Search Results (294)

This paper advances a comprehensive controllability framework for Prabhakar fractional differential systems ($\mathcal{PFDS}$s) of order $\eta \in (1,2)$ with nonlocal initial conditions, where the second-order setting requires the joint specification of both an initial state and an initial velocity. Explicit solution representations for four structurally distinct classes of second-order Prabhakar systems are derived via the Laplace transform method and Neumann series expansions, revealing that the placement of the forcing term directly in the system or under the Prabhakar fractional integral operator produces fundamentally different convolution kernels. For linear integro-differential systems, necessary and sufficient controllability conditions are established through a Gramian rank criterion with an explicit norm-bounded control law, while for nonlinear systems, sufficient conditions are obtained via the Schauder fixed-point theorem under an asymptotic growth condition. Three numerical examples validate the theory: a three-dimensional linear system and a two-dimensional nonlinear integro-differential system achieve terminal errors of order ${10}^{-12}$ and ${10}^{-7}$, respectively, and a Prabhakar fractional mass–spring–damper system with viscoelastic hereditary damping demonstrates direct physical relevance, with all theoretical conditions verified and a terminal error of $7.42\times {10}^{-5}$ confirming precise rest-position steering by the Gramian-based control law. Full article

Photonic and acoustic jets are subwavelength wave localization phenomena formed in the near field of dielectric or elastic scatterers, enabling spatial resolution beyond classical diffraction limits and motivating applications in sensing, imaging, and wave–matter interaction control. This review places photonic and acoustic jets in a unified wave-physics framework and focuses on how composite and layered elements can be used to tune their properties. In photonic systems, refractive index contrast, layer thickness, and optical losses play key roles, while in acoustic systems, acoustic impedance mismatch, dispersion, and viscoelastic damping are critical. Models and numerical approaches, and experimental realizations in both optical and acoustic regimes, are reviewed and summarized to describe jet formation and to analyze the influence of material parameters and geometry. The main findings show that layered and composite scatterers, such as core–shell particles, multilayer spheres and cylinders, and graded-parameter metamaterials, provide additional degrees of freedom for controlling jet intensity, length, focal position, and directionality compared to homogeneous elements. Composite jet-forming elements offer a versatile platform for advanced wave localization and hold promise for metastructures, high-resolution sensing, integration into photonic and acoustic devices, and lab-on-chip technologies. Full article

Poly(ethylene terephthalate) (PET) composites reinforced with reduced graphene oxide (rGO) were investigated in order to elucidate the influence of nanofiller concentration and compatibilization on the viscoelastic relaxation behavior across the glass transition. Composites containing 0.1 and 0.5 wt% rGO were prepared by melt blending, and selected systems incorporated 5 wt% of an ionomeric polyester (PETi) as compatibilizer to enhance interfacial adhesion. The thermomechanical response was characterized using dynamic mechanical analysis (DMA) as a function of temperature. Experimental results revealed a strong dependence of stiffness, damping, and glass transition behavior on filler concentration and interfacial interactions. While low rGO loading produced minor changes, the incorporation of 0.5 wt% rGO significantly increased the glassy modulus and shifted the glass transition temperature, indicating restricted segmental mobility. Compatibilized systems exhibited further stiffness enhancement and modified relaxation dynamics due to improved stress transfer and interphase development. To capture the distributed nature of the relaxation processes, the glass transition region was modeled using a fractional Zener model (FZM) with two spring-pot elements within a cooperative relaxation framework. The model successfully reproduced the experimental $E^{\prime }$ and $tan\delta$ curves and revealed systematic variations in the fractional exponents and cooperative parameters. The results demonstrate that the introduction of rGO and compatibilizer progressively transforms the relaxation spectrum of PET from a relatively uniform segmental process into a heterogeneous, interfacially mediated viscoelastic response that is naturally described by fractional rheology. Full article

Functionally graded multi-material thermoplastic architectures provide a promising route for tailoring viscoelastic energy dissipation through controlled phase contrast and interfacial interactions. However, rational selection of optimal material compositions remains challenging due to competing requirements among stiffness, damping efficiency, thermal stability, and processability. The absence of a quantitative decision framework often limits systematic design of architected polymer systems. This study proposes an Analytic Hierarchy Process (AHP)-based multi-criteria decision model to identify the optimal rigid–elastic thermoplastic composition for enhanced damping performance. Nine performance criteria were considered, including storage modulus, loss factor, damping bandwidth, interfacial adhesion strength, elongation at break, impact resistance, glass transition temperature, thermal stability, and printability. Fourteen alternative material configurations combining different rigid phases, elastomeric interlayers, filler contents, and layer thickness ratios were evaluated. Pairwise comparison matrices were constructed based on experimentally measured thermomechanical data and literature-reported values, and consistency ratios were maintained below 0.1 to ensure decision reliability. Numerical results indicate that a graded PLA/soft-TPU/PLA architecture with optimized layer thickness ratio achieved the highest global priority weight (0.431), outperforming the baseline PLA/TPU system by approximately ~25–30% in overall performance index. Sensitivity analysis confirmed ranking robustness across variations in damping and stiffness weighting factors. The proposed framework establishes a systematic methodology for polymer material selection and multi-material architectural optimization, enabling data-driven design of thermoplastic systems with tunable viscoelastic performance. Full article

The viscoelastic materials used in traditional viscous damping walls (VDWs) typically exhibit high storage moduli, which tend to exacerbate the structural response of adjacent components during earthquakes. Furthermore, existing studies are mostly limited to small-strain characterization and lack investigation into the macroscopic mechanical recovery characteristics of materials under mainshock-aftershock sequences. To overcome these limitations, this study introduces silicone oil (SO) as a softener to prepare a novel viscoelastic polymer blend (PIB-B12-SO). Utilizing a customized self-stabilization dynamic sandwich-type shear (S-DSTS) device, the macroscopic dynamic mechanical behavior of the blend was systematically evaluated, focusing on its low-cycle fatigue and rest-recovery characteristics. The results indicate that the addition of SO effectively reduces the storage modulus and significantly enhances the loss factor of the blend. Notably, at a mixing ratio of 1:4 (SO: PIB-B12), the loss factor increased by 65.6% compared to pure PIB-B12. Furthermore, the introduction of SO effectively suppresses the degradation of the loss modulus under cyclic loading and promotes viscous recovery during the rest periods. The silicone oil blend modification successfully optimizes the macroscopic viscoelastic properties of PIB-B12, significantly enhancing the energy dissipation stability of the material under low-cycle fatigue and interval loading. Full article

Leaks in pipe systems result in significant economic losses, environmental hazards, and public health risks. Transient-based leak detection methods, which exploit the dynamics of pressure waves in response to system anomalies, have emerged as efficient techniques for identifying and characterizing leaks in pressurized pipelines. These methods offer distinct advantages, including minimal data requirements, high sensitivity to low-pressure anomalies, and resilience to the ill-posed conditions often affecting steady-state models. This paper reviews transient-based leak detection, synthesizing findings from over 139 peer-reviewed publications spanning the past three decades. The review categorizes transient-based methods into transient damping, transient reflection, system response, and inverse transient methods, analyzing the prevalence, evolution, and research rate of each category over time. By structuring the review around key aspects such as simulation domain type, analysis approach, system response, solver strategies, adaptability to noise, viscoelasticity, and network complexity, this paper identifies significant trends and shifts in research focus. A comprehensive tabular dataset of 139 studies captures how research activity in various areas has accelerated, slowed, or reached stability, offering insights into the evolving priorities within the field. This review highlights areas for further development, particularly in addressing AI-enhanced applications, transient excitation and measurement sites design, noise resilience, comprehensive leak characterization, validation approaches, and scalability for complex network applications, providing a resource to guide future research in transient-based leak detection. Full article

This paper proposes a machine-learning-assisted framework for modal sensitivity analysis of systems with viscoelastic damping elements, including both classical and fractional rheological models. Surrogate models are trained to approximate natural frequencies over a prescribed parameter space using two sampling strategies (Grid and Latin Hypercube) and two regression approaches: multi-layer perceptron (MLP) and Gaussian process regression (GPR). Sensitivities are obtained from the surrogates by finite differences and complemented by model-interpretability measures, namely permutation feature importance (PFI) and Shapley Additive Explanations (SHAP). The surrogate-based results are compared with analytically obtained sensitivities. Local first- and second-order sensitivities of natural frequencies are derived analytically using the direct differentiation method (DDM) for a nonlinear eigenvalue problem formulated in the Laplace domain and further transformed into dimensionless sensitivity measures. The methodology is demonstrated for a single-degree-of-freedom oscillator with classical and fractional Kelvin damper models and a two-story frame equipped with a fractional Kelvin damper. The results show very good agreement between analytical and surrogate-based sensitivities. Feature-importance rankings obtained by PFI and SHAP are consistent with the dimensionless sensitivities and capture changes in parameter influence under varying damping levels. Dispersion studies indicate only minor ranking variations. Full article

Noise pollution poses significant challenges to human health and quality of life; thus, high-performance damping materials are attracting increasing attention. Rubber has been extensively applied in these materials due to its viscoelasticity. However, the damping performance of these materials is often constrained by the intrinsically limited energy-dissipation capability of the polymer backbone, which lacks sound-absorbing functionalities. Herein, a cross-linked sliding graft copolymer (SGC) was incorporated into isobutylene-isoprene rubber (IIR) and chlorinated butyl rubber (ClIR) to fabricate high-strength damping elastomers. Unlike conventional covalently cross-linked polymers, the cross-linked SGC features mobile junctions, which can slide along the polyrotaxane backbone to redistribute and equalize chain tension, giving rise to the “pulley effect”. Benefiting from the intrinsically high energy-dissipation capability of SGC and the cooperative contribution of interfacial hydrogen bonding, the obtained SGC/IIR and SGC/ClIR blends exhibit both enhanced damping performance and mechanical properties. The synergistic improvement in damping capacity and mechanical robustness renders the SGC/rubber blends as promising candidates for advanced sound-absorption applications. Full article

Viscoelastic solutions are developed for the axial dynamic response of single piles in soil profiles that are inhomogeneous both vertically (with depth) and horizontally (with radial distance from the pile). While vertical soil inhomogeneity has been well explored, horizontal inhomogeneity has received limited research attention. In this work, the problem is treated in the realm of linear elastodynamic theory by employing a rigorous finite-element formulation specifically developed by the authors for the problem at hand. The effect of double soil inhomogeneity is investigated with reference to: (1) pile head stiffness; (2) pile-head radiation damping; (3) soil reaction along the pile; and (4) variation of the above with loading frequency. To this end, four different soil profiles are considered in conjunction with different levels of soil inhomogeneity, pile lengths, pile–soil stiffness contrasts, and boundary conditions at the pile tip. It is shown that the effect of inhomogeneity has unique features that cannot be captured by using a substitute homogeneous profile. Modeling an inhomogeneous soil as a homogeneous layer providing equal pile-head stiffness (to be referred in this work to as “stiffness-equivalent soil”) may grossly overestimate wave radiation, leading to dampened estimates of dynamic pile response. Simulations of two field experiments are reported, and implications of radiation damping in design are discussed. Full article

This study investigates the multi-scale tribo–thermo–viscoelastic performance of a sustainable bio-based FormuLITE epoxy reinforced with single and hybrid carbon nanofillers (0.1 wt.% total loading) under dry sliding up to 50 N. Pin-on-disk tests at 10, 30, and 50 N showed a consistent reduction in contact pressure and wear volume in the order: neat epoxy > 0.1 CNT > 0.1 GNP > 0.1 ND > 0.1 CNT/GNP > 0.1 CNT/ND > 0.1 GNP/ND. At 50 N and 1500 m sliding distance, neat epoxy exhibited a wear volume of 13.43 mm³ and contact pressure of 13.4 N/cm², while the GNP/ND hybrid reduced wear to 4.86 mm³ and contact pressure to 6.2 N/cm², corresponding to reductions of 64% and 54%, respectively. The accelerating wear coefficient decreased from 2.9 × 10⁻⁶ to 8.5 × 10⁻⁷, confirming slower damage accumulation in hybrid systems. Time-dependent contact pressure analysis revealed reduced asymptotic intensity and suppressed mid-cycle pressure spikes, indicating enhanced tribolayer stability. Effective surface hardness increased from 0.18 GPa (neat epoxy) to 0.30 GPa (GNP/ND), while normalized wear decreased from 1.00 to 0.36. Enhanced damping behavior and improved thermal conductivity in hybrid systems promoted stress redistribution and minimized flash-temperature localization. An interfacial energy-partition framework calibrated to experimental wear data quantitatively linked effective driving pressure, tribofilm stabilization, and surface hardness to material removal. The results demonstrate that wear mitigation in sustainable bio-epoxy systems is governed by coupled mechanical, viscoelastic, and thermal energy redistribution, with GNP/ND hybrids providing the most stable tribological interface under severe sliding. The findings contribute to the development of durable and sustainable bio-epoxy composite systems for engineering applications, supporting broader goals of responsible material utilization and sustainable industrial innovation aligned with the United Nations Sustainable Development Goals (SDG 9 and SDG 12). Full article

This paper investigates the linear stability of Navier–Stokes–Voigt (NSV) fluid flow in a channel filled with a homogeneous porous medium under general asymmetric slip boundary conditions. This study bridges the research gap between idealized theoretical models (uniform coating) and realistic engineering surfaces in superhydrophobic channels. In practice, manufacturing defects often lead to non-uniform slip distributions. By solving the generalized eigenvalue problem using the Chebyshev spectral collocation method, we quantify the sensitivity of the critical Reynolds number to symmetry breaking. The results reveal that symmetric slip achieves optimal stability, whereas symmetry breaking causes a significant destabilizing effect. Energy analysis clarifies the physical origin of this instability. Furthermore, we find that increasing the porous medium permeability parameter or the Voigt regularization parameter effectively counteracts the slip-induced instability. Specifically, flow stability can be restored even under highly asymmetric slip conditions if the porous damping or the viscoelastic regularization effect is sufficiently strong. This implies that inevitable manufacturing defects in engineering can be compensated for by optimizing the porous medium matrix. Full article

Underwater acoustic coatings are widely used to suppress low-frequency noise radiation and sonar reflection in underwater vehicles. In this study, an underwater acoustic coating model consisting of viscoelastic rubber layers and micro-perforated panel (MPP) structures is investigated, with particular emphasis on the low-frequency sound absorption mechanism and predictive modeling. Based on an improved transfer function method, a novel Micro-Perforated Panel Acoustic Coating Layer (MPPACL) model is developed to describe the coupled acoustic behavior of multilayer coatings under underwater conditions. The low-frequency sound absorption performance is primarily governed by the viscoelastic characteristics of the rubber layer, including material damping and complex modulus, while the incorporation of the MPP further enhances absorption through resonance effects. To efficiently explore the relationship between structural parameters and acoustic response, an ensemble learning-based deep neural network (ELDNN) is constructed using analytically generated data, enabling both forward prediction of sound absorption performance and inverse prediction of structural design parameters. The results show that the frequency prediction accuracy of the IDNN model is 3.7 times that of the DNN model. Furthermore, the proposed MPPACL model has achieved a significantly enhanced sound absorption effect within the frequency range of 50 to 2000 hertz. This effect has also been further verified through underwater experiments. The proposed framework provides an efficient and reliable approach for the design and optimization of underwater acoustic coatings. Full article

This work addresses the numerical solution of fourth-order initial value problems of the form $y^{\left(4\right)}=f(x,y,y^{\prime })$, extending the capabilities of standard Runge–Kutta–Nyström (RKN) methods which are typically limited to $y^{\left(4\right)}=f(x,y)$. Problems of this type arise naturally in structural and vibroacoustic dynamics, where velocity-dependent damping and coupling effects are essential for realistic modeling. Despite their practical importance, efficient explicit schemes that preserve the fourth-order structure while allowing derivative dependence remain limited. We generally present an explicit s-stage method that incorporates the first derivative into the internal stage approximations, necessitating the introduction of a new matrix parameter D in the order conditions. We successfully derive the algebraic order conditions for this extended method up to the seventh algebraic order. A particular pair of orders 6(4) is constructed at an effective cost of only four stages per step in contrast to eight function evaluations required in conventional RK pairs. This reduction in effective stage cost, together with the direct treatment of derivative-dependent terms, constitutes a structural and computational distinction from existing Runge–Kutta and RKN approaches. To demonstrate the physical relevance of the proposed solvers, we examine coupled fourth-order models arising in structural and vibroacoustic dynamics, including viscoelastic beam systems with aerodynamic (velocity-proportional) damping and structure–acoustic interaction in a thin-walled duct. These examples illustrate the capability of the method to handle coupled dynamics with derivative-dependent damping and source terms that are central to realistic modeling of such systems. On these representative problems, the proposed pair clearly and decisively outperforms existing Runge–Kutta pairs from the current literature, achieving substantially higher accuracy for the same computational effort. The results indicate that explicit fourth-order Nyström-type schemes with derivative-aware internal stages provide both a theoretical extension of classical RKN theory and measurable efficiency gains, offering a competitive alternative to reduction-based first-order formulations for velocity-dependent fourth-order systems. Full article

Coastal erosion is increasingly influenced by anthropogenic alterations to the sediment cycle and morphological transformations. Traditional shallow water models often neglect the mechanical behavior of the seabed and its rheological response to hydrodynamic forcing, limiting their accuracy in forecasting erosion patterns. To address these limitations, this study extends the classical one-dimensional Saint-Venant (shallow water) model by incorporating effects of viscosity, frictional effects, sediment transport and viscoelasticity. The seabed is treated as a Kelvin–Voigt material, characterized by an elastic modulus and a viscous damping coefficient, to account for both immediate and time-dependent mechanical responses. Using the COMSOL Multiphysics platform, the evolution of the water column and seabed was simulated in six idealized case studies under various conditions, including changes in seabed topography and different frictional and dispersive regimes. The results demonstrate the influence of seabed topography, friction $S_f$, diffusion/dispersion regularization term $E$, and viscoelastic properties on wave seabed interactions and morphodynamic bed evolution (Exner-type). The inclusion of viscoelastic damping contributes to the stabilization of morphological evolution, mitigating abrupt changes in bathymetry and enhancing the physical realism of the simulations. The whole research aims to improve the prediction capabilities of erosion processes and advance the current modeling tools. Full article

To investigate the dynamic behavior of smart composite structures with embedded heat sources over a wide temperature range, this study employed thermoplastic polypropylene as the matrix, combined with glass/carbon fiber prepregs and Ni80Cr20 alloy heating wires, and fabricated functional laminated specimens with integrated heating elements via a prepreg molding process. Using a self-developed variable-temperature cantilever beam vibration testing system, the evolution of natural frequencies and damping ratios from room temperature to 140 °C was systematically examined. Results indicate that temperature-induced thermal softening of the polypropylene matrix reduces the effective bending stiffness of the composites, leading to a decline in natural frequencies across all modes. For example, the first-order natural frequency of the sample decreased from approximately 30.8 Hz at room temperature to about 28.3 Hz at 140 °C, representing a reduction of approximately 8.12%. The second-order reduction reached about 8.99%, and the third-order reduction was approximately 9.65%. Carbon fiber-reinforced specimens exhibited relatively smaller frequency reductions due to the high modulus of the fibers. Concurrently, elevated temperatures enhance molecular chain mobility and interfacial viscoelastic dissipation at the fiber–matrix interface, causing a sharp increase in damping ratios at high temperatures (>100 °C). For instance, the damping ratio of the first-order mode increased significantly from approximately 1.02% at room temperature to about 2.9% at 140 °C. By comparatively analyzing carbon fiber and glass fiber systems, the study elucidated the distinct mechanisms underlying the “fiber-dominated” stiffness retention effect and the “resin/interface-dominated” damping dissipation effect under thermal influence. These findings provide critical experimental data and theoretical references for the active thermal regulation of structural performance in thermoplastic composite structures with integrated heat sources, thereby mitigating damage caused by external disturbances. Full article