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For the propellant grain of solid rocket motors (SRMs) with circular inner surfaces, the generalized Maxwell model (GMM) and the generalized Kelvin–Voigt model (GKV) are used to characterize the relaxation properties of the grain’s elastic modulus and the creep properties of Poisson’s ratio, respectively. Based on the elastic–viscoelastic correspondence principle, an analytical expression for viscoelastic stress that simultaneously considers the time-dependent nature of elastic modulus and Poisson’s ratio is derived. Based on this, a parametric analysis of the stress distribution in the grain under internal pressure is conducted. The results indicate that the hoop stress on the inner surface of the grain is most critical at the beginning of loading. As the thickness of the propellant grain increases, this initial tensile stress decreases moderately, but the duration of tensile stress increases. Increasing the thickness or stiffness of the combustion chamber casing moderately reduces the hoop stress during the initial loading and shortens the duration of tensile stress. Accurate measurement of the creep properties of Poisson’s ratio has a significant impact on improving calculation accuracy. The stress calculation results under gradual pressurization are lower than those under instantaneous pressurization. The conclusions provide a reference for analyzing the structural integrity of propellant grains.

Deep coal–rock masses in complex geological environments often contain defects that threaten the long-term stability of engineering structures. To investigate the influence of defect shape on the creep behavior and failure mechanism of coal–rock, an improved creep model was developed by coupling the Kelvin–Voigt contact model with the parallel bond model in PFC. Based on calibrated mesoscopic parameters, simulations were performed on intact specimens and those containing rectangular, trapezoidal, inverted U-shaped, square, and circular cavities under stepwise loading. Results show that cavity defects significantly weaken the creep strength, strain, and elastic modulus of coal–rock, with degradation depending on cavity geometry. Rectangular cavities cause the largest drop in failure stress, inverted U-shaped cavities reduce the elastic modulus most, and square cavities lead to the greatest strain decrease. Under equal cavity areas, wider cavities promote greater compressive deformation. High-stress zones form and propagate differently across shapes: circular cavities generate symmetric stress fields and exhibit better structural stability, while other shapes develop stress zones outside the cavity that connect laterally. Cracks initiate in these high-stress regions and expand along stress paths, showing that cavity geometry dominates stress distribution and failure mode—rectangular and inverted U-shaped cavities favor local shear failure, whereas circular cavities tend toward global shear failure.

This study investigates the propagation of surface seismic waves at the loosely bonded interface of a visco-piezoelectric composite structure, incorporating the flexoelectric effect. The structure consists of a viscoelastic layer placed over a piezoelectric substrate, with the upper layer's shear stiffness modelled using the Kelvin–Voigt approach. An analytical method based on the separation of variables is employed to derive the complex dispersion relations for both electrically open- and short-circuit boundary conditions. Numerical simulations reveal the significant influence of various parameters on the wave's phase velocity and attenuation coefficient. Furthermore, a graphical comparison of three rheological models—Maxwell, Newton, and Kelvin–Voigt—is presented. The results show that the attenuation is lower in the Maxwell and Newton models compared to the Kelvin–Voigt model. Key findings include the bonding parameter's direct proportionality with phase velocity and inverse relationship with attenuation, and the pronounced impact of flexoelectricity on both phase velocity and attenuation. This theoretical framework offers insights into the piezo-flexoelectric coupling, with potential applications in designing sensors, actuators, energy harvesters, and nano-electronic devices.

In recent years, hard-magnetic soft (HMS) structures have emerged with meritorious properties for potential applications in many fields, such as soft robotics, wearable devices, and stretchable electronics. Developments in reliable computationally efficient dynamic models of HMS structures, however, are vital not only to gain a better understanding of their magneto-mechanical behaviors but also to design effective control algorithms. This study proposes a time-dependent computationally efficient magneto-viscoelastic model of a cantilever HMS structure subject to an external magnetic field. The Kelvin–Voigt internal energy dissipation model is utilized to accurately capture the nonlinear time-dependent response behavior of the HMS beam subject to large magnitudes of the magnetic field at different frequencies. The Galerkin modal decomposition scheme and Bogacki–Shampine method are used to discretize and solve the proposed model. A 2D finite element (FE) model is further developed to assess the effectiveness of the proposed nonlinear model in terms of computational efficacy and accuracy. Moreover, A hardware-in-the-loop framework is developed to experimentally characterize the deflection responses of the HMS beam to steady as well as harmonically varying magnetic fields. The nonlinear deflection responses of the proposed magneto-viscoelastic model subject to magnetic flux density up to 30 mT showed very good agreements with the measured data and the FE model, while the response saturation occurred under a field exceeding 15 mT . The measured and model responses were further analyzed to obtain time-histories, phase-plane, and hysteretic response characteristics of the structure considering different magnitudes ( 5 - 30 mT ) and frequencies ( 0.25 - 1 Hz ) of harmonic as well complex harmonic variations in the magnetic field. The simulation results from the developed model aligned well with the experimental findings across all considered excitations. Moreover, the computation time varied from approximately 3.2 to 31 s, depending on the number of generalized coordinates used in the modal decomposition. The computation time of the FE model on the same computing platform was in excess of 4700s.

The stabilization of rock mass vibrations in underground excavations presents a critical engineering challenge due to the interplay of viscoelastic dynamics, impulsive shocks from blasting or rock bursts, and time-varying delays induced by wave propagation and sensor–actuator networks. In this paper, an integral sliding mode control scheme is developed for a Kelvin–Voigt type hyperbolic system subject to such impulsive effects and time-varying delays. To preserve sliding surface continuity under impulsive disturbances, the impulse information is explicitly incorporated into the design of the integral sliding function. The resulting sliding mode dynamics, which include discrete state jumps, are analyzed using a piecewise Lyapunov functional combined with inequality techniques; sufficient conditions are derived to guarantee asymptotic stability. Moreover, a sliding mode control law is synthesized to ensure that the system trajectories reach and remain on the sliding manifold from the initial time onward, despite parameter uncertainties and external disturbances. Numerical simulations with parameters reflecting realistic mining scenarios verify the effectiveness of the proposed control strategy, demonstrating its potential for practical rock mass vibration stabilization in geotechnical engineering.

The paper is devoted to the study of the qualitative behavior of solutions for the Kelvin–Voigt model taking into account memory along fluid motion trajectories. Namely, based on the theory of attractors of noninvariant trajectory spaces, for the model under consideration in the nonautonomous case the existence of a uniform trajectory and a uniform global attractor is proved under certain conditions on the coefficients.

We calculate the mechanical response rx,t of an initially quiescent semi-infinite homogeneous medium to a pulse applied at the origin, and this is achieved within the framework of the Kelvin–Voigt model. Although this problem has been extensively studied in the literature because of its wide range of applications—particularly in seismology—here, we present a solution in a novel integral form. This integral solution avoids the numerical computation of the solution in terms of the inverse Laplace transform; that is, numerical integration in the complex plane. In particular, we derive integral form expressions for both delta-pulse and step-pulse excitations which are simpler and more computationally efficient than those previously reported in the literature. Furthermore, the obtained expressions allow us to obtain simple asymptotic formulas for rx,t as x,t→0,∞ for both step- and delta-type pulses.

Fractional Kelvin–Voigt (FKV) oscillators describe vibrations in viscoelastic structures with memory effects, leading to dynamics that are often more complex than those of classical harmonic oscillators. Since the harmonic oscillator is a simple, widely known, and broadly applied model, it is natural to ask under which conditions the dynamics of an FKV oscillator can be reliably approximated by a classical harmonic oscillator. In this work, we develop practical tools for such analysis by deriving approximate formulas that relate the parameters of an FKV oscillator to those of a best-fitting harmonic oscillator. The fitting is performed by minimizing a so-called divergence coefficient, a discrepancy measure that quantifies the difference between the responses of the FKV oscillator and its harmonic counterpart, using a genetic algorithm. The resulting data are then used to identify functional relationships between FKV parameters and the corresponding frequency and damping ratio of the approximating harmonic oscillator. The quality of these approximations is evaluated across a broad range of FKV parameters, leading to the identification of parameter regions where the approximation is reliable. In addition, we establish an empirical criterion that separates oscillatory from non-oscillatory FKV systems and employ statistical tools to validate both this classification and the accuracy of the proposed formulas over a wide parameter space. The methodology supports simplified modeling of viscoelastic dynamics and may contribute to applications in structural vibration analysis and material characterization.

The entropic nature of elasticity of long molecular chains and reticulated materials is discussed concerning the analysis of flows of polymer melts and elastomer deformation in the framework of Frenkel–Eyring molecular kinetic theory. Deformation curves are calculated in line with the simple viscoelasticity models where the activation energy of viscous flow depends on the magnitude of elastic entropic forces of the stretched macromolecules. The interconnections between deformation processes and the structure of elastomer networks, as well as their mutual influence on each other, are considered.

In this paper, we focus on a generalized singular fractional order Kelvin–Voigt model with a nonlinear operator. By using analytic techniques, the uniqueness of solution and an iterative scheme converging to the unique solution are established, which are very helpful to govern the process of the Kelvin–Voigt model. At the same time, the corresponding eigenvalue problem is studied and the property of solution for the eigenvalue problem is established. Some examples are given to illuminate the main results.