is applied to set up a characteristic determinant. An efficient algorithm to compute Bloch parameters (propagation constants) as a function of the excitation frequency is suggested and the location of band gaps is studied as a function of non-dimensional parameters of the structure's composition. In the case of heavy fluid loading, an infinitely large number of propagating or evanescent waves exist in each unboundedly extended elasto-acoustic element of a periodic structure. Wave motion in each element is then presented in the form of a modal decomposition with a finite number of terms retained in these expansions and the accuracy of such an approximation is assessed. A generalized algorithm is used to compute Bloch parameters for a periodic structure with heavy fluid loading as a function of the excitation frequency and, similarly to the previous case, the location of band gaps is studied.