Additive manufacturing of piezoelectric devices is typically multi-step, limiting scalability and design freedom. This paper introduces a one-step multi-material-extrusion (MMEX) route that co-prints PVDF, a structural substrate, and silver-nanoparticle electrodes, followed by contact poling. Process–structure links are established by correlating MMEX parameters with electroactive (β+γ) phase fractions measured by FT-IR. Dynamic cantilever tests demonstrate bidirectional functionality: the same printed configuration acts as both actuator and sensor. A coupled electromechanical Finite Element model, calibrated against experiments, yields transferable effective d31 values and design rules for 4D-printed architected metamaterials and devices enabling rapid customization of geometry and performance tailored for applications.

In this work, a new numerical model is presented, addressing the challenge of accurately modeling high-frequency transient responses in composite beams with piezoelectric sensors and actuators. Simulations like these are a key aspect of the effective design of wave-based structural health monitoring and impact detection systems. Specifically, Daubechies scaling functions are utilized as basis functions for the spatial approximation of both mechanical and electric variables, extended by the integration of piezoelectric kinematic assumptions, enabling the consistent prediction of electromechanical coupling and the exact modeling of structures with physically modeled actuators and sensors. The beam's mechanical behavior is described using first-order shear deformation theory, while the electric potential through the thickness is captured via a linear layerwise approximation. The developed model is validated and compared with finite element models under static and dynamic simulations. Interestingly, the presented method exhibits remarkably high convergence rates and requires substantially fewer grid points for convergence compared to finite element models. The findings demonstrate the potential of the proposed wavelet-based approach to enable the development of efficient and accurate models for high-frequency wave propagation simulations, which can enhance the transient dynamic analysis of smart electromechanical systems.

This study overcomes a primary limitation of conventional mechanical metastructures, their fixed-frequency anti-vibration performance, which poses a critical barrier to adaptive and real-time vibration control. The key novelty of the current work lies in the development of an in-house finite-element framework for a beam structure employing multiple piezoelectric local resonators shunted with resistive-inductive electrical circuits. This enables the synthesis of frequency-tunable attenuation bands via electrical impedance modulation, bypassing the need for mechanical redesign. Through a meticulous parameter investigation into the resistance, inductance, and capacitance effect, it is demonstrated that spatial attenuation bands, dual stopbands, and multiple antiresonances are presented for each case in the beam’s spatial-frequency response. Furthermore, through a force location study, it is evinced that while the excitation location alters, the multi-resonator array still provides significant spatial attenuation. These results clearly establish that the employment of multiple piezoelectric resonators shunted with inductance and resistance offer a highly adaptable solution for broad multi-modal suppression of bending vibrations in beam structures.

This work addresses the challenge of accurately modeling transient wave responses in composite beams with piezoelectric sensors and actuators, a key aspect for wave-based structural health monitoring and impact detection. The multiresolution finite wavelet domain (MR-FWD) method is extended by incorporating coupled piezoelectric constitutive equations, enabling robust prediction of the electromechanical response of smart composite beams. A mixed-field model is adopted for the thickness-wise approximation of the piezoelectric laminate, where the displacements follow the first-order shear deformation theory, and the electric potential follows linear layerwise approximation. The mixed-field approach is integrated within the MR-FWD framework, leading to a set of discretized coupled electromechanical equations of motion that encompass coarse and fine solutions. The orthogonality and localization capabilities of Daubechies wavelets provide numerical advantages and additional isolation properties to the multiple resolution components. Comparisons with high order finite element models and experimental measurements are presented, demonstrating the remarkable computational efficiency and accuracy of the proposed model. Finally, the presented numerical framework exhibits advanced capabilities regarding the isolation of co-existing wave modes by different solution components, highlighting its potential as an advanced analysis and design tool for ultrasonic guided wave-based SHM systems.

A layerwise laminate FE model capable of predicting the dynamic response of delaminated composite beams with piezoelectric actuators and sensors encompassing local non-linear contact and sliding at the delamination interfaces was formulated. The kinematic assumptions of the layerwise model enabled the representation of opening and sliding of delamination interfaces as generalized strains, thereby allowing the introduction of interfacial contact and sliding effects through constitutive relations at the interface. This realistic FE model, assisted by representative experiments, was used to study the time response of delaminated active sensory composite beams with predefined delamination extents. The time response was measured and simulated for narrowband actuation signals at two distinct frequency levels using a surface-bonded piezoceramic actuator, while signal acquisition was performed with a piezopolymer sensor. Four different composite specimens, each containing a different delamination size, were used for this study. Experimental results were directly compared with model predictions to evaluate the performance of the proposed analytical approach. Damage signatures were identified in both the signal amplitude and the time of flight, and the sensitivity to delamination size was examined. Finally, the distributions of axial and interlaminar stresses at various time snapshots of the transient analysis are presented, along with contour plots across the structure’s thickness, which illustrate the delamination location and wave propagation patterns.

The efficient and robust simulation of transient responses in laminated plates, which may encompass numerous wave modes, is a challenging computational problem with multiple applications. In this direction, an advanced computational method with additional localization capabilities is developed by employing the multiresolution approximation, resulting in the 2D multiresolution finite wavelet domain (MR-FWD) method. Daubechies scaling and wavelet functions are utilized, formulating a novel set of mass-decoupled multiresolution discretized equations of motion that involve four solution components: the coarse, horizontal fine, vertical fine and diagonal fine solution. The multiresolution discretization is combined with the first-order shear laminated plate theory for the effective modeling of composite plates. Numerical case studies focus on guided wave propagation in three lamination cases of increased complexity, showing the remarkable computational efficiency of the MR-FWD method compared to single-resolution approaches and time-domain spectral finite elements. Most importantly, the advanced localization properties of the proposed method are demonstrated, especially in the multi-wave response of an asymmetric composite plate, where each fine solution captures different wave responses depending on their directivity and wavenumbers. This unique feature can pave the way towards a new numerical analysis framework, in which multiple solution components contribute critical information about the structural response.

Multiple and frequency-varying tonal vibrations are a common problem in flexible structures, such as lightweight means of transportation, induced by engine speed/rotor rotations, and their harmonics. A Semi-Active piezoelectric Tuned Mass Damper (SATMD) is developed for the suppression of these excitations, which consists of a resonant mass and a combined spring-piezoelectric device connected to an external resistive-inductive electric circuit. Calibrated alterations of the shunt circuit impedance do not simply adjust the anti-resonance of the auxiliary mass to potential frequency fluctuations, ensuring optimal performance within this frequency range, but also introduce a second—also tunable—anti-resonance, associated with the eigenfrequency of the electric current. As a result, this enables effective multi-tonal vibration control, even in distant frequency vicinities, using a lightweight antivibration device. These vibration suppression effects are first numerically and experimentally demonstrated on a down-scaled simplified airframe model. Then, the SATMD is attached to the airframe of a BO 105 S helicopter, and its vibration control capabilities are tested in actual flight conditions.

The advantages of the multiresolution finite wavelet domain method in terms of convergence speed and solution localization capabilities have been demonstrated in dynamic simulations of one- and two-dimensional solids. The first step in the multiresolution procedure entails a coarse solution, which is subsequently enriched by the calculation of finer solutions, so convergence is achieved without discarding the previous results obtained at coarser resolutions. In this work, the multiresolution structure of the method is thoroughly explored to develop two novel convergence indicators which can provide error indices for the first two steps of the process and focus the fine solutions on specific subregions, enhancing accuracy and computational speed. The first convergence indicator is based on force residuals and the second relies on the maximum ratio of the fine to total solution. Detailed examination of the multiresolution components results in profound comprehension of the way they participate to the total solution. Based on repeated observations, it is deduced that the participation of fine components to the total solution constitute metrics of convergence, permitting the termination of the hierarchical analysis without requiring convergence checks. The proposed convergence indicators can guide targeted refinement techniques and may provide the basis for a new computational paradigm.

A bistable piezoelectric energy harvester (PEH) is presented for harvesting power from vibrations occurring at low frequencies, as is the case of wind turbine blades. The axial compressive prestress of a piezoelectric composite beam at post-buckling serves as the bistability source, leading to high mechanical to electric power conversion. An in-house harvesting circuit connected to the piezoelectric terminals is used for demonstration of its harvesting power capabilities. A finite element (FE) model is used to analyze and optimize the coupled nonlinear electromechanical response of the PEH, including structure and circuit. A physical prototype has been manufactured and tested for validation of the electromechanical design and the FE modeling approach. Predictions and measurements indicate an increase of harvested power with applied prestress up to a transition point, where a sudden drop in power occurs. Good comparison between numerical and experimental results verified the modeling approach, whereas deviations related to physical boundary conditions at large compressive forces affected the prediction of the transition point in harvested power. The harvester produced 1.32 mW of electrical power under tonal base excitation of 1 g at 8 Hz. Hence, the nonlinear PEH has demonstrated its capability to harvest energy at frequencies much lower than its first linear modal frequency and could thus serve as a promising solution for powering IoT devices and sensors in large vibrating structures.

The detection and characterization of impact events on composite structures from the induced wave responses, involves many challenges. Coexisting guided waves of high dispersive nature propagate after impact, entailing continuous time variations in their wavenumber, frequency and group velocity content, which complicate the exact estimation of the time-of-flight and the extraction of impact characteristics. A multiresolution finite wavelet domain computational method, combined with appropriate contact laws, is presented to provide enhanced simulation and characterization capabilities of impact events. An explicit multiresolution time integration scheme involves a coarse solution, followed by finer solutions that are sequentially added to the coarse one, until convergence is achieved. The hierarchical character of the approach makes the impact simulation very fast and accurate. Moreover, due to the filtering properties of Daubechies wavelet functions, each resolution component effectively models and isolates specific wavenumber spectra, providing the capability to separate coexisting wave modes, and to overcome difficulties imposed by the dispersive nature of the resultant guided waves. It is demonstrated that the multiresolution simulation can reveal wave characteristics and time-of-flight features that no other traditional single-resolution method can do, and provides the basis for the development of powerful inverse methods that can localize the impact and characterize the impactor parameters. The method is first applied on impacted composite strips and the structural responses of each resolution component are assessed in order to obtain the desired features for impact location estimation and characterization. Finally, the method is implemented on an impacted composite plate structure and the various wave characteristics simulated by the fine components are presented, evincing the advanced features that the proposed method provides.

The performance of composite materials and structures at high-velocity impacts reaching or exceeding their ballistic limit is crucial for assessing their strength and safety in aerospace applications. In this highly transient impact regime, composite materials are subject to multiple complex failure modes and their properties are susceptible to strain rate effects, making very challenging the simulation and understanding of their ballistic impact performance. This study presents: (1) a multi-scale computational framework for predicting the ballistic limit of composite plates, and (2) experimental results of ballistic impacts on carbon/epoxy plates. The multi-scale model uses a micromechanical approach to account for strain-rate dependency, to calculate micro-stress effects on the matrix and fiber properties, and to predict their coupled effect on effective composite properties. Intralaminar damage initiation and evolution are identified using the maximum stress criterion, but the degradation of properties in the matrix and fibers is predicted with the micromechanics model. Mixed-mode damage laws are implemented to simulate delamination, which guarantees accurate and reliable results. The proposed multi-scale model has been implemented and integrated into ABAQUS/Explicit (VUMAT). Experimental results from high-velocity steel ball impacts on woven IM-65 Carbon/RTM6 epoxy composite plates conducted on a high-speed impact test bench are also presented including non-destructive evaluation of the types of damage and failure. The experimental results are finally used to validate the model predictions for the ballistic limit and the predicted types of damage and failure.

A wireless monitoring system based on piezoelectric energy harvesting (PEH) is presented to provide fatigue data of wind turbine blades in operation. The system comprises three subsystems, each respectively providing the following functions: (i) the conversion of mechanical to electric energy by exploiting the bistable vibration of a composite beam with piezoelectric patches in post-buckling, (ii) harvesting the converted energy by means of a modified, commercial, off-the-shelf (COTS) circuit to feed a LiPo battery and (iii) the battery-powered acquisition and wireless transmission of sensory signals to the cloud to be elaborated upon by the end-user. The system was verified with ground tests under representative operation conditions, which demonstrated the fulfillment of the design requirements. The measurements indicated that the system provided 23% of the required power for fully autonomous operation when subjected to white noise base excitation of 1 g acceleration in the range of 1–20 Hz.

Multiple and altering tonal vibrations are common problem in flexible structures, such as lightweight means of transportation, induced by engine speed/rotor rotations, and their harmonics.A Semi-Active piezoelectric Tuned Mass Damper (SATMD) is developed for the suppression of these excitations, which consists of a resonant mass and a combined springpiezoelectric device connected to an external resistive-inductive electric circuit.The proposed anti-vibration device introduces two anti-resonances to the host structure, which can be manipulated through changes in the shunt impedance, to highly suppress two dominating excitation frequencies or adjust the device to potential frequency fluctuations and maintain its performance.The vibration suppression capabilities of the SATMD are numerically and experimentally demonstrated on a down-scaled simplified airframe model.The anti-vibration device is experimentally proven to effectively adjust its performance to tonal frequency alterations, or to suppress two tonal excitations in distant frequency ranges, even in lower frequency vicinity than the initially tuned auxiliary mass.Finally, one tonal frequency and its 1 st high amplitude harmonic are experimentally shown to be highly suppressed, using a SATMD which adds negligible mass to the structure.

Τhe piezoelectric energy harvesting from nonlinear vibrating structures has greatly attracted the attention of scientific community over the last decades, as it seems to provide one of the more promising ways for high electromechanical energy conversion. Current study deals with the development of a robust and accurate numerical tool capable of modelling and designing piezoelectric structures undergoing severe nonlinear vibrations. Specifically, a coupled multi-field generalized nonlinear mechanics framework for piezoelectric beams subjected to initial stresses and large rotations, extended to include passive external electric circuits in order to predict the dynamic response of the structure and the power generated at the external resistive load. An experimental setup was also developed providing great correlations with the numerical results in case of a vibrating axially prestressed composite beam under the prebuckling regime. At the end, a computational investigation was performed studying the complex dynamic behavior of the piezoelectric beam, in the postbuckling regime. The model successfully captures the measured energy harvesting response of the beam including additional effects induced by the asymmetric configuration of the piezoelectric film.

An inverse procedure for damage identification on 1D and 2D solids based on wave propagation using the multiresolution finite wavelet domain (MR-FWD) method is presented. The forenamed method utilizes Daubechies wavelet and scaling functions for the approximation of state variables and as such, it involves two types of solutions, the coarse and the fine solutions. In that way, the multiresolution nature of the method can be utilized for efficient damage estimation in experimental applications since the fine solutions of the method have manifested remarkable localization and isolation capabilities and high sensitivity to damage. In order to fully take advantage of the additional benefits of the MR-FWD method, full-field displacement measurements of the wave propagation are taken into consideration. Wavelet decomposition using Daubechies wavelets is now applied on the measurements, leading to approximation and detail components that are directly comparable to the coarse and fine solutions of the multiresolution simulation, respectively. Therefore, MR-FWD models can be created using the same Daubechies wavelets as the decomposition of the experimental data, so as to compare the simulation results with the measured ones. Numerical results reveal that comparing the detail component of the experiments with the fine solution of the simulations using appropriate metrics can lead to efficient damage identification. In such manner, an optimization process can be conducted in order to characterize the investigated damage scenarios. This procedure can lead to more sensitive and accurate damage estimation due to the advantages of the multiresolution analysis.

The dynamic response of composite structures under impact loading conditions is a complex problem which is attracting substantial attention. Specifically, the case of hailstone impact introduces additional challenges that are urging to be encountered. Hence, the main goal of this paper is to present the development and validation of a computationally efficient impact model that encompasses a novel semi-empirical viscoplastic contact law for crushable ice impactors together with a new time domain spectral shear plate finite element formulation including nonlinear effects due to large displacements and rotations. The new viscoplastic contact law, which provides the coupling between the hailstone impactor and the targeted composite plate, is derived from analytical expressions and observations based on experiments and high-fidelity finite element simulations which utilize a fully integrated ice failure material model. High-velocity spherical hailstone impact experiments on woven glass/epoxy composite plate target structures are conducted using a high pressure pre-charged gas gun Obtained results are validated against high fidelity finite element models and experimental measurements. The results demonstrate the adequacy of the proposed contact law to capture the impact loading, as well as the accuracy, computational efficiency and additional benefits of the presented computational framework compared to other well-established numerical tools.

A high-order layerwise multiresolution method that utilizes Daubechies wavelet and scaling functions for the approximation of state variables is presented for the enhanced simulation of guided waves in composite strips. The multiresolution approximation yields a hierarchical set of equations of motion involving the coarse component of generalized displacements, and finer components can be added on the coarse one, forming improved predictions until the desired precision is accomplished. The multiresolution approach is combined with a high-order layerwise laminate theory, enabling the accurate prediction of both symmetric and antisymmetric wave modes, the modeling of surface traction, and localized intra-ply and delamination damage types. Numerical results for the simulation of guided waves in laminated composite strips are presented, exhibiting significant reduction in computing times and remarkable convergence rates compared to single-resolution approaches and traditional finite element methods. Moreover, it is shown that each resolution can model specific bandwidths of wavenumbers, thus providing unique inherent capabilities to localize and isolate coexisting wave modes and detect converted and reflected waves, induced by degraded material regions and delaminations.

A semi-active electromechanical Tuned Mass Damper (SATMD), which consists of a combined spring-piezoelectric device connected to an external resistive-inductive electric circuit is pre-sented, aiming to provide robust multi-modal vibration suppression capabilities in large flexible structures. The combined spring-piezoelectric device provides the stiffness for the resonant mass, and also electromechanical energy conversion and coupling. A reduced-ordered mode super-position structural dynamics model coupled with the SATMD device and the RL shunt electric circuit is formulated, to simulate the response of the integrated structural system. The broadband vibration reduction capabilities of the proposed SATMD are numerically and experimentally evaluated and quantified on a down-scaled simplified airframe model. Very good correlation between numerical and measured results is obtained. The results illustrate that a SATMD configuration with an auxiliary mass equal to 1% of the structural mass and combined resistive -inductive impedance, yields substantial simultaneous vibration suppression over the range of 3 low-frequency structural modes, and can be easily retuned to accommodate in-flight changes in structural and loading parameters.