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Vibration-based piezoelectric energy harvesting has received significant attention recently due to its ability to convert vibration energy from the surrounding environment into electric energy to power wireless sensors. In this work, two typical types of vibration sources, that is, engine-induced floor vibration and train-induced bridge vibration, are considered. The array of piezoelectric energy harvesters (PEHs) is adopted to harvest the energy of vibration with different frequencies. The aim of this work is to give a stable system-level modeling method and present a method to select operating point for designing energy harvesters connected with nonlinear energy harvesting circuits under complex excitations. The system-level modeling method is based on Krylov’s subspace model order reduction algorithm. With the help of this method, the harvester can be modeled using conventional finite element software and co-simulated with nonlinear circuits at a system-level. The proposed method is validated using equivalent circuit method, equivalent impedance method and experiment results, and then employed to investigate the performances of harvesters under typical real vibrations. Finally, design suggestions for PEHs under different types of vibration sources are presented.

In this work, a theoretical model is established for piezoelectric energy harvesting from pavement subjected to a moving vehicle. The pavement is simplified as a Bernoulli–Euler beam resting on a Winkler foundation. The quarter car model is adopted to represent the vehicle–pavement interaction. The dynamic response of the pavement is derived by the modal superposition method. The voltage output is then explicitly obtained by solving a first order differential equation that describes the electrical behavior of the piezoelectric harvester. Additionally, a numerical parametric study is conducted based on the proposed model to investigate the effects of several important factors such as the vehicle types, speed, external resistive load, the arrangement of harvesters and the road surface roughness on energy output. The results show that there is an optimal distance between piezoelectric transducers to improve the efficiency of energy harvesting and the estimate formula of optimal distance is also recommended to conduct the layout of the transducers.

To break the limitation of large mass required for low-frequency topologically protected interface modes (TPIMs), a novel inertial amplified topological metamaterial beam is proposed in this work. Detailed analytical and numerical studies are conducted to investigate the dynamic characteristic of this system. The Dirac cone (DC) is formed at the boundary of the Brillouin zone through the zone-folding method. Thanks to the inertial amplification mechanism, the lower-frequency DC and wider local resonance bandgaps (LRBGs) are obtained without sacrificing total stiffness or increasing total mass. Besides, the DC and LRBG can be tuned effectively by the arm length ratio of the lever. In order to realize the TPIM, two topologically distinct supercells are constructed by space modulation of resonators. Transmission simulation confirms the existence of TPIM between two domains with different topological properties. The energy concentration of TPIM is quantified by the quality factor. Moreover, the tunability and robustness of TPIM are also verified. Besides, to further enlarge the response area of TPIM, the sandwich structure is proposed. Although the peak displacement is reduced with the enlargement of response area, the displacement is still well confined within the sandwich layers. This novel inertial amplified topological metamaterial beam is expected to promote the application of topological devices, especially in the low-frequency lightweight challenging conditions.

A detailed investigation is carried out to investigate the use of periodic piles as wave barriers for Rayleigh wave isolation from the perspective of periodic theory in solid state physics. Specifically, this study tries to figure out two questions: At what frequency can the Rayleigh wave be blocked by multi-rows of piles? And in what way does the Rayleigh wave decay? From above point of view, the Biot's theory and Floquet-Bloch theory are employed to simplify the analysis of the pile-soil system. Based on the derived formulation, the attenuation zone of Rayleigh waves is calculated by dispersion analysis using finite element method in three-dimensional contexts. Through comparison with harmonic response, it is found that the frequency range of Rayleigh wave reduction and the screening capability agree well with the theoretical attenuation zone and the attenuation coefficient, respectively. It is concluded that the dispersion analysis provides basic information for Rayleigh wave isolation using piles, including the frequency range and the form of decay. The present investigation could open up new horizons for the design of wave barriers.

Wave barriers have been commonly used to reduce impact of ambient vibrations. In this paper, inspired by the concept of the invisibility cloak and Fermat’s principle, a new type of wave barrier, named as wave guided barrier, is proposed to effectively isolate areas of interest (e.g., buildings) from vibrations due to antiplane elastic waves. This new wave guided barrier is made of anisotropic metamaterial with layered structure and can guide the elastic waves to propagate along specific direction. Wave propagation characteristics of anisotropic metamaterial are first derived. Then, a specific wave guided barrier is designed. The designed wave guided barrier only uses two materials commonly used in practical engineering. Numerical results from both frequency domain and time domain analyses showed that the wave guided barrier can effectively isolate antiplane elastic waves.

Urban trees are often planted in a periodic arrangement in space. This study takes urban trees as natural metamaterials. Based on the metamaterial theorem, a three-dimensional unit cell is used to represent the entire forest, and finite element analysis via COMSOL software is implemented to identify dispersion relationships. The surface-wave band gaps of urban forests are identified using the sound cone method and strain energy method. The influences of soil elastic modulus, tree spacing, trunk radius, and tree height on band gaps are discussed. Finally, a three-dimensional simulation model is established to verify the effect of urban trees on vibration reduction. The results show that numerical frequency-reduction zones are consistent with theoretical surface-wave band gaps. An increasing soil modulus results in a wider and higher-frequency band gap. Urban forests with larger trunk diameters and smaller tree distance can generate lower-frequency and wider band gaps. It is beneficial to obtain low-frequency band gaps with increasing tree height. A manmade engineered array of trees can be designed with Rayleigh wave band gaps at a low frequency of ≤80 Hz. This study provides a new concept for the quantitative design of urban forests to reduce ground vibration in specific frequency ranges.

Seismic surface wave mitigation using metamaterials is a growing research field propelled by intrinsic theoretical value and possible application prospects. Up to date, the complexity of site conditions found in engineering practice, which can include layered stratigraphy and variable water table level, has been discarded in the development of analytical frameworks to favor the derivation of simple, yet effective, closed-form dispersion laws. This work provides a further step towards the analytical study of “seismic metasurfaces” in real site conditions considering the propagation of Rayleigh waves through a layered porous substrate equipped with local resonators. To this aim, we combine classical elasticity theory, Biot’s poroelasticity and an effective medium approach to describe the metasurface dynamics and its coupling with the poroelastic substrate. The developed framework naturally includes simpler configurations like seismic metasurfaces atop homogeneous dry or saturated soils. Apart from known phenomena like wave-resonance hybridization and surface wave band gaps, we predict the existence of an extended frequency range where surface waves are attenuated due to energy leakage in the form of slow pressure waves, as a result of the fluid-solid interaction. Besides, we demonstrate that the surface wave band gap and the related surface-to-shear wave conversion is robust to variations in the water table level. Conversely, when the dry and saturated layers have different material parameters, for example, due to different porosity ratios, the surface-to-shear wave conversion can be accompanied by the excitation of higher-order surface modes, which remain channeled below the metasurface. These analytical findings, augmented and confirmed by numerical simulations, evidence the importance of accounting for fluid-solid interaction in the dynamics of seismic metasurfaces.

This paper proposes a novel inertial-amplification-mechanism (IAM) to enhance the vibration mitigation performance of the classical tuned mass damper (TMD). To this aim, the IAM is coupled to a standard TMD to form a so-called IAM-TMD. Analytical derivations are developed to extend the theory of the classical TMD to the IAM-TMD. Next, H∞ and H2 optimizations are performed and closed-form solutions for the optimal parameters of the IAM-TMD are obtained. Parametric studies are conducted to evaluate the influence of the geometrical configuration of the IAM system on the performance of the IAM-TMD. Finally, numerical simulations are performed to validate the efficiency of the IAM-TMD. In details, time history analyses of a structure without TMD, with TMD, and with IAM-TMD under harmonic and earthquake ground motions are computed and compared. Results show that when using the classical TMD, dynamic responses of the primary structure are suppressed, but the responses of the absorber are relatively large. Conversely, when using the IAM-TMD, dynamic responses of both the primary structure and the absorber are mitigated at the same time.

In this work, the periodic structure theory is used to analyze the vertical vibration properties in periodic frame structures. The simplified model of the periodic unit cell is built, and governing equations for vertical vibration/waves propagation in the infinite system are derived. With the help of the state space transfer matrix method/SS-TMM, governing equations of the considered system are solved, from which the dispersion curves are obtained and attenuation zones are observed. Numerical simulations are conducted to investigate the dynamic property of the finite periodic frame structure. It is found vertical vibrations are propagated in frame structure selectively. This filtering effect could be used to isolate harmful environmental vibrations.

Periodic structure has an inhibitory effect on the propagation of elastic waves when their frequencies fall in the attenuation zone. Using this property, this work proposes a new kind of periodic layered slab track structure to mitigate the vibration caused by rail transit. First, combining the elastic wave theory and the Bloch theory, dispersion curves of the layered periodic structure are calculated, and the attenuation zones are obtained. The geometrical and material parameters of the present periodic system are optimized. Second, the theoretical model of the vehicle-rail-periodic slab track coupled system is developed. The correctness of the coupled system is verified through a comparison study. The displacement of the slab track is analyzed to guarantee the stiffness of the structure. Third, the rail harmonic disturbance is introduced to simulate the wheel–rail irregularity, and dynamic response analysis of the coupling model is carried out. Vibration reduction properties of the periodic layered slab track are studied both in frequency and time domains. For the reason of comparison, a floating slab track is also considered. Numerical results show that the periodic layered track can reduce the vibration effectively.

Disposition of artificial boundary condition (ABC) is important in numerical analysis of elastic waves propagating in infinite medium. A variety of ABCs have been proposed targeting different applications. However, the relatively high complexity or unsatisfactory accuracy of some of the methods make it difficult to broadly apply those boundaries. In this paper, a new ABC called material damping layer boundary (MDLB) is proposed, which not only ensures high accuracy and is easy to implement but also has a wider range of applications. Firstly, based on the u-U formulation of Biot's theory and the Kelvin damping model, the MDLB suitable for saturated porous media is constructed by introducing monotonically increasing material damping into the constitutive equations. Secondly, the MDLBs suitable for both 1D and 2D problems in single-phased media are degenerated directly from that for saturated media by neglecting the porosity. The attenuation functions of MDLB are recommended and the effects of the parameters of the attenuation functions on the performance of MDLB are investigated. It is found that the proposed MDLB could produce tremendous absorbing ability. In addition, the region for choosing the parameters of the attenuation functions is quite large, which makes the use of MDLB very convenient in many practical numerical simulations. Finally, comparisons with other ABCs are conducted and the better performance of the proposed MDLB are demonstrated.

The purpose of this study is to investigate surface-wave isolation by periodic piles from the perspective of attenuation zones. There are three major components. The first is the dispersion equation, which is derived based on periodic theory of solid-state physics. The second component is the main new part of this paper. Finite element method is adopted to calculate the dispersion relation and attenuation zones for surface waves in a periodic pile and layered soil system. Moreover, effects of geometric parameters on attenuation zones and the amplitude reduction spectra are thoroughly investigated. As a result, harmonic responses show that the isolation region on amplitude reduction spectra is consistent with the theoretical attenuation zone. The third component is the feasibility of ground vibration isolation by periodic pile barriers, which is verified in the time domain by investigating train-induced ground vibrations. Using the concept of attenuation zone, one can manipulate the propagation and attenuation of surface waves artificially. This work provides a new insight into the design of periodic piles as wave barriers.

Piezoelectric energy harvesting from vehicle-bridge coupling vibration is tested in this work. Firstly, a vehicle-bridge coupling platform is introduced, and the dynamic response of the bridge is measured and analyzed. Based on the vibration characteristics of the coupling platform, two piezoelectric energy harvesters (PEHs) with different fundamental frequencies are designed and manufactured, denoted as PEH-1 (designed with the natural frequency of the bridge) and PEH-2 (designed with the frequency of vehicle-bridge coupling vibration). The electromechanical characteristics of the PEHs are tested experimentally. Then, the voltage outputs of the PEHs are measured under nine different cases and the energy harvesting performance of the PEHs are discussed. Finally, the influences of the resistance load on energy harvesting are analyzed theoretically. Experimental results show that the voltage output of PEH-1 has its peaks when the vehicle enters into or leaves the bridge, and is almost zero when the vehicle moves on the bridge. The voltage output of PEH-2, by contrast, is still obvious when the vehicle moves on the bridge. The experimental results also show that more energy can be harvested when the PEHs are installed at the middle of bridge. An interesting result is found. The harvested energy is different even if the PEHs are installed at two symmetric positions of the bridge.

Because of computation difficulties, investigations about the complex band structures and the evanescent wave modes in phononic crystals are very limited. In this paper, a novel k ( ω ) method, referred to as the Extended Differential Quadrature Element Method (EDQEM), is successfully developed to investigate the complex dispersion relations and the evanescent wave modes in periodic beams. At first, based on the Bloch-Floquet theorem and the two widely used beam theories, i.e., the Euler-Bernoulli beam theory and the Timoshenko beam theory, the EDQEM is developed to solve the dispersion equations of flexural waves in periodic beams. Comparisons with other related investigations are conducted to validate the correctness of the proposed method. Furthermore, considering three important factors, the shape of the unit cell, the pattern of the sampling point as well as the number of the sampling point, the convergence of the proposed method is investigated. Second, with the help of the EDQEM, complex dispersion relations of periodic beams are investigated and wave mode analysis is conducted, from which all possible waves, including propagative waves, purely evanescent waves and complex waves, in the complex dispersion curves are discussed. It is found that complex wave modes in periodic beams arise from two situations: (1) at the boundary of the first Brillouin zone and (2) within the first Brillouin zone. These complex wave modes are the transition modes between two propagative waves, or between the propagative wave and the complex wave. When the damping effect is included, all waves in periodic beams transfer into the complex waves. And, band gaps are not truly apparent anymore.

Single in-filled trench barriers have been widely investigated to mitigate ground vibrations. However, investigations on the application of multiple rows of in-filled trenches are very limited. This paper investigates the attenuation of surface waves by periodic geofoam-filled trenches in single-phased elastic soil deposits. First, a field test of train-induced ground vibration is carried out, from which the corresponding acceleration record and main frequency are obtained. Second, attenuation zones for surface waves in periodic geofoam-filled trenches are studied based on the periodic theory of solid-state physics. Finally, a numerical model for ambient vibration isolation is built under the conditions of plane strain, and the responses are performed both in frequency domain and in time domain by finite element method. The screening effectiveness of the proposed wave barrier is studied by conducting an extensive dimensionless parameter investigation. Results show that the proposed periodic geofoam-filled trenches can attenuate surface waves effectively, when the frequencies of surface waves are located in the attenuation zones. The present study provides a new concept for designing periodic in-filled trench barriers to mitigate ground vibrations.

A type of novel embeddable spherical smart aggregate (SSA) has been developed successfully in the latest work. The SSA is formed by encapsulating a radially polarized spherical piezoceramic shell with epoxy resin and a spherical ultra-high performance concrete (UHPC) case, and its omnidirectional actuating and sensing capabilities in concrete structures have also been verified. Comparing to the early developed compressive and shear mode smart aggregates (SAs) that can only generate or receive the stress wave in a single direction, the SSA can generate or receive omnidirectional stress waves, which has a promising application in structural health monitoring of civil engineering structures. To understand better the performance of the SSA and guiding further its optimized design, a theoretical model is proposed to study the vibration characteristics of the SSA in this paper. Based on the linear theory of piezoelasticity, the dynamic analytical solution of an SSA subjected to a harmonic voltage excitation is derived, and the analytical expression of the electrical impedance is obtained. Furthermore, a parametric analysis is conducted to discuss the effects of the outer radius of the UHPC case, the thickness of the epoxy layer, the inner radius of the piezoceramic shell, the piezoelectric material types, and the piezoelectric material parameters on the vibration characteristics, such as the first and second resonance and anti-resonance frequencies. Furthermore, comparisons with some special cases in the previous work, the ANSYS simulation results and the experimental data of the SSA are also given to validate the reliability of the proposed model. The present investigations contribute to the comprehensive understanding of the vibration characteristics of the SSA, which is helpful to design the working frequencies range of the SSA.

In the existing electromechanical model for cantilevered piezoelectric energy harvesters, the electric field in the piezoelectric layer is generally considered as a uniform field. In the present study, it is found and described in detail that the oversimplified uniform electric field assumption could lead to critical issues regarding the fundamental of piezoelectricity. Further, inspired by the electric field distribution obtained using the exact solutions for plane problems, a non-uniform electric field is proposed. Accordingly, an improved distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters including both unimorph and bimorph configurations is established, in which the bending stiffness term involved in the electromechanical governing equations is explicitly corrected, and the aforementioned critical issues are perfectly addressed. The present proposed non-uniform electric field is then validated by comparing the static analysis results of the present model with finite element results and the results obtained using exact solutions for plane problems. Dynamic analysis of the present model is also conducted, and the electromechanical characteristic corrections for the traditional distributed parameter model adopting uniform electric field assumption is carried out including bending stiffness correction, resonant frequency correction, voltage output correction and power output correction.

This article formulates the problem of vibration-based piezoelectric energy harvesting from a simply supported beam subjected to moving harmonic load excitations. The piezoelectric harvester can be installed at arbitrary position of the beam. The acceleration of the beam is obtained by the mode superposition method. It is also the base acceleration input of the energy harvester to couple with the generalized electromechanical equations for moving harmonic load excitation. An exact analytical solution is then presented for the problem. Furthermore, the result expressions for the coupled mechanical response and the electrical outputs are derived, and a closed-form exact expression is obtained for the undamped case. Additionally, a numerical parametric study is conducted to highlight the effects of load frequencies and the installing positions of harvesters on electrical outputs. The phenomenon of two energy peaks is observed and its physical mechanism is explored in detail. The research results demonstrated an effective strategy to design broadband vibration energy harvesters used in bridge systems.

Dispersion differences and consistency of artificial periodic structures, including phononic crystals, elastic metamaterials, as well as periodic structures composited of phononic crystals and elastic metamaterials, are investigated in this paper. By developing a $K(\omega )$ method, complex dispersion relations and group/phase velocity curves of both the single-mechanism periodic structures and the mixing-mechanism periodic structures are calculated at first, from which dispersion differences of artificial periodic structures are discussed. Then, based on a unified formulation, dispersion consistency of artificial periodic structures is investigated. Through a comprehensive comparison study, the correctness for the unified formulation is verified. Mathematical derivations of the unified formulation for different artificial periodic structures are presented. Furthermore, physical meanings of the unified formulation are discussed in the energy-state space.

This work investigated the dispersion curves of phononic crystals with quasi-Sierpinski carpet unit cells via improved plane wave expansion method. The position vector derivative method was applied to generate Sierpinski and quasi-Sierpinski carpet unit cells. Wave dispersion mechanisms of fractal phononic crystals were investigated by calculating the vibration modes of unit cells. The results show that (quasi-)fractal phononic crystals are benefit for obtaining multiple and wider band gaps, especially for the second stage case. For quasi-Sierpinski carpet unit cells, the multiple band gap feature becomes much more obvious due to the increase of the filling fraction. Numerical analysis of a finite quasi-fractal phononic crystal indicated the potential application of phononic crystals with quasi-Sierpinski carpet unit cells.

In this study, the propagation of surface waves in both one- and two-dimensional periodic structures is investigated. By combining finite element method, an energy distribution parameter is defined and a new method for identifying surface wave modes is suggested. The effectiveness of this new method is validated by comparing with some related studies. Furthermore, this method is used to study a two-dimensional periodic pile-soil system based on a three-dimensional numerical model and the dispersion curves of surface waves are easily obtained. To show the efficiency of attenuation zone, the responses of a finite periodic pile-soil system to a surface wave input are simulated. Results demonstrate that the region of excitation frequency in which vibration reduction occurs is fully consistent with the theoretical attenuation zone for surface waves. The advantage of this method is that it makes the study of surface waves more convenient and accurate.

A layered periodic structure is proposed to construct a periodic wave barrier, which is defined by extended typical cells consisting of two different components. The periodic structure with reasonable design has attenuation zones (AZs) which can block wave propagation. The surface-wave dispersion curves and material/geometric parameters of layered periodic structures were investigated using finite element method. A typical three-dimensional simulation model was applied to verify the efficiency of the proposed periodic wave barrier in terms of ground vibration isolation. The results showed that simulated frequency zones of vibration reduction are consistent with the theoretical surface-wave AZs, and that periodic wave barriers can greatly reduce train-induced vibrations.