Exp. Theo. NANOTECHNOLOGY 3 (2019) 19-25 https://doi.org/10.56053/3.1.19 Phononic band gap with/without a defect layer in periodic and quasi- periodic structure Arafa H. Aly*, Ahmed Mehaney, Shrouk Eid Physics Department, Faculty of Science, Beni-Suef University, Egypt *) Email: arafa.hussien@science.bsu.edu.eg, arafa16@yahoo.com Received 28/8/2018, Accepted 25/12/2018, Accepted 15/1/2019 In the present paper, we focus on the ability of phononic crystals to treat the different elastic wave's frequencies at the same structure. Changing the periodicity of the structure from perfect and defect structure can modify the width/position of phononic band gaps. By comparing between one, two and four defect layers inside perfect ones, interesting results concerning the localized peaks with the band gaps were obtained. Since the width of band gaps and the number of localized peaks is increased by increasing the defect layers. Moreover, we pay more attention in comparing the band gaps between periodic and quasi-periodic structures. A multifunctional PnC structure could be obtained depend on periodicity and materials types were investigated and discussed. These results may be of potential importance in many engineering applications such as mechanical filters and vibration isolation devices. Keywords: Phononic band gap; Defects; Crystal. 1. INTRODUCTION Phononic Crystals (PnCs) are periodic composites structures can produce exceptional control over the propagation of elastic and acoustic waves [1-6]. The term ''phononic'' was derived from the name '' phonon'' which considered a quantization of lattice vibrations. PnCs was proposed in analog to photonic crystals, which have been introduced to control electromagnetic waves propagation [7-8]. PnCs can manipulate wavelengths from centimeters to nanometers ranges [9-10]. Therefore, PnCs were able to control, transmit and attenuate the propagation of sound, ultrasonic, hypersonic and heat frequencies. The intellectual property in PnCs is the existence of the so-called phononic band gaps. Within these band gaps, all frequencies are not allowed to propagate, while any frequencies outside band gaps are free to propagate. Based on these novel properties of PnCs, many different applications can be introduced in the field of