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This study illustrates the successful achievement of tunable defect bands in one-dimensional defective phononic crystals (PnCs) through the incorporation of piezoelectric defects with synthetic negative capacitances (SNCs) for the first time. The efficacy of SNCs in creating tunable bandpass filters across a broad frequency range is thoroughly examined using the proposed analytical and numerical models. A newly developed electroelastically coupled transfer matrix that incorporates SNCs is presented, considering either series or parallel connection between bimorph piezoelectric elements. Defect band and transmittance analyses are conducted using the transfer matrix and S-parameter methods. Two key findings emerge from this investigation. First, when the total equivalent capacitance of the bimorph piezoelectric elements and SNC becomes zero, the defect band representing the point-symmetric defect-mode shape can be customized throughout the entire phononic bandgap. Second, the constant transmittance value, resembling short-circuit conditions, highlights the remarkable ability of SNCs to tune defect bands without energy dissipation, paving the way for fully tunable bandpass filters. To propel this research forward, future investigations could explore expanding the design space with double defects, adopting enhanced modeling techniques to account for lateral and shear effects, developing a control algorithm for the automatic optimization of SNC values in actively tunable bandpass filters, and incorporating artificial intelligence into design methods for piezoelectric defects with electrical connections. [ABSTRACT FROM AUTHOR]

This paper proposes an explicit solution for the design of a target-frequency-customized, one-dimensional phononic crystal (PNC) with a defect for piezoelectric energy harvesting under longitudinal waves. Due to the innate narrow bandwidth nature of the defect modes of a PNC at the target frequency, there is a great need to generate an electromechanically coupled defect band of a piezoelectric-defect-introduced PNC. This work considers the transfer matrix method which has been widely used in analytical approaches. The need for defect bands to be included in a bandgap inspires the use of a quarter-wave stack as a unit cell to match the bandgap's central frequency with the target frequency. In band structure analysis, considering that the electromechanically coupled defect band corresponds to a set of real wavenumbers despite being within the bandgap, several possible solutions for the piezoelectric defect's length are derived in an explicit fashion. Since switching from a short- to an open-circuit condition causes defect bands to slightly increase due to piezoelectric effects, an explicit solution that reflects the piezoelectric defect's electrical characteristics is finally proposed. Finite-element-based numerical validation studies are conducted to study two aspects, specifically parametric studies (i.e., the natural numbers in the solution to the piezoelectric defect's length, the supercell sizes, and the defect locations) and supporting studies (i.e., the electrical boundary conditions and unit cell designs). At the target frequency, it is demonstrated that the proposed PNC design actualizes the formation of one defect band and the representation of the peak output voltage. [ABSTRACT FROM AUTHOR]

Phononic crystals (PnCs) have been utilized to amplify the amount of input energy transferred to a piezoelectric energy harvesting (PEH) device by manipulating elastic wave propagation. When introducing a defect that has material properties and/or geometry different from a unit cell, mechanical resonance of the defect leads to localizing elastic waves inside the defect. This is called a defect mode. Several prior studies have explored a defect mode for PEH purpose; however, they have focused only on a single defect. When introducing an additional defect into a PnC, the coupling between two defects leads to splitting the defect band. Incorporating such split defect band phenomena into PEH can potentially widen frequency bandwidth and realize broadband energy harvesting. Thus, this study newly proposes a PnC-based PEH system that uses double defect modes under elastic waves. In particular, this study examines how an electrical circuit connection (i.e., Independent, Series, or Parallel) between two PEH devices attached on each defect affects PEH performances. Key findings from this study include (1) the shift in split defect bands as well as harvesting performance varies with the type of electrical circuit connection; (2) split defect band phenomena amplify the output electric power at double resonance peaks in an Independent connection; and (3) despite displacement amplification at certain resonance frequencies, no peak output voltage occurs due to the current source direction (for Series connections) and voltage cancellation (for Parallel connections). These key findings can provide design and selection guidelines for electrical circuit configurations between double defects for enhanced PEH. [ABSTRACT FROM AUTHOR]

Extensive prior research has delved into the localization of elastic wave energy through defect modes within phononic crystals (PnCs). The amalgamation of defective PnCs with piezoelectric materials has opened new avenues for conceptual innovations catering to energy harvesters, wave filters, and ultrasonic receivers. A recent departure from this conventional paradigm involves designing an ultrasonic actuator that excites elastic waves. However, previous efforts have mostly focused on single-defect scenarios for bending-wave excitation. To push the boundaries, this research takes a step forward by extending PnC design to include double piezoelectric defects. This advancement allows ultrasonic actuators to effectively operate across multiple frequencies. An analytical model originally developed for a single-defect situation via Euler–Bernoulli beam theory is adapted to fit within the framework of a double-defect set-up, predicting wave-excitation performance. Furthermore, a comprehensive study is executed to analyze how changes in input voltage configurations impact the output responses. The ultimate goal is to create ultrasonic transducers that could have practical applications in nondestructive testing for monitoring structural health and in ultrasonic imaging for medical purposes. [ABSTRACT FROM AUTHOR]

Significant prior research has explored elastic wave-energy localization via defect modes of phononic crystals (PnCs). The integration of defect-introduced PnCs and piezoelectric materials has paved the way for the development of new conceptual products for applications in energy harvesters, wave filters, and ultrasonic sensors. Recently, an attempt has been made to deviate from this paradigm and design an ultrasonic transducer that generates elastic waves. Unfortunately, previous work has been limited to a single-defect situation. Therefore, as an advanced approach, the present work aims to expand the PnC design space into double defects, which will make ultrasonic transducers useful at several frequencies. As a first step, this study targets longitudinal wave generation. To predict the wave-generation performance, a previous analytical model that was built for energy-harvesting purposes under a single-defect situation is modified to be suitable for the present wave-generation purpose under a double-defect situation. Moreover, two parametric studies are executed to analyze how the output responses change based on changes to the input voltage setting and the spacing between the double defects. We hope that these ultrasonic transducers could be potentially applicable for nondestructive testing in structural health monitoring and ultrasonic imaging in medical science. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive analytical framework for one-dimensional phononic crystals (PnCs) integrated with piezoelectric defects, leveraging an electroelastically coupled stiffness matrix under longitudinal wave propagation. This matrix effectively captures the mechanical coupling between defects and piezoelectric devices, as well as the piezoelectric coupling within the devices, providing a robust foundation for predicting key behaviors such as band structures, defect mode shapes, and frequency responses. The stiffness matrix method employed in this study overcomes the numerical instabilities inherent in traditional transfer matrix approaches, thereby enhancing the reliability and precision of the framework. The versatility of the proposed framework is evident in its application across diverse engineering domains, including tunable bandpass filters, high-sensitivity ultrasonic sensors, and energy harvesters. The accuracy of the model is validated through finite-element simulations, which demonstrates significantly reduced computation times. To encourage further research and practical implementation, the study provides MATLAB codes. This study establishes the foundation for extending the framework to bending waves, miniaturized PnCs, and oblique wave propagation scenarios. [Display omitted] • A stiffness matrix method is proposed for defective phononic crystals. • The method is validated numerically for bandpass filters, sensors, and energy harvesters. • The analytical model's high predictive capabilities are confirmed. • It is demonstrated to reduce computational time dramatically. • The computational stability of the proposed model is ensured for large unit cell counts. [ABSTRACT FROM AUTHOR]

• This is the first attempt to achieve tunable defect bands for double defect cases. • Coupling degree between double defects is controllable without altering structures. • Electrically controllable coupling is valid regardless of double defect settings. • The analytical approach reduces computation time for predicting coupling degrees. Research in the field of phononic crystals (PnCs) has traditionally focused on single defects for energy localization and frequency-selective filtering. Recent attention has turned to exploring double defects to expand frequency options. Advancements in this area have introduced differently patterned double defects, which can be either coupled or decoupled. Yet, the conventional mechanical approach locks in double-defect characteristics early in the design process. To overcome this limitation, this study proposes a novel electrical control method to adjust the coupling degree between double defects for the first time. By attaching bimorph piezoelectric elements with respective inductive circuits to defects, this work offers a flexible means of manipulating their interaction, allowing them to interactively behave as double defects or independently function as single defects, depending on the user's purpose, even after mechanical design finalization. Through analytical and numerical models, the proposed approach is comprehensively validated, demonstrating its effectiveness in two scenarios of double defects with identical and different structural configurations. Two main contributions of this work are as follows. First, this is the first attempt to achieve electrically controllable and reversible coupling degrees of double defects. Second, the developed analytical model enables the rapid prediction of tunable defect-band frequencies, thereby reducing computational time. We believe this research opens new avenues for dynamically controlling defective PnC behaviors, promising advancements in applications like structural health monitoring, prognostics health and management, and medical imaging. [ABSTRACT FROM AUTHOR]

This paper proposes a one-dimensional, defect-introduced phononic crystal design for target frequency matching. A quarter-wave stack is used as a unit cell. The supercell-technique-based transfer matrix method enables the defect's length to be explicitly derived; this generates a defect band at the target frequency in band-structure analysis. For the verification through time-harmonic analysis, the perturbation-theory-incorporated S-parameter method is used. The results show that the proposed design enables the realization of defect-mode-induced energy localization at the desired frequency, regardless of the harmonic number, supercell size, and defect location. The proposed design is validated by numerical examples through the finite element method. [ABSTRACT FROM AUTHOR]

In this paper, four groups of graphene oxide and carbon fiber hybrid-reinforced resin matrix (GO-CF/EP) composites with different layering ways were prepared by a vacuum infiltration hot pressing system (VIHPS). The damping properties of the specimens with different layering ways were tested by the force hammer method, and the micromorphology of the specimens was photographed by scanning electron microscope. The experimental results showed that the damping properties of GO-CF/EP composites gradually increased with the increase in the number of Y-direction layers. The [XYXYXY]6 has the best damping property, with a damping ratio of 1.187%. The damping ratio is 5.3 times higher than that of [XXXXXX]6 layer mode, and the first-order natural frequency is 77.7 Hz. This is mainly because the stiffness of the X-direction layer is larger than that of the Y-direction layer, and its resistance to deformation is considerable. Therefore, its decay rate is slower. The Y-direction layer has weak resistance to deformation and fast energy attenuation. The increase in the number of Y-direction layers will lead to the overall increase in, and the improvement of, the damping properties of GO-CF/EP composites. [ABSTRACT FROM AUTHOR]

• Electrical resonance induces new defect bands. • New defect bands are electrically controllable over the wide range of frequencies. • Defect-band splitting occurs when electrical and mechanical resonances align. • Inductive circuits are favorable due to resistors' induction of mechanical loss. Research in defective phononic crystals (PnCs) has garnered increasing interest for their unique properties of energy localization and bandpass filtering. Despite their utility, conventional defective PnCs suffer from a fixed defect band, limiting adaptability in scenarios requiring frequency adjustments. Addressing this limitation, this study proposes a novel approach—integrating inductive-resistive circuits into defective PnCs—to introduce electrically controllable defect bands. Key findings include the emergence of additional defect bands through electrical resonance in inductive and inductive-resistive circuits. Notably, the phenomenon of defect-band splitting is newly observed when mechanical and electrical resonance frequencies align. An essential observation is the superiority of inductive circuits in maximizing transmittance efficiency. Conversely, resistive or inductive-resistive circuits exhibit limitations, such as rapid transmittance decrease. The significance of this work lies in two main contributions. First, it presents a pioneering approach to build a bridge between inductive-resistive circuits and defective PnCs, offering tunable narrow bandpass filters to users. Second, this study offers a comprehensive guideline for selecting optimal electrical circuit configurations to maximize transmittance. These endeavors aim to advance the field of tunable energy-localized behaviors in defective PnCs, opening up new avenues for future research and practical applications, such as enhancing ultrasonic sensors and actuators for structural health monitoring and medical imaging. [Display omitted] [ABSTRACT FROM AUTHOR]

This research aims to advance the existing analytical model, which was based on the Euler–Bernoulli beam theory, for predicting the velocity amplitude of bending waves excited while amplified by defective phononic crystals (PnCs) with piezoelectric elements. The previous analytical model falls short for thick defective PnCs and is limited to low frequencies. Hence, the Timoshenko beam theory is newly incorporated to address these issues, considering shear deformations and rotational inertia. Its performance is validated against a finite element model. It confirms that the proposed analytical model outperforms its predecessor, which was suitable for thin defective PnCs with a slenderness ratio above 10 and frequencies around 2 kHz. Remarkably, the improved analytical model demonstrates excellent predictive capabilities up to 40 kHz for thick defective PnCs with a slenderness ratio of around 2.5. With a relative error of less than 1% compared to the finite element model, this advanced approach also demonstrates time-efficient and stable computational performance. This work introduces three contributions. First, it pioneers the proposal of an electromechanically coupled analytical model for predicting the performance of defect-mode-enabled bending wave excitation. Second, this enhanced analytical model surpasses existing counterparts in terms of both accuracy and computational stability, particularly for thick defective PnCs, even at high frequencies. Last, the analytical model dramatically reduces the computation time. [Display omitted] • An electromechanically coupled analytical model of defective phononic crystals (PnCs) is newly developed for actuators. • The analytical model is designed to suit thick PnCs by incorporating shear deformation and rotational inertia. • The analytical model presents high accuracy and stable computing capabilities even in high frequencies. • The analytical model dramatically reduces the computation time. • The dependence on the defect position and Timoshenko shear coefficient is deeply analyzed. [ABSTRACT FROM AUTHOR]

• A one-dimensional PnC with differently patterned double defects is newly analyzed. • The coupling degree between the double defects relies on the nature of each solely isolated defect. • Double defects are decoupled when defect bands of each solely isolated defect are dissimilar. • Interactive defect-mode shapes are presented, where each defect shows different symmetries. • Frequency jumping is observed in which energy is mainly trapped in one structurally fixed defect. Several studies relevant to double-defect-mode-induced energy localization of a phononic crystal (PnC) have progressed. However, most works have examined the typical setting in which the double defects and adjacent lattices in a PnC have the same configuration. This work thus focuses on investigating the energy-localized behaviors of a one-dimensional PnC with closely arranged but differently patterned double defects under longitudinal waves for the first time. A quarter-wave stack is used as the unit-cell design. Three cases are considered, each with double defects applied to the same (Cases I-DD and II-DD) or different (Case III-DD) kinds of stacks in two unit cells. Defect-band analysis is performed on various combinations of the double-defect lengths. Two significant findings of this work are outlined as follows. First, although the imposition pattern of the double defects is different, defect-band splitting and double-defect-mode-enabled energy localization appear if the defect-band frequencies of each defect, independently imposed as a single defect, are the same. Second, unlike the conventional double-defect-mode shapes, the interactive energy-localized behaviors of the defects where each defect shows different symmetries are newly observed. In future works, it is expected that adaptively tuning defect properties via the incorporation of smart materials will open a new avenue in the field of PnC-based wave tailoring. [Display omitted] [ABSTRACT FROM AUTHOR]

• This is the first attempt to utilize a defective PnC as wave-generation systems. • An analytical model is newly proposed to predict sensitivities and electrical admittance. • The proposed model dramatically shortens the computational time with high accuracy. • The proposed system and model are effective, regardless of the boundary conditions. This paper aims to bridge the energy-localized behaviors of a phononic crystal (PnC) and an ultrasonic-wave-generation (UWG) system. A defective PnC manifests an intriguing phenomenon in which input ultrasonic-wave energy is confined near the defect in several defect-band frequencies that appear in the phononic band-gap range. Using the inverse of this energy localization, remarkably amplified ultrasonic waves can be generated compared to a UWG system without the PnC. This work proposes an analytical model that predicts the UWG system's sensitivities and electrical admittance. The mechanical equation of motions and the electrical circuit equation of the piezoelectric-patch-bonded defect are derived using the Rayleigh-Love rod theory and the extended Hamilton's principle. Through the use of Green's functions, these electroelastically coupled equations are solved. With two assumptions, specifically, (i) continuity conditions throughout the PnC and (ii) no incident waves toward the UWG system, the S-parameter-method-based analytical approach presents the system performances explicitly. Furthermore, the modified analytical model for application to engineering situations with finite boundary conditions is also proposed. The predicted results of the proposed analytical model match well with those of the finite element model and show that the UWG performances are amplified to several times their prior value. The main contributions of this work are as follows: (i) this is the first attempt to utilize a defective PnC as UWG systems, (ii) the analytical model is newly proposed and dramatically shortens the computational time compared to the finite-element-method, and (iii) the proposed defective-PnC-incorporated UWG system and its analytical model are effective, regardless of the boundary conditions. [Display omitted] [ABSTRACT FROM AUTHOR]

• A lumped-parameter model is used to reveal energy localization mechanisms of a PnC. • The asymptotic approach is applied into defect-band analysis for the first time. • Evanescent waves in a band gap result in a fixed-like boundary condition. • Mechanical resonance by the fixed-like boundary condition leads to defect modes. Phononic crystals (PnCs) have received growing attention in recent years, due to their ability to manipulate elastic waves, such as in the case of defect-mode-enabled energy localization. Although previous studies have explored defect modes of PnCs – from phenomenon observations to their potential applications – little effort has been made to date to reveal fundamental mechanisms of defect-mode-enabled energy localization. Thus, this study proposes a lumped-parameter analytical model to reveal the underlying principles of the formation of defect bands of a one-dimensional PnC when a single defect is introduced, or the splitting of defect bands when double defects are introduced. Through the investigation of 1) evanescent wave characteristics in the defect-mode shapes, and 2) the asymptotically equivalent behaviors of defect bands and defect-mode shapes with limiting behavior approaches, this study demonstrates a new aspect of why a band gap should be the prerequisite for achieving defect-mode-enabled energy localization. It is confirmed that defect-mode shapes are normal modes, rather than propagating wave modes. The key findings of this study are as follows: 1) the exponentially attenuating characteristics of evanescent waves in a band gap generate a fixed-like boundary condition, which surrounds single or double defects, and 2) mechanical resonance, attributed to the fixed-like boundary condition, leads to the formation and splitting of defect bands. [Display omitted] [ABSTRACT FROM AUTHOR]

• Lateral movements of a piezoelectric defect are considered. • Three coefficients are newly presented for quantification of the lateral effects. • An improved electromechanically coupled transfer matrix is derived in an explicit manner. • Output results from the analytical model agree well with those from a finite element model. This paper aims to improve the existing electromechanically coupled analytical model that was developed for defect-induced phononic crystals (PnCs) designed for piezoelectric energy harvesting (PEH). The work outlined in this paper improves the model by considering lateral movements, which are not negligible when the slenderness ratio of the rods is small. Based on the Rayleigh-Love rod theory, the proposed method uses the generalized Hamilton's principle to derive two governing equations in the mechanical and electrical domains. An explicit form of the solutions to the governing equation is then used to derive an improved electromechanically coupled transfer matrix. Based on the transfer matrix method and the S-parameter method, the proposed electromechanically coupled analytical model enables the prediction of defect bands and PEH performance. To evaluate the predictive capabilities under a small slenderness ratio of the rods, the results from the proposed Rayleigh-Love rod-theory-based analytical model are compared with those found by the existing analytical model based on classical rod theory and by a finite element model. The novelties of the research outlined in this paper are as follows: 1) the proposed method considers, for the first time, lateral inertia in analytical modeling of defect-induced PnCs for PEH purposes and 2) three coefficients are newly presented to quantify the effects of lateral motions on the electromechanically coupled transfer matrix. [Display omitted] [ABSTRACT FROM AUTHOR]

• An analytical model of a phononic crystal with a piezoelectric defect is newly proposed. • An electroelastic coupling of the piezoelectric defect is considered. • An electroelastically coupled transfer matrix is explicitly derived. • Output performances of the analytical model agree well with those of finite element methods. Phononic crystal (PnC)-based piezoelectric energy harvesting (PEH) has been recently introduced to amplify the input energy fed into PEH devices. If a defect is imposed into a PnC, as a result, defect bands are created within the band gap. At a defect band frequency, elastic waves can be localized inside the defect. By attaching a PEH device to the defect, output electric power can be significantly enhanced. However, since the attachment of the PEH device leads to the shifting of the defect band frequency, the output electric power can drop significantly if an excitation frequency does not align with the shifted defect band frequency. Thus, this study aims to develop an electroelastically coupled analytical model of a PnC with a piezoelectric defect; the proposed model considers the inertia and stiffness effects. An electroelastically coupled transfer matrix is derived by simultaneously solving a mechanical equation of motions and an electrical circuit equation, with the help of Green's function. The proposed electroelastically coupled analytical model can be used to predict defect band frequencies and defect mode shapes (based on a transfer matrix method; TMM) and output electric power (based on an S-parameter method; SPM) across an external electrical resistance. Results of the proposed electroelastically coupled analytical model are in very good agreement with those of a finite element method (FEM). The contributions of the proposed electroelastically coupled analytical model are two-fold: (1) this is the first attempt to propose analytical model of a PnC with a piezoelectric defect for energy harvesting; and (2) the model allows physical parameterization of the electroelastically coupled transfer matrix in an explicit manner. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• Material property requirement to enable rectangular-like and parallel-line-like equi-frequency contours (EFCs) is newly proposed. • Adjoining the frequency ranges of two EFCs achieves the broadband self-collimation. • Broadband self-collimation of an anisotropic phononic crystal is experimentally validated. One extraordinary phenomenon exhibited by phononic crystals (PnCs) is that they can manipulate oblique incident waves in a target direction via proper refraction, commonly called wave self-collimation. Although prior studies have demonstrated self-collimation of electromagnetic and acoustic waves, only a few studies have examined elastic waves in this context. If a PnC is designed to represent rectangular-like and/or parallel-line-like equi-frequency contour (EFCs), elastic waves can be self-collimated in either horizontal or vertical directions. However, in the existing literature, there is no theoretical rationale for realizing rectangular-like and/or parallel-line-like EFCs; besides, broadband self-collimation of elastic waves has not yet been explored. Therefore, we propose to derive the material property requirement for an anisotropic PnC to exhibit rectangular-like EFCs (a range of low frequencies) and parallel-line-like EFCs (a range of high frequencies) in the case of elastic waves. Furthermore, by inherently adjoining two frequency ranges of the rectangular-like and parallel-line-like EFCs at a certain frequency, broadband self-collimation covering the entire range of frequencies can be achieved. With the designed anisotropic PnC that fulfills the proposed material property requirement, self-collimation for S 0 Lamb waves is numerically simulated and experimentally demonstrated over a broad range of frequencies. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• A graded phononic crystal (PnC) with decoupled double defects is newly proposed. • The graded PnC is a superposition of two graded PnCs with a single defect. • The graded PnC enables to separately design defect band frequencies of each defect. • The graded PnC can achieve broadband energy localization. Several research efforts have been devoted to exploring defect modes of uniform phononic crystals (PnCs) with single or double defects. However, they have difficulties in achieving broadband energy localization under realistic environments. This study thus proposes a new design concept of a graded PnC with double defects for broadband energy localization. A graded PnC refers to a PnC built by varying one or more design variables of its lattices. The double defects are introduced to be sufficiently far from each other to make them decoupled; each of the defects behaves as an independent single defect. Unlike a uniform PnC, the graded PnC enables to separately design defect band frequencies corresponding to each of the double defects by changing a degree of the variation in the height of the circular stub. The graded PnC with double defects can broaden the bandwidth for elastic wave localization. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• Unlike acoustic waves, transversely polarized defect mode shapes are observed under elastic waves. • Electroelastic coupling of piezoelectric energy harvesting (PEH) is incorporated into defect band analysis. • There is a trade-off between the fulfillment of resonance formation and the amplitude of evanescent waves. • As supercell size increases, the PEH performance asymptotically increases up to a certain extent. • There exists an optimal defect location where the maximum PEH performance can be achieved. Metamaterial-based energy harvesting (MBEH) has recently received much attention due to its capability of amplifying input mechanical wave transferred to a piezoelectric energy harvesting (PEH) device. A phononic crystal (PnC), one representative example of a metamaterial, is an artificially-engineered structure constituted by a periodic repetition of unit cells that can manipulate the propagation of elastic waves at the scale of the wavelength. If a defect is introduced in the PnC by replacing one unit cell with another cell that has different geometric or material properties, the periodicity of the PnC is locally broken; thereby, defect bands are created within the band gap. Since the defect can mechanically resonate with a certain defect mode shape at the defect band frequency, an evanescent wave can be localized inside the defect. By attaching the PEH device to the defect, the output electric power can be dramatically enhanced. However, there is presently no thorough design rationale to inform decisions on supercell size and optimal defect location of a PnC for energy localization and harvesting. Thus, this study investigates effects of supercell size and defect location on energy localization and harvesting performances. For a given defect location, the output performance of the PnC-based PEH system monotonically increases and converges toward the maximum value as the supercell size increases. For a given supercell size, there exists an optimal defect location where maximum output performances of the PnC-based PEH system can be achieved. The key findings of this study lie in that there is a trade-off relationship between the fulfillment of resonance formation and the attenuation of evanescent waves. It can be concluded from this study that the supercell size and defect location can be properly designed to improve the output performances of a PnC-based PEH system under elastic waves. Image, graphical abstract [ABSTRACT FROM AUTHOR]

This paper proposes a tapered cantilever beam flow induced vibration piezoelectric energy harvester, for optimizing the tapered beam and improving the output characteristics. The physical model of the tapered beam harvester is conceived, a two-dimensional CFD simulation model is established, and experimental validation as well as investigation is conducted. The output voltage and displacement response of the harvesters with various tapered beams are explored. The results show that the tapered beam possesses more uniform strain distribution and larger equivalent stiffness, and increasing the fixed end width results in enhancing output voltage and reducing vibration displacement. The optimal tapered beam with a tip width of 25 mm and fixed end width of 45 mm is obtained. The maximum output voltages of the tapered beam VIVPEH and GPEH are increased by 58.30% and 33.16% over the rectangular beam, respectively. The vibration displacements of the tapered beam VIVPEH and GPEH are reduced by 18.31% and 25.12% over the rectangular beam, respectively. The tapered effect in the flow field reduces the vortex shedding distance, increases the shedding frequency, enhances the aerodynamic forces, and thus improves the energy harvesting performance. This work lays the important foundation for exploring the cantilever beam flow induced vibration harvester system. [Display omitted] • A tapered beam flow induced vibration piezoelectric energy harvester is first investigated. • The optimal tip width of 25 mm and fixed end width of 45 mm are obtained. • The voltages of the tapered beam VIVPEH and GPEH increase by 58.30% and 33.16% over the rectangular beam. • The vortex shedding mode and enhancement mechanism are revealed. [ABSTRACT FROM AUTHOR]

• This is the first study to employ deep-learning techniques in designing defective PnCs. • A deep-learning-based framework is newly proposed to design a narrow bandpass filter. • Four deep learning models are compared to tackle the nonunique response-to-design problems. • The proposed framework provides an optimal design for the arbitrary defect-band frequency. • The proposed framework facilitates a streamlined and automated inverse design process. This paper proposes a deep-learning-based inverse design framework for a one-dimensional, defective phononic crystal (PnC) as a narrow bandpass filter under longitudinal elastic waves. The purpose of the design-optimization problem is to maximize the transmittance at the defect-band frequency, which is equal to the target frequency. The framework comprises three steps: (i) inverse design generation and filtering, (ii) forward analysis of frequencies and filtering, and (iii) forward analysis of transmittance and near-optimal design selection. Four deep-learning models are considered in the inverse model: a deep neural network, a tandem neural network, a conditional variation autoencoder, and a conditional generative adversarial network. The frameworks developed with each deep-learning model are evaluated using a test dataset and an arbitrarily defined defect-band frequency and phononic band-gap range. The results show that the frameworks proposed using the conditional variation autoencoder and the conditional generative adversarial network effectively present the best performance by solving the nonunique response-to-design mapping problem through probabilistic approaches. The deep-learning-based framework reduces the need for manual intervention and simplifies the inverse design process, making it a promising approach for finding the near-optimal design solution for the use of defective PnCs as narrow bandpass filters. [Display omitted] [ABSTRACT FROM AUTHOR]

This review paper addresses the critical need for structural prognostics and health management (SPHM) in aircraft maintenance, highlighting its role in identifying potential structural issues and proactively managing aircraft health. With a comprehensive assessment of various SPHM techniques, the paper contributes by comparing traditional and modern approaches, evaluating their limitations, and showcasing advancements in data-driven and model-based methodologies. It explores the implementation of machine learning and deep learning algorithms, emphasizing their effectiveness in improving prognostic capabilities. Furthermore, it explores model-based approaches, including finite element analysis and damage mechanics, illuminating their potential in the diagnosis and prediction of structural health issues. The impact of digital twin technology in SPHM is also examined, presenting real-life case studies that demonstrate its practical implications and benefits. Overall, this review paper will inform and guide researchers, engineers, and maintenance professionals in developing effective strategies to ensure aircraft safety and structural integrity. [ABSTRACT FROM AUTHOR]

Digital Twin (DTw) model is a numerical model in a virtual world that supports engineer decisions using observed data from a real system. However, uncertainty in the physical model parameters of DTw degrades the predictive performance of a DTw. Bayesian calibration utilizes both observed data and prior knowledge to estimate uncertain model parameters in a statistical manner using Bayes’ theorem. Markov Chain Monte Carlo (MCMC) is an effective searching algorithm that can be used to estimate a complex posterior distribution. In the MCMC method, the point that is used to initiate the MCMC sampling significantly affects the burn-in period impacting the accuracy and efficiency of the estimation. However, a proper initial point is hard to select because of the computational cost of searching high-dimensional parameter space. Previous optimization algorithms or random sampling algorithms have focused on solution convergence for a local or global optimum solution. However, the initial points searching method for DTw required suggesting multiple feasible optimum points where a solution can be existed to make proper engineering decisions based on DTw analysis based on each optimum. This paper describes the development of a cost-effective, stochastic algorithm, called the Greedy Stochastic Section Search (GSSS) algorithm that can systematically explore high-dimensional parametric space to select proper initial points for DTw. We verified the new algorithm's performance by applying it to a numerical example with a Mixture of Gaussian (MoG) 6 and by calibrating an engineering example, specifically a digital twin approach for an on-load tap changer. [ABSTRACT FROM AUTHOR]

• A quarter-wave stack (QWS) is first incorporated into piezoelectric energy harvesting (PEH) under elastic waves. • A standing wave pattern in a host medium is manipulated in favor of PEH by considering the phase change within the QWS. • An increase in the number of unit cells corresponds to the effect of amplifying input loading for enhanced PEH. • Since a standing wave pattern varies with frequency, electroelastic coupling varies accordingly. Extraordinary phenomenon (e.g. , band gap) exhibited by a phononic crystal (PnC) has recently been incorporated into piezoelectric energy harvesting (PEH) as a means to amplify input waves for improving the power generation capability. For a systematic design of PnC-based PEH using band gap reflection, it is required to identify a standing wave pattern (i.e. location of nodes and antinodes) in order to determine the optimal placement of a piezoelectric layer. In this context, we propose a quarter-wave stack (QWS)-based PEH system under elastic waves. The foundational idea of this study is to manipulate a standing wave pattern formed in a host medium by considering the phase change within the QWS. The key to creating an optimal standing wave for PEH is to intentionally form a displacement node at the interface between the host medium (here, continuous copper bar) and QWS at a target design frequency; thereby, the placement of the piezoelectric layer can be systematically determined in order that its center is aligned with the strain antinode to generate the maximum output power. To deeply explore the effect of the standing wave pattern on the output performances of the QWS-based PEH system, two key parameters are thoroughly investigated: 1) the number of unit cells and 2) the excitation frequency. Numerical analysis results suggest the followings: First, an increase in the number of unit cells corresponds to the effect of amplifying input loading for enhanced PEH; thereby, the output performances increase gradually and converge asymptotically. Second, since the standing wave pattern varies with the excitation frequency, the electroelastic coupling varies accordingly. These new findings provide guidelines on design parameters that can be manipulated to yield the best performance of the QWS-based PEH system under elastic waves for various potential applications. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

• A rule-based Duval method is incorporated into a deep neural network. • An unsupervised task is added to regularize partially incorrect labeled data. • A parameter transfer delivers pseudo-labeled information to labeled target data. • The proposed method is validated with real data acquired in sites. This paper proposes a new framework, named BDD, which bridges Duval's method with a deep neural network (DNN) approach for power transformer fault diagnosis using dissolved gas analysis (DGA). The proposed BDD consists of the following three key points. First, to overcome an important issue that most DGA data found in real-world industrial settings is unlabeled, Duval's method is newly used to provide knowledge, which is called pseudo-labeling information, to a DNN for unlabeled DGA data. Second, motivated by the fact that the pseudo-labeled data does not always declare correct answers, a DNN architecture with an auxiliary regularization task is newly proposed, which is somewhat robust to the noisy labeled data. Last, a parameter transfer learning approach is applied to evolve the pre-trained DNN model, which is trained from a large amount of pseudo-labeled source DGA data, for diagnosing the sparse labeled target DGA data. Four case studies are executed through the use of KEPCO's massive unlabeled DGA data and IEC TC 10′s sparse labeled DGA data: (i) a comparison with the existing methods, (ii) examination of the effectiveness of parameter freezing via feature space investigation, (iii) studying the robustness of the regularization task under noisy labeled DGA, and (iv) probing the hyperparameter effects. Moreover, to strengthen the proposed model's effectiveness, the last fifth case study performs a comparison with the existing methods for KEPCO's sparse labeled data instead of IEC TC 10 data. We confirm that the proposed BDD method outperforms existing methods, thanks to the Duval method's weak supervision, the regularization task, and parameter transfer. [ABSTRACT FROM AUTHOR]