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Large offshore wind turbines are founded on jacket structures. In this study, an elastic full-space jacket structure foundation in an elastic and viscoelastic medium is investigated by using boundary integral equations. The jacket structure foundation is modeled as a hollow, long circular cylinder when the dynamic vertical excitation is applied. The smooth surface along the entire interface is considered. The Betti reciprocal theorem along with Somigliana’s identity and Green’s function are employed to drive the dynamic stiffness of jacket structures. Modes of the resonance and anti-resonance are presented in series of Bessel’s function. Important responses, such as dynamic stiffness and phase angle, are compared for different values of the loss factor as the material damping, Young’s modulus and Poisson’s ratio in a viscoelastic soil. Results are verified with known results reported in the literature. It is observed that the dynamic stiffness fluctuates with the loss factor, and the turning point is independent of the loss factor while the turning point increases with load frequency. It is seen that the non-dimensional dynamic stiffness is dependent on Young’s modulus and Poisson’s ratio, whilst the phase angle is independent of the properties of the soil. It is shown that the non-dimensional dynamic stiffness changes linearly with high-frequency load. The conclusion from the results of this study is that the material properties of soil are significant parameters in the dynamic stiffness of jacket structures, and the presented approach can unfold the behavior of soil and give an approachable physical meaning for wave propagation.

This research deals with the nonlocal dynamic buckling analysis of embedded microplates reinforced by single-walled carbon nanotubes (SWCNTs). The material properties of structure are assumed viscoelastic based on Kelvin–Voigt model. Agglomeration effects are considered based on Mori–Tanaka approach. The elastic medium is simulated by orthotropic visco-Pasternak medium. The motion equations are derived applying higher-order shear plate model based on sinusoidal kinematic in which the size effects are considered using Eringen’s nonlocal theory. The Navier method in conjunction with the Bolotin’s methods is applied for calculating resonance frequency and dynamic instability region of structure. The effects of different parameters such as volume percent of SWCNTs, agglomeration, volume percent of SWCNTs in volume, nonlocal parameter and structural damping on the dynamic instability of visco-system are shown. The results are compared with other published works in the literature. Results indicate that the agglomeration effects have an important role in dynamic stability of structure. In addition, increasing volume percent of SWCNTs leads to higher resonance frequency.

In engineering applications, composite structures supported by elastic foundations are being vastly utilized in various operating environmental conditions. The nonlinear hygrothermal effect on vibration analysis of a magnetostrictive viscoelastic laminated composite sandwich plate rested on two-parameter Pasternak’s foundations is studied in the present article. The material properties of the viscoelastic plate’s layers are considered based on the Kelvin–Voigt model. The governing equation system is derived according to Hamilton’s principle. The analytical solution is obtained to study influences of the hygrothermal change, half wave number, magnitude of the feedback control gain, aspect ratios, thickness ratio, and structural viscoelastic damping coefficients on vibration damping characteristics of the plate including the frequencies, the damping rate, and the deflection. The obtained results indicate that the natural frequency and deflection reduce with increasing the structural viscoelastic damping value. The plate takes a long time for suppressing its vibration due to increasing the hygrothermal factor.

We present a novel formulation of the Rayleigh–Plesset equation to describe stable gas bubble dynamics in viscoelastic media, using bubble volume variation, rather than radius, as the primary variable of the resulting nonlinear ordinary differential equation. This formulation incorporates the linear Kelvin–Voigt model as the constitutive relation for the surrounding fluid, capturing both viscous and elastic contributions, to track the oscillations of a gas bubble subjected to an ultrasonic field over time. The proposed model is solved numerically, subjected to a convergence analysis, and validated by comparisons with theoretical and experimental results from the literature. We systematically investigate the nonlinear oscillations of a single spherical gas bubble in various viscoelastic environments, each modeled with varying levels of rheological complexity. The influence of medium properties, specifically shear elasticity and viscosity, is examined in detail across both linear and nonlinear regimes. This work improves our understanding of stable cavitation dynamics by emphasizing key differences from Newtonian fluid behavior, resonance frequency, phase shifts, and oscillation damping. Elasticity has a pronounced effect in low-viscosity media, whereas viscosity emerges as the dominant factor modulating the amplitude of oscillations in both the linear and nonlinear regimes. The model equation developed here provides a robust tool for analyzing how viscoelastic properties affect bubble dynamics, contributing to improved the prediction and control of stable cavitation phenomena in complex media.

This article investigates bending, buckling, and vibration analysis in viscoelastic functionally graded curved nanobeam embedded in an elastic medium under different boundary conditions. The stresses can be calculated based on not only the nonlocal stress field but also the strain gradient stress field according to the nonlocal strain gradient elasticity theory. The present higher order refined curved nanobeam theory which captures shear deformation influence does not need any shear correction factors. Two power-law models are used to describe the continuous variation of material properties of viscoelastic functionally graded curved nanobeam. Governing equations of nonlocal strain gradient viscoelastic functionally graded curved nanobeam are obtained using Hamilton’s principle. To establish the present model, the results are compared with those of functionally graded curved nanobeams. The effects of nonlocal parameter, length scale parameter, viscoelastic damping coefficient, spring stiffness, boundary conditions, and power-law exponent on the bending, buckling, and vibration responses of viscoelastic functionally graded curved nanobeam are discussed.

Considering the geological bodies as a viscoelastic medium, rather than an elastic medium, is more reliable for the issues of blasting vibration because of the damping characteristic of the geological bodies. However, the analytical solution for ground vibration subject to spherical charge in a viscoelastic medium has never been reported yet. In this study, an approximate analytical solution is first proposed to address such a problem. Its accuracy and validity are verified by direct numerical simulation (finite difference method) and extensive experiences in construction. Based on the present analytical solution, the ground and underground vibration characteristics are systematically studied. The results show that both blasting parameters and medium parameters affect the blasting vibration, especially, the viscosity modulus of the medium will significantly change the waveform and amplitude of blasting vibration. The attenuation coefficients for underground and ground vibration vary from 1.4 to 2.0 and 0.7 to 2.0 with the increasing viscosity modulus. This analytical solution provides reliable prediction and analysis for blasting vibration.

The aim of this study is to study nonlinear damped torsional vibration of single-walled carbon nanotubes (SWCNTs) surrounded by nonlinear viscoelastic medium under thermal stresses. The novelty of this paper is accounting for nonlinear damping of viscoelastic medium. It means that not only the geometrical nonlinearity is considered but also the nonlinearity raised from viscoelastic medium has been considered and effect of the nonlinear damping of viscoelastic medium on torsional response and frequencies has been included. Nonlocal Eringen’s elasticity as a continuum theory has been adapted to consider the small size effect. The nonlinear strain derived using Green–Lagrange strain relation. Hamilton’s principle conducted to derive equation of motion and boundary conditions. Multiple time scale and Galerkin’s methods have been employed to obtain the nonlinear torsional frequencies and responses. The effect of nonlinear damping and stiffness raised by the viscoelastic medium, nanotube length and diameter, thermal stresses, vibration amplitude, nonlocal scale coefficient and boundary conditions on nonlinear torsional vibration are studied. Results reveal that natural torsional frequencies decrease by increasing damping coefficient of viscoelastic medium at both high and low temperatures. However, nonlinear torsional frequencies increase by increasing elastic medium stiffness and vibration amplitude at both high and low temperatures. Temperature influence on frequencies depends on damping and stiffness of viscoelastic medium, length and diameter of nanotube, and nonlocal scale coefficient. From the results obtained, it is observed that the nonlinear torsional frequencies decrease at as the temperature increase for both Clamped–Clamped (C–C) and Clamped-Free (C-F) nanotubes for all modes of vibration. This study provides important insights into how natural frequencies and corresponding responses are influenced by nonlinear viscoelastic medium and geometrical nonlinearity. As nonlinear damping coefficient of viscoelastic medium increases, the nonlinear torsional frequencies decreases. However, higher values of nonlinear frequency obtained when the value of viscus damping decreases, this is true for all vibration modes. By increasing the diameter, the torsional stiffness increases and leads to an increase torsional vibration which causes response to be damped faster.

This study investigated an influence of the temperature field on thickness distribution of thermoformed products using complex and high-aspect-ratio mold. The optimum temperature field was obtained to achieve a more uniform thickness distribution in the thermoformed products by using finite element simulation. The material properties of acrylonitrile-butadiene-styrene (ABS) polymer sheet were obtained by two rheological measurement tests. The linear viscoelastic properties, such as the storage modulus and loss modulus, were measured by a small amplitude oscillatory shear (SAOS) test for wide ranges of frequency and temperature. The discrete relaxation time and discrete relaxation modulus were obtained by nonlinear regression. The fitting parameters C 1 and C 2 for the WLF model were obtained by curve fitting. The nonlinear viscoelastic property, such as stress relaxation modulus, was measured by a step strain test. The damping function and fitting parameter α of Wagner-Demarmels (WD) model were determined by curve fitting. Then, the Kaye–Bernstein-Kearsley-Zapas (K-BKZ) constitutive equation was utilized to the thermoforming simulation in order to investigate the material behavior of the polymer sheet. The numerical results showed that a more uniform thickness distribution could be achieved with the optimum temperature field of the sheet. The thinnest part of the products was improved by more than 30%.

In this paper, we study the component configuration issue of the line-shaped wave networks which is made of two viscoelastic components and an elastic component and the viscoelastic parts produce the infinite memory and damping and distributed delay. The structural memory of viscoelastic component results in energy dissipative and the damping memory arouses the instability, and the elastic component is energy conservation, such a hybrid effects lead to complex dynamic behaviour of network. Our purpose of the present paper is to find out stability condition of such a network, in particular, the configuration condition of the wave network under which the network is exponentially stable. At first, using a resolvent family approach, we prove the well-posed of the wave network systems under suitable assumptions on the memory kernel g(s), the damping coefficient μ1 and delay distributed kernel μ2(s). Next, using the Lyapunov function method, we seek for a structural condition of the wave networks under which the wave networks are exponentially stable. By constructing new functions we obtain the sufficient conditions for the exponential stability of the wave networks, the structural conditions are given as inequalities.

Machining vibrations and dynamic instability of machine tools is an important consideration in machining systems. Common approaches for improving their dynamic performance target either the process, or intelligent, yet complex control systems with actuators. Given that machine tools’ dynamic characteristics are largely defined by the characteristics of the joints, this article proposes a novel concept, attempting to create a new paradigm for improving the dynamic behaviour of machine tools—introducing modular machine tools components (Joint Interface Modules—JIMs) with joints deliberately designed for increasing dynamic stiffness and enhancing damping with the use of viscoelastic materials. Through a systematic model-based design process, a prototype replicating a reference tool holder was constructed exploiting viscoelastic materials and the dynamic response of the machining system was improved as a result of its introduction; in machining experiments, the stability limit was increased from around 2 mm depth of cut to 4 mm depth of cut, without compromising the rigidity of the system or changing the process parameters. The article also includes the results of investigations regarding the introduction of such prototypes in a machine tool and discusses the shortcomings of the stability lobe diagrams as a method for evaluating the performance of machine tool components with viscoelastically treated joints.