Group in Appl. Mech., College of Eng., San Diego State Univ., San Diego, CA 92182
An elastic structure with a series of uniformly spaced structural discontinuities is known to have a unique pass--stop band in the wave-number space. In this paper, an infinite membrane, the simplest type of elastic structure, is selected. The uniformly spaced structural discontinuities are chosen to be composed of a mass-spring system. The solution in wave-number space can be written in closed form. The pass--stop band structure when viewed in the wave number versus kl space resembles a floor tile appearance. The tile appearance is periodic when viewed in the constant k plane, but has a nonperiodic pattern if viewed in the constant l plane. The relative magnitudes of the different bands are presented. If the evenly spaced inhomogeneity is masslike, then the pass-band structure will start with a pass-band at low values of kl. If the inhomogeneity is springlike, then the first band will be a stop band. For a structural inhomogeneity that has a mass--spring behavior, the pass--stop band acquires a more complex structure with a pass-band window of much larger than expected width at the natural vibration conditions of the inhomogeneity.