General expressions that govern free wave propagation in an infinite mono-coupled continues periodic system with one of its periodic constraints displaced have been set up and applied to study free flexural waves in beam-type system resting on simple supports with one of the periodic supports displaced to different locations. Attenuation of free waves that occur even in the propagation zones varies with the frequency and the support displacement and it is very large near the bounding frequencies of the propagation zones, in general. Variation of resonance frequencies ( in various resonance zones) with support location has also been studied and the conditions have been identified under which the system with displaced support behaves like a periodic system and does not attenuate free waves. The study is quite useful in introducing disorders for the control of vibrations.
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