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This mathematical analysis has been accomplished for the purpose of understanding the propagation behaviour like phase velocity and attenuation of Love-type waves through visco-micropolar composite Earth’s structure.

The considered geometry of this problem involves a micropolar Voigt-type viscoelastic stratum imperfectly bonded to a heterogeneous Voigt-type viscoelastic substratum. With the aid of governing equations of motion of each individual medium and method of separation of variable, the components of micro-rotation and displacement have been obtained.

The boundary conditions of the presumed geometry at the free surface and at the interface, together with the obtained components of micro-rotation, displacement and mechanical stresses give rise to the determinant form of the dispersion relation. Moreover, some noteworthy cases have also been extrapolated in detail. Graphical interpretation irradiating the impact of viscoelasticity, micropolarity, heterogeneity and imperfectness on the phase velocity and attenuation of Love-type waves is the principal highlight of the present study.

In this study, the influence of the considered parameters such as micropolarity, viscoelasticity, heterogeneity, and imperfectness has been elucidated graphically on the phase velocity and attenuation of Love-type waves. It has been noticed from the graphs that with the rising magnitude of micropolarity and heterogeneity, the attenuation curves shift upwards, that is the loss of energy of these waves takes place in a rapid way. Hence, from the outcomes of the present analysis, it can be concluded that heterogeneous micropolar stratified media can serve as a helpful tool in increasing the attenuation or in other words, loss of energy of Love-type waves, thus reducing the devastating behaviour of these waves.

Till date, the mathematical modelling as well as vibrational analysis of Love-type waves in a viscoelastic substrate overloaded by visco-micropolar composite Earth’s structure with mechanical interfacial imperfection remain unattempted by researchers round the globe. The current analysis is an approach for studying the traversal traits of surface waves (here, Love-type waves) in a realistic stratified model of the Earth’s crust and may thus, serves as a dynamic paraphernalia in various domains like earthquake and geotechnical engineering; exploration geology and soil mechanics and many more, both in a conceptual as well as pragmatic manner.

This paper aims to study the motion trajectory of the oil seal for shaft in eccentric state and derive equation of lip motion trajectory.

This paper analyzes the force during the motion of the eccentric lip by considering the material viscoelasticity, and a cam-plate mechanism is established as an equivalent model for the motion between the shaft and the lip; according to this, the equation of lip motion trajectory is derived.

The trajectory of the lip lags that of the shaft in the eccentric state because the viscoelasticity-affected lip recovery velocity is lower than the shaft recovery speed. The lip trajectory enters the lag phase earlier and the lag phase’s duration is longer with the increase of the eccentricity and rotational speed, because the deviation of the recovery velocities between the lip and the shaft will be exacerbated.

Innovatively, by considering the viscoelasticity of the material, the cam-plate mechanism is used to equivalent the motion of the shaft-lip to derive the equation for the radial motion trajectory of the eccentric lip. The regularity of lip motion is the key to determining the performance of oil seals, and the eccentric lip trajectory research method revealed in this paper provides a research basis for the performance research and optimization of eccentric oil seals.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2023-0161/

This paper presents a viscoelastic model for analysing the mechanical behaviour of SnPb solders which has been developed by combining grain boundary slip with viscoelasticity theory. On the basis of the model, and by using Boltzmann's integral constitutive equation of viscoelasticity, the mechanical behaviour (i.e., the relationships between stress (load) and strain (displacement)) of SnPb solders for one‐dimensional shearing deformation has been investigated and experimentally verified.

The purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick heat-radiating nanofluid over a linearly stretching sheet in the presence of uniform transverse magnetic field taking Dufour and Soret effects into account.

The governing boundary layer equations are transformed into a set of highly non-linear ordinary differential equations using suitable similarity transforms. Finite element method is used to solve this boundary value problem. Effects of pertinent flow parameters on the velocity, temperature, solutal concentration and nanoparticle concentration are described graphically. Also, effects of pertinent flow parameters on the shear stress, rate of heat transfer, rate of solutal concentration and rate of nanoparticle concentration at the sheet are discussed with the help of numerical values presented in graphical form. All numerical results for mono-diffusive nanofluid are compared with those of double-diffusive nanofluid.

Numerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Viscoelasticity, magnetic field and nanoparticle buoyancy parameter tend to enhance the wall velocity gradient, whereas thermal buoyancy force has a reverse effect on it. Radiation, Brownian and thermophoretic diffusions tend to reduce wall temperature gradient, whereas viscoelasticity has a reverse effect on it. Nanofluid Lewis number tends to enhance wall nanoparticle concentration gradient.

Study of this problem may find applications in engineering and biomedical sciences,e.g. in cooling and process industries and in cancer therapy.

Analysis of fast transient flow in water pipe systems is an important issue for the prevention of unfavorable pressure oscillations and severe damage to the pipelines. This paper aims to present the performance of three-dimensional (3D) simulation of laminar water hammer caused by fast closure of valve.

The viscoelastic behavior of pipe wall is mathematically modeled by using the rheological model of Maxwell. The arbitrary Lagrangian–Eulerian (ALE) method is also used to simulate fluid–structure interaction. In this method, unlike the classical water hammer theory, the acoustic wave velocity is calculated during the numerical simulations and therefore it is not predetermined.

Investigating the velocity profiles and the shear stress diagrams for transient flow in elastic pipe showed that the strong effect of viscous forces on the near wall region in conjunction with the influence of inertial forces in the central region of the pipe leads to creation of reverse flow near the pipe wall. Comparing the numerical results obtained for elastic pipe with those of viscoelastic pipe revealed that during transient condition, the viscoelastic wall absorbs the energy of fluid and therefore pressure fluctuations of viscoelastic pipe are damped more quickly. Moreover, the 3D simulation of water hammer confirmed the plane wave hypothesis of water hammer.

The 3D Navier–Stokes equations are solved considering the viscoelasticity of the pipe and the ALE method using the software package of COMSOL Multiphysics.

The purpose of this paper is to examine the dependency of dispersion and damping behavior of Love-type waves on wave number in a heterogeneous dry sandy double layer of finite thickness superimposed on heterogeneous viscoelastic substrate under the influence of hydrostatic initial stress.

The mechanical properties of the material of both the dry sandy layers vary with respect to a certain depth as quadratic and hyperbolic function, while it varies as an exponential function for the viscoelastic semi-infinite medium. The method of the separation of variables is employed to obtain the complex frequency equation.

The complex frequency equation is separated into real and imaginary components corresponding to dispersion and damping equation. After that, the obtained result coincides with the pre-established classical equation of Love wave, as shown in Section 5. The response of all mechanical parameters such as heterogeneities, sandiness, hydrostatic stress, thickness ratio, attenuation and viscoelasticity on both the phase and damped velocity against real wave number has been discussed with the help of numerical example and graphical demonstrations.

In this work, a comparative study clarifies that the Love wave propagates with higher speed in an isotropic elastic structure as compared to the proposed model. This study may find its applications in the investigation of mechanical behavior and deformation of the sedimentary rock.

Cantilever plates subject to axial flow can lose stability by flutter and properties such as viscoelasticity and laminar friction affect dynamic stability. The purpose of the present study is to investigate the dynamic stability of viscoelastic cantilever plates subject to axial flow by using the differential quadrature method.

Equation of motion of the viscoelastic plate is derived by implementing Kelvin-Voigt model of viscoelasticity and applying inverse Laplace transformation. The differential quadrature method is employed to discretize the equation of motion and the boundary conditions leading to a generalized eigenvalue problem. The solution is verified using the existing results in the literature and numerical results are given for critical flow velocities

It is observed that higher aspect ratios lead to imaginary part of third frequency becoming negative and causing single-mode flutter instability. It was found that flutter instability does not occur at low aspect ratios. Moreover the friction coefficient is found to affect the magnitude of critical flow velocity, however, its effect on the stability behaviour is minor.

The effects of various problem parameters on the dynamic stability of a viscoelastic plate subject to axial flow were established. It was shown that laminar friction coefficient of the flowing fluid increases the critical fluid velocity and higher aspect ratios lead to single-mode flutter instability. The effect of increasing damping of viscoelastic material on the flutter instability was quantified and it was found that increasing viscoelasticity can lead to divergence instability.

This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount.

The rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model.

The performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery.

This paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.

The purpose of this paper is to develop a numerical (finite-difference) model exploring phase and group velocities of SH-wave propagation in initially stressed transversely isotropic poroelastic multi-layered composite structures and initially stressed viscoelastic-dry-sandy multi-layered composite structures in two distinct cases.

With the aid of relevant constitutive relations, the non-vanishing equations of motions for the propagation SH-wave in the considered composite structures have been derived. Haskell matrix method and finite-difference scheme are adopted to deduce velocity equation for both the cases. Stability analysis for the adopted finite-difference scheme has been carried out and the expressions for phase as well as group velocity in terms of dispersion-parameter and stability-ratio have been deduced.

Velocity equations are derived for the propagation of SH-wave in both the composite structures. The obtained results are matched with the classical results for the case of double and triple-layered composite structure along with comparative analysis. Stability analysis have been carried out to develop expressions of phase as well as group velocity in terms of dispersion-parameter and stability-ratio. The effect of wavenumber, dispersion parameter along with initial-stress, porosity, sandiness, viscoelasticity, stability ratio, associated with the said composite structures on phase, damped and group velocities of SH-wave has been unveiled.

To the best of authors’ knowledge, numerical modelling and analysis of propagation characteristics of SH-wave in multi-layered initially stressed composite structures composed of transversely isotropic poroelastic materials and viscoelastic-dry-sandy materials remain unattempted inspite of its importance and relevance in many branches of science and engineering.

The purpose of this study is to develop a comprehensive size-dependent piezoelectric thermo-viscoelastic coupling model that accounts for two fundamentally distinct size-dependent models that govern fractional dual-phase lag heat transfer and viscoelastic deformation, respectively.

The fractional calculus has recently been shown to capture precisely the experimental effects of viscoelastic materials. The governing equations are combined into a unified system, from which certain theorems results on linear coupled and generalized theories of thermo-viscoelasticity may be easily established. Laplace transforms and state–space approach will be used to determine the generic solution when any set of boundary conditions exists. The derived formulation is used to two concrete different problems for a piezoelectric rod. The numerical technique for inverting the transfer functions is used to generate observable numerical results.

Some analogies of impacts of nonlocal thermal conduction, nonlocal elasticity and DPL parameters as well as fractional order on thermal spreads and thermo-viscoelastic response are illustrated in the figures.

The results in all figures indicate that the nonlocal thermal and viscoelastic parameters have a considerable influence on all field values. This discovery might help with the design and analysis of thermal-mechanical aspects of nanoscale devices.