Dynamic Characteristics of Phononic Metamaterials with Amplified Bandgaps for Wave Manipulation and Seismic Shielding Applications

Abstract

Vibration and noise are ubiquitous and remain a fundamental problem in engineering sciences over a wide range of disciplines, scaling from nano/micro mechanical/electromechanical systems to hazardous earthquakes, posing risks to lives and property of mankind. The advancement of present and future societies is dependent on the sustainable, safe, efficient, and environmentally friendly technologies. Radically new approaches in civil infrastructure, transportation and energy production industries have substantially modified the urban and interurban vibrations and acoustic landscapes. Natural disasters, such as climate change and earthquakes, are other fundamental issues that require immediate and sustainable solutions. Vibration and noise mitigation are amongst other major challenges that need to be resolved. Breakthrough technologies and efficient approaches to cater these challenges are an essential and demanding field of research.

Amongst various approaches developed during the last two decades, phononic crystals and acoustic metamaterials have emerged as potential candidates for vibration and noise control due to their peculiar mechanical and dynamic characteristics, that are unattainable from naturally occurring materials. These fantastic wave phenomena are observed in frequency bandgap region where wave propagation is restricted. The primary aim of this thesis was to investigate the specific mechanical and dynamical characteristics of phononic crystals and acoustic metamaterials in both periodic and aperiodic solid structures for both acoustic and elastic waves manipulation. More emphasise was attributed to the amplification/enlargement of bandgap, which is conducive to broadband wave manipulation by means of various approaches, including composite periodic structure designs, lightweight architected lattices, actively controllable piezoelectric shunted array technique, mechanical metastructure designs etc.

The thesis is divided into total of ten chapters. The first chapter comprehensively discusses the scope of the study, defines the problem statement, and highlights the study objectives. The second chapter is centred around the research background. A comprehensive analysis of the historical context, recent progress and governing physical concepts of photonic crystals and electromagnetic metamaterials, phononic crystals and acoustic metamaterials, topological phononic metamaterials, pillared acoustic metamaterials and actively controllable and tunable acoustic metamaterials is performed.

The third chapter includes a detailed theoretical and numerical investigation of the topological properties of one-dimensional (1-D) periodic elastic beam structure. The topological characteristics of elastic beam subjected to bending and longitudinal elastic waves are investigated. Under the conditions of this system, the topologically protected interface modes generation is scrutinised through a set of numerical calculations, formulating the geometric Zak phases of Bloch bands at the centre and edges of the Brillouin zone through the band structure study. Employing the Dirac cone dispersion plot, the mode transition frequency, resulting from the wave mode transition and accidental degeneracy, is identified. The mode transition frequency provides valuable information regarding the existence of interface mode. When the mode transition frequency is prevailing between the bandgaps of topologically distinct phononic beams, the interface modes with wave energy localised at the interface of topologically distinct beams with decaying energy fields away from it are observed. The validation of the aforementioned findings is established through a rigorous theoretical model based on transfer matrix and spectral element methods, and finite element (FE) numerical simulations.

The discussion of the fourth chapter is evolved around the pillared acoustic metamaterials subjected to plane and surface acoustic waves. The chapter is initiated by proposing a multi-resonant pillar-plate model, aimed at enhancing the effective mass density of the system, thus achieving the low frequency wide local resonance bandgap. This is followed by the drilling of periodic array of holes inside the plate to generate the trampoline effect. The inclusion of holes ensures that the plate functions as a compliance base, which intensifies the vibration of the pillar-plate structure. The reduction of the plate area supporting the pillar structure results in the enhancement of the system stiffness property and closing bounding edge of bandgap (optical band) shift towards the higher frequency region. Thus, the multi-resonant structure enhances the effective mass of the resonant system, which facilitates the generation of low frequency bandgap, while the trampoline effect reinforces the system stiffness, broadening the local resonance bandgap by shifting the optical band to higher frequency region. Therefore, the multi-resonant trampoline metamaterial of this research generates the conditions, under which the variation in mass density and stiffness properties of the resonant system is evident. The medium dissipative nature caused by larger material mismatch and material damping further broadened the bandgap by merging the separated local resonance bandgaps, forming broadband vibration attenuation zone spread over the wide frequency range. The subsequent research was dedicated to the examination of the properties of whispering gallery modes induced by hollow phononic pillars upon interaction with surface waves propagation at the surface of semi-infinite half-space. When the frequency of localised cavity modes lies within the bandgap of solid pillars, the robust vibrational energy localisation is observed. The subwavelength waveguiding and wave multiplexing phenomena, caused by the wave energy localisation by cavity modes, are demonstrated. The following context expands on the design of a three-dimensional (3-D) periodic composite layered phononic pillar. The design features incorporate the capability of manipulating both plane and surface acoustic waves. The two-dimensional (2-D) and three-dimensional (3-D) bandgaps induced by composite pillars are analysed. The plane and surface acoustic waves propagation, wave attenuation inside the bandgap frequencies and robust wave energy localisation at the defects are demonstrated.

The fifth chapter provides a detailed summary of the theoretical and numerical investigations, as well as the design and application of seismic metamaterials for seismic shielding of important civil infrastructure. The chapter commences by proposing a composite thin-plate elastic metamaterial to manipulate the antisymmetric Lamb wave at the subwavelength frequency regime. The theoretical and numerical models for the proposed composite plate are developed. The wave dispersion spectra showed the presence of low frequency wide pseudo and local resonance bandgaps. The reported bandgaps are positioned within the seismic frequency range of interest. Further research was assigned to the effects of geometric and material parameters that define the resonant system’s effective mass density and stiffness, which eventually alter the width and position of bandgaps. Lastly, the low frequency Lamb wave attenuation inside the bandgap frequencies is demonstrated by performing the frequency response study. The wave attenuation inside the reported bandgaps is highlighted. The following research point was developed around the thorough study of the surface Rayleigh wave propagation and interaction with resonant modes of the surface resonators. Rigorous modelling methods were employed to investigate the propagation and attenuation of Rayleigh wave by the surface resonators. The wave dispersion spectra of the proposed surface resonator revealed that the wave mode coupling and hybridisation of Rayleigh wave with the longitudinal resonant mode of the surface resonator induce bandgap where no Rayleigh wave propagates at the surface. Near the longitudinal resonant frequency, all the wave modes are unstable dispersive radiation modes that are propagating deep into the substrate. At the later stages the frequency response study demonstrated, that within these radiative mode frequencies, which lie inside the sound cone, the Rayleigh wave deviates from the surface deep into the substrate in the form of bulk compressional and shear waves. Hence, for these particular frequencies no Rayleigh wave tend to propagate on the free surface of elastic half-space. Therefore, the periodic array of surface resonators mitigated the surface Rayleigh wave, ensuring the safety of civil infrastructures. The deviation of Rayleigh wave deep into the ground as bulk shear waves presents a captivating process, as it eliminates the reflection of waves and prevents any potential damage to the surrounding infrastructures. This mechanism is referred to as the wave mode conversion phenomenon in this report.

The third major component of this chapter provides an investigation on the feasibility study on the effectiveness of built-up structural steel sections as seismic metamaterials. Two types of built-up steel sections are proposed, and by means of adopting the wave dispersion study the low frequency extremely wide Rayleigh wave bandgap is evident. The extent of Rayleigh wave attenuation at the free surface is demonstrated via the application of the frequency response and time transient studies. In the fourth and fifth constituents of this chapter rigorous numerical simulations have been utilised to inspect the effectiveness of forest trees in mitigating the ground born low frequency ambient vibrations and seismic waves. The outset of this process was the development of the theoretical and numerical models aimed at achieving the band structures, followed by the examination of surface wave propagation in an array of forest trees. The consecutive activities included a thorough investigation of the surface Rayleigh wave propagation and attenuation for multiple arrangements of forest trees. The primary discussion is constructed around the influence of trees arrangement types on the Rayleigh wave propagation and attenuation. The forthcoming discourse within the chapter considered the effects of tree branches attached to the main stem on the Rayleigh wave bandgap. It has been deduced that the tree branches enhanced the effective mass density of the surface resonators that shift the bandgap to lower frequency region. Both parts incorporate the usage of real-time earthquake records obtained from PEER ground database as an input excitation force, with an investigation on the potentiality of forest trees in mitigating the input signal in the bandgap frequencies.

The sixth aspect of the chapter introduces two types of ground born engineered metabarriers, which are proven to have the sufficient capacity to attenuate Rayleigh wave over broadband frequency range in the earthquake frequency range of interest. The proposed metabarriers integrate a composite design comprised of commonly available construction materials. The study is based on analytical modelling, coupled with extensive real-time 3-D numerical simulations. The effectiveness of proposed metabarriers in attenuating Rayleigh wave over broadband frequency range is substantiated. A detailed discussion on the bandgap generation mechanism and governing physical phenomena for Rayleigh wave attenuation is demonstrated.

The focus of the sixth chapter is directed towards the novel lightweight architected lattice phononic metamaterial, which is competent at inducing the broadband and low frequency multiband vibration attenuation capability. The architected lattice structure consists of sinusoidal shape ligaments connected with a solid circular disc. The disc plays an important role to increase the effective mass density of the periodic lattice, that eventually induces the low frequency bandgaps. The transformation of the straight ligament into the sinusoidal shape ligament enhances the effective stiffness of the periodic system, which drives the closing bounding edge of the bandgap frequency towards the higher frequency region. As a result, it has been observed that an increase in the number of sinusoidal shape/wavelengths of ligament induces the broadband bandgap, while an increase in the radius of circular solid disc opened multiband low frequency bandgap at lower frequencies. The multiband and broadband vibration mitigation characteristics of architected lattice structures are studied for different types of lattice arrangements. Finally, the findings are corroborated by performing low amplitude vibration test on the 3-D printed specimens.

In chapter seven analytical and numerical models were developed to envisage the novel application possibility of acoustic metamaterials in bearing housing. This has been accomplished by embedding the composite structure/inclusion in the bearing housing to mitigate the bearing generated low frequency vibration and noises over broadband frequency range. The process was initiated by proposing a multi-resonant elastic sphere, consisting of coatings of materials with varying stiffnesses. The elastic metamaterials in the bearing housing are applied in five different layers. A continuous frequency bandgap, ranging from 3 kHz to 52 kHz, has been reported, considering the material damping effect. All the bearing generated vibrations and noises, lying inside the bandgap frequencies, diminish. The next steps of the process included the employment of the inertial amplification mechanism to design a composite Euler beam, which is embedded in certain arrangements inside the bearing housing. The bandgap in the composite beam is induced due to the inertial amplification phenomena, where flexural hinge is formed. The vibration attenuation from the periodic array of beams is demonstrated via the frequency response and time transient analyses. This composite beam under the presented conditions has a potential to mitigate all the bearing generated vibration and noise when embedded inside the bearing housing, provided that the frequency of vibrations and noises falls within the bandgap frequencies.

Chapter eight, as a whole, describes the new class of novel monolithic and composite 3-D mechanical metastructure designs and manufacturing, which are capable of inducing the low frequency ultrawide 3-D bandgap. Such an ultrawide bandgap is dependent upon the structural morphology of the metamaterials and the bandgap is induced by the principal of mode separation where global and local resonant modes of the unit cell structure are markedly responsible for the bandgap opening and closing. Analytical and numerical models were employed to evaluate the opening and closing of the bandgap. The wave dispersion study is applied to interpret the mechanism of bandgap generation, where the vibrational energy localisation for global and local resonant modes is distinguished and elaborated. The wave attenuation in the ultrawide frequency region is envisaged by performing frequency response study on a finite array of unit cell structures. These analytical and numerical findings are further corroborated by manufacturing the 3-D printed prototypes of finite array and performing low amplitude vibration tests. In this chapter multiple types of monolithic and composite metastructures were proposed, which are both periodic and aperiodic in their nature.

Chapter nine elaborates on actively tunable and controllable beam type acoustic metamaterials, that can manipulate the flexural wave over broadband frequency region. A theoretical analysis of the dynamic characteristics has been conducted using the proposed design of the array of active beam-type resonators. The piezoelectric shunted array technique is applied to each engineered resonator to actively tune the band structures. The spectral element method assisted in the explicit derivation of the dispersion relation of an infinite system, as well as the wave transmission equation of a finite system. The effects of negative capacitance shunt and negative capacitance enhanced resonant shunt techniques on the band structure and bandgaps are discussed. It has been established that, on the one hand, the negative capacitance shunts can sensitively control the widths and locations of local resonance bandgaps, and on the other hand, when a negative capacitance enhanced resonant shunt is applied, the meta-damping phenomenon emerges, leading to development of extra wide and low-frequency bandgap. The resistance in the shunt induces damping to the system, which alongside the local resonance motion generates the rise to meta-damping behaviour. Such an effect is further enhanced by the negative capacitance, which increases the system electromechanical coupling property. Furthermore, the numerical simulations indicate that such a novel bandgap can be realised only when the negative capacitance is in the proximity of the instability boundary and resistance in a certain region. In addition, the inductance of the shunt can optimise the attenuation performance distribution in the extra broadband bandgap. Particularly, the transmission analyses demonstrate that the attenuation property of such extra wide bandgap is in no way inferior to the general Bragg scattering bandgap. Such an extremely wide and low-frequency bandgap can be implemented in a wide range of engineering applications, such as vibration suppression, sound absorption, acoustic filter, etc.

Finally, chapter ten summarises the findings reported in the previous chapters and forecasts an insight on the possible future outcomes. The research limitations and some potential recommendations for future research and foster research spin-off are also discussed.

Date of Award	26 Jul 2021
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	C W LIM (Supervisor)