Locally Resonant Structures: Band Gap Tuning And Properties Of Vibration And Noise Reduction

In the past few years, the new concept of “locally resonant phononic crystals” and“acoustic metamaterials” developed in the frontiers of acoustical physics providedsome new ideas for the control of vibration and noise of engineering structures. Byanalogy with locally resonant phononic crystals and acoustic metamaterials, locallyresonant periodic engineering structures (called “locally resonant structures” in thisdissertation) can be constructed by attaching periodic arrays of local resonators tostructural waveguides such as rods, beams, plates, etc. Some initial studies have shownthat locally resonant structures can exhibit notable elastic wave band gaps, andstructural vibrations can be significantly attenuated within the frequency ranges ofband gaps. These studies provide a novel approach to control vibration and noise ofengineering structures. However, to achieve practical applications of locally resonantstructures in engineering, there exist still many important problems required to beexamined, such as the performance prediction, behavior tuning, mechanismsexplanation, as well as the lightweight and broadband design.The purpose of this dissertation is to investigate some crucial theoretical andtechnical problems systematically to promote the applications of locally resonantstructures in the field of vibration and noise control. The following three aspects havebeen considered:(1) the methods for calculating band gaps and the methods forpredicting vibration/noise properties of locally resonant structures;(2) the tuningbehavior of band gaps and the underlying band-gap formation mechanisms;(3) themethods for broadening band gaps and the study of resulting performance ofbroadband vibration/noise reduction. The main findings of this dissertation are listed asfollows:1. A wave/spectral element method is proposed to predict vibration transmittanceof general locally resonant rods/beams, and a plane wave expansion method isdeveloped for the calculation of band gaps and sound transmission properties ofgeneral locally resonant thin plates. These methods are provided as efficient tools forthe study of band gap and vibration/noise reduction properties of locally resonantstructures.2. The tuning band gap behavior of locally resonant structures by changing designing parameters is analyzed in a systematic manner, and some valuable new bandgap phenomena and effects have been discovered. It is shown that two types of bandgaps (locally resonant and Bragg band gaps) can exactly couple together to form acombined super-wide band gap. It is also found that when the location of two types ofband gaps is tuned to be very close to each other, not only that the locally resonanteffect can broaden Bragg band gap, but also that the Bragg scattering effect can widenthe locally resonant band gap. In addition, it is found that the resonance frequency oflocal resonators can appear in a Bragg band gap, and even more surprisingly, in a passband.3. The band gap formation mechanisms of locally resonant structures have beenclarified in depth. A number of explicit analytical design formulas are derived to enablean exact prediction of the dependence of band edge frequencies on the designingparameters of locally resonant structures. Furthermore, explicit formulas are alsoprovided to enable a direct determination of the conditions of coupling or transitionbetween two types of band gaps. These results provide guidelines for the band gapdesign in locally resonant structures.4. Three band gap broadening methods are proposed, respectively based on theband gap coupling mechanism, the design of disordered structural parameters, and theutilization of multi-resonant local resonators. These methods provide technical supportto realize lightweight locally resonant structures with broadband vibration/noisereduction performance.5. For the first time, the sound transmission loss (STL) behavior of locallyresonant thin plates is investigated. It is found that, under the condition ofsubwavelength lattice constant, if the resonance frequency of local resonators is tunedto the mass-law region of sound transmission for the host plate, the locally resonantplate can achieve much higher STL than a homogeneous plate with the same surfacemass. While, if the resonance frequency is tuned to the coincidence region of soundtransmission, the locally resonant plate can break the coincidence effect, resulting in asignificantly increased STL over the whole coincidence region. These properties are ofgreat interest for the application of locally resonant plates in the noise control field.In summary, this dissertation is concerned with some crucial theoretical andtechnical problems involved in the investigations and applications of locally resonantstructures for the purpose of reducing structural vibration/noise. The maincontributions of this dissertation include:1) some efficient methods are developed for the calculation of band gaps and for the prediction of vibration/noise properties ofgeneral locally resonant structures;2) the dependence of band gap behavior on somekey designing parameters is explored, and the underlying band gap formationmechanisms are clarified;3) several band gap broadening methods are proposed, and anumber of design formulas, principles and suggestions are provided. The results of thisdissertation present significant theoretical foundations and technical guidelines tofacilitate the application of locally resonant structures in reducing structural vibrationand noise.