This book derives physical models from basic principles, studies the effect of equivalent models on the dynamic characteristics of phononic crystals and acoustic metamaterials, and analyzes the physical mechanisms behind vibration and noise reduction. It first summarizes the research status of vibration and noise reduction, and research progress in phononic crystals and acoustic metamaterials. Based on this, one-dimensional periodic beam, two-dimensional thin plate with circular hole, and corresponding gradient structures are introduced, and their dynamic characteristics are discussed in detail. Therefore, different equivalent methods for different models are proposed through theoretical analysis, modal analysis and transmission rate analysis. Finally, a Helmholtz-type acoustic metamaterial, i.e. a multi-layer slotted tube acoustic metamaterial, is studied. Aiming at the low-frequency band gap of this model, a theoretical model for solving the inverse problem of acousto-electric analogue equivalent is proposed, and the effect of structural parameters on the low-frequency band gap is studied using this equivalent model. 
This book closely revolves around how to conduct equivalent research on artificially fabricated periodic structures. The methods and conclusions presented in this book provide a new theoretical basis for the application of artificial woven periodic structures in the field of low-frequency vibration reduction and noise reduction and are also an innovation in the discipline of vibration and noise control. This book is suitable for undergraduate students, graduate students and teachers in vibration and noise majors in universities, and can also provide references for engineering and technical personnel in related fields. 

Nansha Gao is currently Associate Professor in School of Marine Science and Technology, Northwestern Polytechnical University, P. R. China. He received the B.E. degree in process equipment and control engineering from Northwest University, China, in 2010, the Ph.D. degree in mechanical engineering from Xi'an JiaoTong University, China, in 2016. Prof. Gao has published over 40 International SCI. journals; 22 International and Domestic patents; and 3 academic monographs. He presided 8 research funds, including National Natural Science Foundation of China, et al. Prof. Gao's research interests includes materials physics, sound wave control, and acoustic metamaterial design.
Jie Deng serves as Associate Professor in Northwestern Polytechnical University. He received the PhD degree from the School of Engineering, Universitat Ramon Llull, Spain, in 
2020, and won the title of excellent doctoral dissertation (Cum Laude). In 2021, he received 
the second PhD degree from the School of Mechanical and Transportation Engineering,
Chongqing University, China. He has authored and coauthored over 20 journal papers. He
mainly studies the vibration and noise control, bending wave manipulation and vibration energy harvesting of acoustic black hole structures, as well as the theoretical research and Structural design of underwater and air vibration and noise control.