Truncation resonances reside within the bandgap of periodic systems as a result of a finite-length system being truncated from its infinite chain. Because they exist in the band gap, truncation resonance modes are often localized on boundaries, and as such, they have prominent practical applications such as wave guiding, vibration attenuation, and flow control. Several papers have investigated the energy transmission rate, energy localization, and existence conditions of truncation resonances, and recent work has shown how nonlinearity affects topologically protected modes, which are a specific type of truncation resonance. However, current work does not explicitly study the characteristics of the truncation resonance mode shape, which quantifies the energy localization, when nonlinearity is introduced. This article bridges this gap by investigating the evolution of the mode shape of truncation resonances in a grounded diatomic chain with hardening and softening nonlinear springs. We use nonlinear normal mode analysis to characterize the energy dependence of the truncation resonance mode shape, and then present a mathematical functional fit of the mode shape evolution as a function of energy to quantitatively identify major energy-dependent characteristics of the nonlinear system. This article shows how the delocalization energy determined through mode shape analysis depends on system parameters, and specifically, it correlates linearly with the bandwidth between the truncation resonance and nearest propagating band edge in hardening nonlinear systems. This study provides a methodology to analyze nonlinear effects on truncation resonances and emphasizes the importance of understanding the mode shape evolution to quantify system characteristics.
Rotary axial percussion drilling is a high-speed drilling technology that has been widely applied. However, the traditional single-impactor arrangement has low drilling efficiency, is prone to intensify drillstring vibration, and increases the risk of drillstring failure. To address these problems, this study proposes a rotary axial percussion drilling scheme with multiple impactors. A combination of physical experiments and numerical simulations is used to analyze the sensitivity of drilling performance to different drillstring configurations, impact load levels, and load distribution methods. Results show that (1) the multi-impactor scheme improves the stress condition of the drillstring and helps reduce the risk of failure; (2) it significantly increases the rate of penetration and reduces torsional and axial vibrations. Adjusting the impact amplitude improves drilling efficiency, while changing the impact frequency helps reduce axial vibration; (3) stress waves naturally change during transmission, which allows the impactors to operate at the same frequency but different phases. This phase difference reduces resonance risk at a lower cost and improves drilling performance.
Tunable elastic metamaterials based on dynamic vibration absorber (DVA) concepts typically achieve frequency adjustment by varying a single resonator parameter, resulting in limited tuning range or bandwidth expansion. In contrast, this study introduces a fundamentally different reconfigurable mechanism based on threaded coupled dual-beam resonators with a shared tip mass mounted on a homogeneous host beam, enabling a dual-parameter coupled tuning strategy. Unlike conventional approaches that modify either stiffness or mass independently, the proposed design simultaneously and continuously modulates the effective bending stiffness and mass distribution of the resonator through coordinated adjustment of beam length and moment of inertia. This coupled mechanism produces a substantially amplified shift of the local resonant (LR) band gap while preserving structural compactness and passive operation. Furthermore, gradient LR metamaterials are systematically constructed by spatially programming the dual-tunable parameters along the beam, enabling broadband vibration attenuation that surpasses the bandwidth limitations of uniform configurations. The band gap behavior of infinite periodic systems and the transmission characteristics of finite structures are rigorously analyzed using spectral element and finite element methods, followed by experimental validation. The results demonstrate a maximum 5.7-fold shift in band gap center frequency and up to 191% higher relative bandwidth compared to corresponding uniform configurations, achieving approximately 500-Hz coverage within the sub-kilohertz regime. The proposed mechanism establishes a new paradigm for tunable LR metamaterials by enabling wide-range, continuous, and passive band gap reconfiguration without altering the host structure, offering significant potential for adaptive vibration control and wave manipulation in engineering systems.
An active structural-acoustic control (ASAC) algorithm based on Stochastic Linear Quadratic Regulator (LQR) is developed and implemented numerically in the present work for attenuating turbulent boundary layer (TBL)-induced energy transmission through a double-wall panel into an acoustic enclosure. Goody's single-point wall-pressure spectrum and combined Corcos-Mellen's spatial correlation function are used to generate the TBL cross-power spectra on the exterior panel. Mindlin's first-order shear deformation theory is used to model the deformation behavior of the structural panels, the classical wave equation is used to model the two acoustic enclosures, and finally, Green's theorem is used to couple the structure-acoustic model. Necessary governing equations for surface-mounted collocated polyvinylidene dichloride (PVDF) sensors and IDE-PFC actuators connected using a stochastic LQR feedback algorithm are appended with the structural model. The developed governing equations are then computed using finite element (FE) codes developed in-house to predict the acoustic power level inside the enclosure, with and without control. The structural model developed is generic in nature, capable of incorporating orthotropic laminates, functionally graded materials, frequency-dependent structural damping, and variable stiffener orientation, if any, in predicting the energy transmission into a double-wall backed enclosure. Hence, the developed numerical model enables the designers for precise quantification of transmitted sound with and without ASAC and greater flexibility in terms of the number of panel leaves, boundary, and stiffening condition of the aircraft panel-cavity-panel-enclosure system, made of isotropic or orthotropic laminates.
Many acoustic studies on urban environments focus on soundscapes and subjective perception, analyzing environmental parameters such as loudness, fluctuation strength, and roughness. However, room acoustic parameters have rarely been applied in this context, even though public squares are frequently used for musical events. Considering classical concerts in historical or archeological sites in Italy, or pop music performances in public squares amplified through audio systems, a key challenge is that the acoustic characteristics of these spaces remain largely unknown. This study addresses this gap by conducting acoustic measurements in Piazzale San Francesco in Parma, a public square already used for summer musical events, and by implementing its audio rendering in a virtual reality (VR) environment. The acoustic survey was carried out following the standards for enclosed rooms, in accordance with ISO 3382, while the digital model of the space was created using photogrammetry. The piece Ti trad & igrave; quell'alma ingrata from Il Trovatore was used as the audio signal in Unreal Engine, enabling a navigation of the digital space calibrated with measured impulse responses (IRs). The resulting VR rendering allows users to be fully immersed in the virtual space, freely exploring it with six degrees of freedom (6DoF), as they would in reality, while listening to the same musical performance.
Addressing synergistic low-frequency vibration isolation and energy harvesting needs in precision equipment, a coupled quasi-zero-stiffness dynamic vibration absorber system with integrated piezoelectric energy harvesting is proposed. Two configurations are established: a linear primary system with a quasi-zero-stiffness absorber (LP-QZS) and a two-stage quasi-zero-stiffness system (TQZS). Nonlinear dynamic models are developed, and approximate analytical solutions under harmonic excitation are derived via the harmonic balance method, validated by the Runge-Kutta simulations. Both systems significantly enhance low-frequency vibration isolation: TQZS reduces the primary amplitude below a QZS-primary-linear-absorber system. Piezoelectric harvesters generate substantial voltage outputs in specific frequency bands, confirming vibration-to-electric energy conversion. Parametric analysis reveals that increasing mass ratio mu simultaneously reduces the primary system amplitude and increases both the peak value and operational bandwidth of the harvested voltage in both configurations. However, the effect of damping is fundamentally different between the two configurations: In the LP-QZS system, higher damping enhances vibration suppression despite impairing energy harvesting; while in the TQZS system, it increases the primary system's amplitude and severely diminishes the harvesting output and bandwidth. In contrast, small variations in the stiffness ratio exert a negligible influence on both vibration isolation and energy harvesting performance for both systems. The parametric tuning laws elucidated in this work lay a theoretical foundation for the design of advanced integrated equipment capable of simultaneous vibration control and energy harvesting.
Stochastic analysis traditionally assumes excitations to be independent. However, correlations among excitations are prevalent in engineering systems and often disregarded for analytical simplicity. Such neglect introduces fundamental errors in response predictions. For instance, correlated excitations can induce an asymmetric response probability density function (PDF) and a nonzero-mean response-phenomena that an independence assumption would fail to capture, leading to substantial predictive error. This study investigates the response of nonlinear systems driven by Poisson white noise with correlated pulse amplitudes. To account for this correlation, additional terms are incorporated into the generalized Fokker-Planck (FP) equation. The modified FP equation is solved using the exponential-polynomial closure (EPC) method, yielding an approximate PDF for the system response. The accuracy of this solution is validated by comparing its predictions with Monte Carlo simulations. Analyses of linear, Duffing, and Dimentberg oscillators quantitatively reveal how the sign and magnitude of the pulse correlation shape the response statistics. These findings confirm that excitation correlation significantly influences the system response and must be explicitly included for accurate analysis.
With the expansion of the industrial applications of magnetic bearings, in many scenarios, the installation base of magnetic bearings is not rigid. That is, there is a flexible support relationship between the supporting base of the magnetic bearing and the ground. In this case, the installation base of the magnetic bearing will move under the influence of external excitation or rotor motion, which in turn affects the dynamic characteristics of the maglev rotor (magnetic levitation rotor). At present, most studies assume that the supporting base is rigid or only the base's motion relative to the ground is considered, ignoring the flexible support relationship between them. However, for the base flexible support, the influence of base support parameters and external base excitation on the dynamic characteristics of the maglev rotor remains to be studied. This article establishes a dynamic model of the maglev rotor with base flexible support. Through numerical simulations and experiments, it investigates the rotor's dynamic characteristics under different base support parameters, as well as the influence of these parameters on the rotor's dynamic response when the base is subjected to external disturbances. The research results indicate that properly increasing the base mass and base support damping while reducing the base support stiffness can effectively improve the rotor's levitation accuracy, enhance system stability, and mitigate the impact of external base disturbances on the system. This study can provide a reference for expanding the industrial application scenarios of maglev rotors and their vibration and noise control.
Lightweight materials and design, though economically and ecologically attractive, typically suffer from poor vibro-acoustic performance, for which locally resonant metamaterials have recently emerged as promising solutions. They enable stop bands, targeted frequency zones of strong vibration attenuation, through subwavelength integration of resonant inclusions to a host structure. However, their limited broadband performance and lack of mass-manufacturing methods currently hinder industrial adoption. Injection molding is therefore gaining attention as a viable manufacturing process. To transition toward mass-manufacturable metamaterials with broadband-enhanced vibration attenuation, this work investigates how advanced multimaterial injection molding strategies may be leveraged. In particular, a design methodology is introduced for multimaterial resonant inclusions where mass is efficiently added via small inserts and overmolding to tune the targeted frequency bands, while highly damped material is strategically applied to widen and even merge stop bands. Specifically, acrylonitrile-butadiene-styrene (ABS) provides strength and stiffness, and thermoplastic polyurethane (TPU) increases material damping. First, the influence of different ABS-TPU distributions and interfaces on the bond strength and resulting stiffness and damping is investigated. The outcomes reveal how material layout may be best leveraged in resonator design for broadband performance. Next, the parametrized ABS-TPU layout within the resonator is optimized to enhance broadband vibration attenuation. Small masses are included to tune the resonance frequencies. Vibration measurements on the manufactured metamaterial plate with optimized multimaterial resonator additions confirm broadened vibration attenuation, demonstrating the potential of multimaterial injection molding for mass-manufacturing of locally resonant metamaterials with broadband-enhanced performance.
Enhanced transmission of sound across the air-water interface is modeled with a system of three parallel elastic plates connected by periodically spaced columnar ribs. Maximum transmitted energy combined with optimal frequency bandwidth occurs when the central plate is far thicker than those facing air and water. This allows it to be replaced by a mass-like impedance, resulting in a simpler and accurate two-plate model. Asymptotic analysis based upon the air-to-water impedance ratio, supported by simulations, provides explicit formulae for the system dimensions required for maximum broadband transmission.
Enhancing the energy efficiency in controlling an overhead crane during repeated rest-to-rest movements can result in significant energy savings. Moreover, it influences both maintenance expenditures and safety. This study focuses on optimizing a smooth wave command shaping profile to reduce energy usage and enhance the motion efficiency of an overhead crane. A smooth single-mode command shaper is modified to reduce the energy required during the trolley maneuver. The nonlinear equation of motion for a simple crane is derived, linearized, and then solved to determine the optimal controller performance. An extra constant is added to a smooth waveform command shaper and then optimized to enhance the required energy. Furthermore, the selectable maneuvering time feature of the smooth command shaper is utilized to further enhance the maneuver's efficiency. The results obtained are compared with several well-known input/command shapers. The optimized command shaper profile can eliminate all residual vibrations induced and reduce energy consumption by 30% compared to the most effective unoptimized input shaper and 45% compared to the classical smooth command shaper. The performance of all shapers is numerically and experimentally validated on an experimental overhead crane.
Driving-point receptance of a structure, defined as the displacement amplitude of the structure at the same point and in the same direction as a unit point harmonic force causing the displacement, is a well-established and widely applied quantity in structural dynamics. However, as noted and discussed by the correspondence author in 2018, because of the use of point force, driving-point receptance is essentially singular (i.e., infinite) by its definition, except when the structure is modeled as a beam, plate, or shell. Nevertheless, with the evolvement of structural dynamics, various methods have been developed to calculate the above-defined driving-point receptance, but without considering the singularity issue, giving rise to concerns about the validity of the various structural dynamic analyses based on the calculated driving-point receptance. This article, as a continuation of the previous study, aims to further raise awareness of the singularity issue in numerical models, explore how the singularity causes nonconvergence in several typical driving-point receptance calculation methods, and propose ways to address the issue.
A nonlinear torsional vibration model of precision harmonic drives is developed, incorporating stiffness degradation, static transmission errors, piece-wise backlash, and periodic torque excitation. Dynamic responses are quantified through angular domain solutions of the dimensionless governing equations using the Runge-Kutta method. The research identifies two types of bursting oscillations caused by stiffness and backlash, and reveals their triggering mechanisms. Furthermore, the effects of factors such as the damping coefficient, excitation torque, and speed on the chaotic characteristics are analyzed using bifurcation diagrams, time histories, phase trajectories, and Poincar & eacute; maps. The results indicate that with prolonged service time, interface damage-induced stiffness degradation or enlargement of backlash may simultaneously induce bursting oscillations and chaotic motion. Furthermore, the amplitude of the torque fluctuation component critically governs the emergence of bursting oscillations, with these phenomena occurring when A(b)' >= T-o '. The dynamic behavior of harmonic drives exhibits strong dependence on operating conditions, with numerical simulations demonstrating that progressive increases in speed and load torque induce transitions toward increasingly unstable chaotic regimes. Increasing damping can suppress this transition. These findings elucidate the mechanisms underlying undesirable nonlinear oscillations in the system, while establishing theoretical foundations for control strategies in precision harmonic drive applications.
Piezoelectric energy harvesters (PEHs) represent a compelling alternative to batteries for powering low-power Internet of Things (IoT) electronics, particularly in maintenance-constrained applications. However, the inherently cross-disciplinary scope of the research in this field has impeded the development of a unified multi-physics model that accounts for external excitation, mechanical-to-electrical energy conversion, nonlinear interface circuit behavior, energy management, and system-level power dynamics. This study introduces a system-level simulation framework to overcome the challenge. Using a plucking-mode PEH as an example, we first established its dynamic model and converted it into an equivalent circuit. We then analyzed the energy charging-release cycle and dynamic response characteristics of the harvester. The equivalent circuit model was further used to demonstrate the superior energy transfer efficiency of the self-powered synchronous electronic charge extraction circuit. In addition, the circuit simulation incorporated an energy management module and a wireless IoT node to emulate realistic system operation. This integrated approach bridges the gap between theoretical modeling and practical application evaluation. Finally, experimental tests validated the capability of the plucking-mode PEH to enable self-powered sensing. The methods and findings presented in this work contribute a critical understanding toward improving energy-harvesting efficiency and reliability, supporting the development of practical and scalable self-powered IoT systems.
We present a cyclically-arranged split-ring resonator metamaterial design that is capable of simultaneously attenuating P, SH, and SV-waves. The design targets tonal vibration frequencies in electric vehicles (EVs) caused by inverters and electric machines. The metamaterial's plate-like nature facilitates straight-forward integration with unibody sheet metal structures commonly found in automotive applications. The basis for the unit cell is a sub-cell with nearly-coincident in-plane and out-of-plane resonant frequencies. This sub-cell effectively blocks SV-waves and P or SH-waves in a single polarization direction dependent on the resonator orientation. To achieve a total bandgap in all propagation directions, we cyclically rotate and replicate the sub-cell to form a unit cell containing 2 & times; 2 sub-cells. We then compute the unit cell's band structure using a finite element model, documenting the expected bandgaps. To validate the numerical predictions, we fabricate a square polylactic acid plate embedded with 25 unit cells and subject it to P, SH, and SV-wave excitation on one edge using an electrodynamic shaker. We measure the displacement of the structure on the opposite edge using a laser Doppler vibrometer and compute the response transfer function. Results demonstrate significant attenuation of P, SH, SV-waves within the targeted frequency range of at least 35 dB, with SV-waves exhibiting the highest attenuation. This enhanced suppression of SV-waves is attributed to a greater number of sub-cells per unit cell participating in resonance compared to P and SH-waves. The measured performance demonstrates the strong potential for the proposed metamaterial to attenuate tonal frequencies in EV applications, potentially without additional mass.
Resonances of the externally forced Mathieu equation under quasiperiodic excitation are studied. The external forcing frequency is assumed to be independent of the parametric-stiffness frequency and the system's natural frequency. The response is analyzed by using a second-order multiple-scale approach. The system has secondary resonances at O (& varepsilon;) and O(& varepsilon;(2)) due to quasiperiodic forcing. These resonances occur when the forcing frequency matches the Mathieu equation's natural response frequencies, which themselves are functions of the parametric frequency and the natural frequency without excitation. In addition, at specific frequencies where the unforced Mathieu equation exhibits instabilities, resonances are observed at O(& varepsilon;) and O(& varepsilon;(2)) simultaneously. For a few selected resonances, the steady-state amplitude and phase are determined, and the multiple-scale solutions are compared to numerical simulations for verification. The effects of system parameters, such as the damping ratio and the parametric stiffness, on the response near the resonances are evaluated.
The post-buckling dynamics of wrinkled film-substrate structures has attracted sustained attention due to its potential for tunable functional devices and critical role in the reliability of flexible electronics. To accurately predict the dynamic performance of wrinkle-based devices, establishing a comprehensive post-buckling dynamic model is essential, though dynamic substrate characterization presents challenges owing to its inherently complex deformation and interfacial coupling with film morphology. In this study, a vibration-wave coupled parameter excitation dynamic model for wrinkled film-substrate structures is developed. To characterize dynamic film-substrate interactions, a dynamic Navier-Winkler foundation model is proposed that incorporates the inertial effect and elastic wave propagation within the substrate. The results reveal an evanescent-to-traveling wave transition in the substrate under periodic surface-distributed loads, leading to threshold-activated damping above a critical frequency. A complex effective dynamic stiffness is derived, which comprehensively characterizes the transition of substrate behavior from elastic to damping and finally to inertial with increasing excitation frequencies. By using linear perturbation analysis, the steady-state vibration responses of wrinkled films under periodic axial excitations are derived. The results demonstrate characteristic amplitude-frequency responses indicative of both substrate and film-dominated resonances, and substantially lower resonant frequencies and amplitudes than previously reported values attributed to substrate inertia and wave-induced dissipation. This model advances the fundamental understanding of wrinkle dynamics in film-substrate structures and establishes a theoretical framework for designing tunable wrinkle-based functional devices with optimized dynamic performance.
Acoustic rainbow trapping has demonstrated significant potential in applications such as noise control, acoustic sensing, and stealth or isolation technologies. Its unique advantage lies in its ability to isolate specific sound frequencies and trap them at precisely defined spatial locations. By exploiting this property, broadband acoustic trapping can be achieved through gradient frequency designs, while the precise regulation of specific frequency bands can be realized by adjusting acoustic parameters, such as material gradients and geometric configurations. In this work, we propose a modular and tunable acoustic side-branch tube structure (MTAS), which integrates modular design and tunable parameters to achieve broadband acoustic trapping. The dispersion relations, trapping positions, and spatial field distributions are systematically derived. Building on the broadband trapping characteristics, we employ a genetic algorithm (GA) combined with finite element methods (FEM) to realize effective sound insulation over an extensive frequency range of 120-10,000 Hz. Furthermore, leveraging the multiband response, frequency separation, and spatial control inherent to rainbow trapping, we design a band-pass filter-like structure. This structure enables precise frequency selection and efficient sound energy concentration, offering a novel approach for tailored acoustic control. Experimental validation showed transmission below 0.1 across most frequencies from 100 to 2000 Hz, further supporting the reliability of the simulations.
Acoustic nonreciprocity has received significant interest, particularly in the context of enabling logic devices. One way to break reciprocity is through strategic spatiotemporal modulation of a material's properties. In this work, we propose and analytically, computationally, and experimentally explore a concept composed of a quasi-one-dimensional nonlinear system, where the shear stiffness depends on longitudinal strain, with the aim that nonreciprocity of transverse-rotational waves could be enabled by the simultaneous propagation of a longitudinal wave injected from the boundary. Such an approach should require less computational overhead in contrast to systems wherein spatiotemporal modulation is accomplished by active control distributed throughout the material, and potentially enable scaling to smaller system sizes and higher frequencies. While good agreement, showing significant nonreciprocity, is found between our analytical predictions and our reduced-order, discrete element model (DEM) simulations, our higher fidelity, finite element model (FEM) simulations, and experiments do not show the same. We suggest that this qualitative difference is due to mechanical instability of the chain, which is not present in either DEM simulations or the analytical model. While providing a theoretical proposal for an all-acoustic spatiotemporally modulated nonreciprocal system, this work also identifies a critical limitation, namely, that of instability, which should be addressed in future related concepts.
This article presents a study of the inverse design of vibroacoustic responses of beam structures for vibration and noise control. The aim is to develop an efficient method for designing structural shapes that achieve desired vibroacoustic behaviors. To this end, we propose a tandem neural network architecture capable of directly mapping desired vibroacoustic response to the optimal geometry of non-uniform beams. Unlike traditional approaches, our method enables rapid design by leveraging tandem neural networks. We explicitly incorporate physical constraints relevant to shape optimization into the loss function of the tandem neural network. This ensures that the generated designs are not only computationally feasible but also physically realizable and practical for engineering applications. The proposed method is validated through several case studies, demonstrating its ability to generate shapes with precise tuning of natural frequencies, suppression of vibrations, or realization of specific vibroacoustic phenomena such as acoustic black hole-like responses. This study provides valuable insights for the development of innovative solutions to complex vibroacoustic design problems.
