Band-gap Stucture Design For Reducing Vibration And Sound And Topology Optimization Of Anechoic Coating

Control of low-frequency and broadband structural vibration and sound has gained increasing attentions of researchers in the field of ship engineering.The band gaps found in periodic structures are able to inhibit wave propagation in certain frequency ranges,which provide a new way to reduce structural vibration and sound.Design of periodic plate and beam structures using band gap properties are of great significance to solve technical challenges and key problems in vibration suppression and sound attenuation as they are usually regarded as fundamental components to construct ship structures.Even though previous studies have provided a novel approach to design periodic plates and beams to reduce structural vibration and sound,there are still much more efforts should be paid to control low-frequency wave propagation and achieve lightweight and broadband design.In addition,it was rarely found in previous studies to predict sound transmission loss of double-panel structures combined with the concept of band gaps.Therein,this dissertation develops the structural design of periodic plate and beam and the sound insulation design of double-panel structures to promote low-frequency and broadband attenuation performance using band gap properties.Anechoic coatings,which are general attached to the surface of submarine to promote the stealth technology,can also be regarded as periodic structures.Since the ability of absorbing low-frequency and broadband sound has been recognized as a technical feature of anechoic coating design,this dissertation aims to find an optimal layout of anechoic coating with limited thickness to satisfy the sound absorption requirement.The purpose of this work is to investigate low-frequency and broadband problems systematically to promote the performance of periodic structures in the field of vibration suppression and sound attenuation.Based on this idea,designs of periodic structures focus on band gap properties and sound absorption characteristics are carried out in this dissertation.Plate and beam periodic engineering structures that can suppress wave propgation at low-frequency while retaining broadband enhancement are expected to construct by adjusting band gap properties,such as increasing bandwidth of low-frequency gap,enhancing attenuation degree of flexural waves and inducing multiple stop bands,etc.In addition,we introduce the concept of band gaps to the calculation of sound transmission in double-panel structures with poroelastic cores,which obviously expands the application of band gaps innoise control field and improves the ability of double-panel structures to isolate low-frequency and broadband incident waves.For anechoic coatings,which regard sound absorption performance as an important indicator,this dissertation determines to combine periodic structure theory and topology optimization method to establish the optimization model.This optimization model directly regards material distribution as design variable and aims to find an optimal material layout with low-frequency and broadband sound absorption targets.The main content and results are obtained as follows:(1)Design of periodic plate and beam based on localized resonant mechanisms.The proposed local resonant plate consists of negative modulus acoustic metamaterial microstructures as its local resonators.The proposed local resonant beam is constructed by transforming the underlying host medium that is general made up of one type material to the host medium with multi-phases materials.These periodic structures are expected to show the ability of creating gaps with multi-frequency bands,wide bandwidth and high attenuation degree.The complex band diagrams obtained by the transfer matrix method and the plane wave expansion method demonstrate the effectiveness of these structures on tuning flexural wave propagation.(2)Generating ultra wide low-frequency gap for transverse wave isolation via inertial amplification effects.The effects of enhanced effective inertial are more suitable to complete the lightweight and broadband design compared to other generation mechanisms.This dissertation extends the inertial amplification concept to the design of phononic beams for transverse wave attenuation in continuous structures.The proposed one-dimensional system consisting of the elastic beam and periodically attached inertial amplification mechanisms is expected to show an ultra wide low-frequency gap.We derive the complex dispersion relation via a combination of the Bloch theorem and the transfer matrix method.The numerical results show that the periodic beam can produce an ultra wide gap at low-frequency to stop wave propagation.One can also find that the anti-resonance frequency generated by the hybridization between the inertial amplification mechanism and the underlying beam is able to clamp the motion of the base foundation,resulting in wave suppression in the periodic beam.The comparison with local resonance gap at low frequency further demonstrates the superior performance of the inertial amplification induced gap,which indicates that the proposed beam has the ability to isolate transverse wave over exceedingly broad low-frequency range.(3)Reduction of sound transmission of double-panel structures with poroelastic cores using the localized resonant mechanisms.The phenomenon of blocking elastic wave propagation due to the localized resonant mechanisms has been widely applied in single-wall panels to realize the application of sound insulation,while the double-panel structures that exhibit more superior sound insulation performance are rarely considered.In this context,this work determines to apply the concept of acoustic metamaterials in the double-panel structures to enhance the sound insulation performance.The poroelastic materials are set as inner cores and are modeled by Biot's theory.The sound transmission loss of double-panel structures with local resonators is predicted by the effective medium theory and plane wave expansion method when the resonator array satisfies the subwavelength assumption and not.Compared to a conventional double-panel structure,the double-panel structure with localized resonance mechanisms has more design space and is able to achieve sound insulation enhancement at low frequencies due to the tunable local attachments..(4)Topology optimization of anechoic coating for maximizing sound absorption.A method combining the Bloch theory and finite element method is adopted to analyze the sound characteristics of the anechoic coating.Based upon the idea of SIMP approach of topology optimization method,the viscoelastic material layer is set as design domain and the relative density of elements in the design domain is considered as design variable.The optimization model is constructed to obtain the optimal layout,with the maximum absorption performances under set frequency and frequency band as targets.Sensitivity information of objectives with respect to design variables is also presented for the utilization of the typical gradient based method.The numerical examples show that the optimal results enhance the sound absorption performance at low-frequency and over wide band significantly,which demonstrates the validity of the proposed topology optimization methods.The numerical examples also provide that the resonance is the main absorption mechanism of the optimal material distributed configuration.When local resonance of the structure is induced,more incident wave energy is dissipated by the viscoelastic medium,thus the sound absorption ability of the anechoic coating is enhanced.