Thanks to the use of modern intelligent materials, such as composites consisting of piezoceramic fibers embedded in epoxy resin and covered with alternating electrodes, electroactive polymers, dielectric elastomers, magnetostrictive composites with epoxy resin or ferromagnetic alloys with shape memory, it is possible to control the geometry or properties of materials using pressure, external magnetic or electric fields. The paper analyzes multilayer quasi-one-dimensional phononic structures in which the selected layer is made of a material with time-varying acoustic impedance. The influence of the shape of the material properties changes over time (square wave, triangle wave, sawtooth wave) on the propagation of mechanical waves in the structure is analyzed.