Voigt Scheme Research Articles

Tin diselenide/zirconium disulfide terahertz acoustic multi-layer superlattice for liquid sensing applications of acetonitrile; reconsidering Voigt-Reuss-Hill schemes

Studying the mechanical properties mismatching of SnSe2/ZrS2 2D materials with Voigt-Reuss-Hill (VRH) schemes promise a novel structure for sensing applications. For the first time, we studied the effect of mechanical mismatching properties of SnSe2/ZrS2 multilayers with VRH schemes on the acoustic wave’s propagation through acoustic superlattice (AS). We proposed [(SnSe2/ZrS2)4] superlattice with VRH schemes as a new THz multichannel sensor for acetonitrile sensing. The [(SnSe2/ZrS2)4] with Voigt scheme introduced several resonant peaks for acetonitrile inside the superlattice bandgap compared to Hill and Reuss schemes. The appropriate relation between resonance frequency shift and resonance bandwidth is the key to improving the multichannel sensor's sensitivity to liquid characteristics. Further, we studied the effect of low and high temperatures on our multichannel sensor. Furthermore, the highest sensitivity and resonance frequency were recorded by our AS with the Voigt scheme towards acetonitrile having values of 0.287 (GHz/(kg/m3)) and 0.237 THz at 0 °C. The results show a novel sensitivity of acetonitrile for low-temperature environments.

Measurement and simulation of electrical resistivity of cement-based materials by using embedded four-probe method

The electrical resistivity of cement-based materials is an important index that can be used for designing durable, multifunctional, and smart concrete structures. However, the measurement and prediction of electrical resistivity are far from being well addressed for cement-based materials. In this study, a modified four-probe test using embedded fine copper rods as electrodes was developed to measure the electrical resistivity of cement-based materials. A coupled thermal-electrical analysis was conducted to verify the feasibility of the modified four-probe method. The simulated results show that a linear relation between the electrical resistivity and the apparent electrical resistance. The contact resistance of the interface between the specimen and the electrodes has little effect on the electrical resistivity. The applied voltage ranging from 4 V to 28 V has a minor influence on the measured electrical resistivity. The electrical resistivity of the specimens cured under standard condition is greater than that under sealed condition. The electrical resistivity of cement-based materials cured under both sealed and standard conditions increases with increasing curing age. A higher volume fraction of sand contributes significantly to a higher electrical resistivity of cement-based materials. Moreover, the homogenization results indicate that the differential scheme predictions coincide quite well with the measured electrical resistivity of cement-based materials with a wide range of sand volume fractions (0%∼60%). The Voigt scheme, the self-consistent scheme, and the Mori-Tanaka scheme can predict well the electrical resistivity of cement-based materials with a low volume fraction of sand (<20%), but fail to give a good prediction at a higher sand content.

Vibrational analysis of viscous thin beams stressed by laser mechanical load using a heat transfer model with a fractional Atangana-Baleanu operator

This article investigates the thermoelastic responses of an initially stressed viscoelastic microbeam considering the Kelvin–Voigt scheme. For this purpose, fractional heat conduction models with phase lags and Euler–Bernoulli beam theory are used to derive the governing system equations. In the formulation, for the first time, the fractional Atangana-Baleanu (AB) operator without singulars and non-localized kernels is introduced. The microbeam is thermally loaded and exposed to a heat source moving along its axis in the form of a laser pulse. The system of equations is solved using the usual Laplace transform approach, and the resulting expressions for beam deflection, displacement, temperature change, and associated thermal stress are presented. The findings are graphed and the impacts of the fractional order parameter, viscosity factor, applied, and laser pulse length are investigated. The results show that the presence of the Atangana-Baleanu fractional operator and the viscosity coefficients leads to a decrease in the propagation of mechanical and thermal waves compared to the classical case.

MODEL OF DEFORMATION OF FIBROUS MATERIALS OF MULTIDIRECTIONAL REINFORCEMENT WITH NONORIENTED FIBERS

A model of deformation of multidirectional reinforcement fibrous materials with differently oriented fibers is proposed. The solution to the problem is built in two stages. At the first stage, the known properties of fibers and binder are used to determine the effective thermoelastic properties and stress-strain state of the subsystem with fibers oriented in a certain way relative to the main coordinate system. It is based on stochastic differential equations of the physically nonlinear theory of elasticity using the method of conditional moments. At the second stage, using a given distribution function based on the Voigt scheme, a model of deformation of the entire system is constructed from the calculated properties of the subsystems. Strain curves are obtained for simple loading, and the deformation of materials at uniform orientation of fibers is investigated. It was found that a fibrous composite material with differently oriented fibers in a macrovolume is isotropic, and its effective thermoelastic constants substantially depend on the volumetric content of fibers.

A continuum viscoelastic model of Timoshenko NSGT nanobeams

Developed and solved in this article, for the first time, is a coupled continuum viscoelastic model for Timoshenko nonlocal strain gradient theory (NSGT)-based nanobeams; this is performed using a finite difference analysis (FDA). The viscosity of infinitesimal elements of the Timoshenko NSGT nanobeams is incorporated via the Kelvin–Voigt scheme (as a two-parameter rheological scheme) for both the transverse/longitudinal/rotational motions. The NSGT for the normal/shear stress fields is used for ultrasmall size influences on the continuum model. Rotary inertia is automatically present due to the Timoshenko-type rotation. The viscosity in the Timoshenko NSGT nanobeam is responsible for energy dissipation formulated via negative work. Hamilton’s balance scheme is utilised and resulted in the coupled continuum viscoelastic dynamic model for Timoshenko NSGT nanobeams, which is solved via a FDA for nonlinear mechanics. A nonlinear bending test is conducted via development of a finite element method model in the absence of the NSGT.

Nonlinear oscillations of viscoelastic microcantilever beam based on modified strain gradient theory

A viscoelastic microcantilever beam is analytically analyzed based on the modified strain gradient theory. The Kelvin Voigt scheme is used to model the beam viscoelasticity. Applying Bernoulli-Euler inextensibility of the centerline condition via Hamilton’s principle, the nonlinear equation of motion and related boundary conditions are derived based on shortening effect theory and discretized by Galerkin method. Inner damping, nonlinear curvature effect, and nonlinear inertia terms are applied. The generalized derived formulation in this article, allows modeling of any nonlinearity combinations such as nonlinear terms arises due to inertia, damping, and stiffness, as well as modeling the size effect via considering modified coupled stress or modified strain gradient theories. First mode nonlinear frequency and time response of the viscoelastic microcantilever beam are analytically evaluated utilizing multiple time scale method and validated by numerical findings. Results indicate that the nonlinear terms have an appreciable effect on natural frequency and time response of a viscoelastic microcantilever. Furthermore, the investigation reveals that due to the size effects, natural frequency enhances drastically, especially when the thickness of the beam and the length scale parameter are comparable. Outcomes clarify the importance of size effects in analyzing of the mechanical behavior of small scale structures.

Large-amplitude parametric response of fluid-conveying nanotubes due to flow pulsations

In this article, the nonlinear parametric response of viscoelastic nanotubes conveying pulsatile flow is investigated. A two-parameter scale-dependent elasticity-based model is developed within the framework of a nonlocal theory with strain gradient influences. To model the effects of fluid molecules, which slip on the internal nanotube wall, on the parametric response, Karniadakis–Beskok approach is used. Viscoelastic effects are also described via Kelvin–Voigt scheme. Hamilton law, Galerkin and continuation techniques are, respectively, utilized in this analysis for obtaining, discretising and solving nonlinear coupled equations. Both subcritical and supercritical nonlinear parametric responses are examined considering various parameters such as the speed variation amplitude and frequency. The viscoelastic nanotube conveying pulsatile flow exhibits a hardening nonlinearity in the subcritical regime while it displays a softening nonlinearity in the supercritical regime.

Resonant vibrations of FG viscoelastic imperfect Timoshenko beams

An investigation is performed on the viscoelastic nonlinear vibrations of functionally graded imperfect Timoshenko beams. The internal viscosity is incorporated using the Kelvin–Voigt scheme. Beam's centerline stretching is the cause of geometric nonlinearities. Material property distributions follow the Mori–Tanaka model. Shear deformation and rotary inertia are incorporated using the Timoshenko theory. A slight curvature is included to account for a geometric imperfection. The coupled axial/transverse/rotational motion model is developed using Hamilton's energy/work/energy loss. Galerkin's method is used, without neglecting the longitudinal inertia/displacement, and a large dimensional discretized/truncated model is obtained. Numerical integrations, using a continuation-based technique, are employed for force/frequency diagrams. Viscosity, material gradient index, and imperfection effects on the system vibrations are investigated.

Vibrations of shear deformable FG viscoelastic microbeams

This is the first paper which investigates the nonlinear forced dynamic response of shear deformable functionally graded (SDFG) microscale beams with viscoelastic properties. A third-order model of shear deformations, which satisfies both the lower and upper boundary conditions, is utilised. The influences of viscoelastic properties are incorporated via the Kelvin–Voigt scheme. Furthermore, the influences of being at a miniature scale are captured via a modified couple stress theory (MCST). The material distribution of the microsystem is modelled via application of the Mori–Tanaka approach. Nonlinear three-dimensional coupled equations, which govern the size-dependent motions of the SDFG microbeam, are derived and then numerically solved. The present results show that for large coupled motions, the nonlinearity caused by viscosity plays a crucial role in the dynamics of SDFG microbeams.

Viscoelastically coupled dynamics of FG Timoshenko microbeams

Viscosity effects on the mechanical behaviour of functionally graded (FG) Timoshenko microbeams are investigated; the model possesses both linear nonlinear viscous terms. The Mori–Tanaka homogenisation method is used for the continuous variations of the material properties of the microsystem along the thickness; the Kelvin–Voigt scheme is employed for the internal damping; the shear deformation and rotary inertia are modelled for the viscoelastic microbeam via the Timoshenko theory; the modified couple stress theory is used for size influences. An energy loss/balance via Hamilton’s principle is used for obtaining the equations of motion. Galerkin’s approach together with a continuation method is employed for the mechanical responses. The simultaneous effects of viscosity, being small, and FG materials on the mechanical behaviour are investigated.

Stability and bifurcation characteristics of viscoelastic microcantilevers

The stability and bifurcations of viscoelastic microcantilevers is investigated via the Kelvin–Voigt scheme and the modified couple stress (MCS) theory. All the nonlinearities due to large deformations (due to the movement of the free end) are taken into account. The viscous segments of the deviatoric segment of the symmetric couple stress tensor and the stress tensor itself are considered. The energy loss due to viscosity is balanced with the energy input to the microcantilever. The equations for the transverse and axial motions are obtained and the inextensibility condition is applied, yielding an integro-partial-differential equation with inertial and stiffness nonlinearities. A continuation method is used for numerical solutions, with highlighting the viscosity effect on the large-amplitude motions.

On the viscoelastic dynamics of fluid-conveying microtubes

This paper is the first to analyse the coupled fluid-structure viscoelastic dynamical characteristics of a fluid-conveying viscoelastic microtube resting on a nonlinear elastic bed subject to large rotations. None of the axial and transverse motions/accelerations is neglected in the modelling and simulations. The dissipation is modelled using the Kelvin–Voigt scheme for the deviatoric segment of the symmetric couple stress tensor and the stress tensor. Based on the Euler–Bernoulli theory, in which the microtube cross-section remains perpendicular to the centreline, and the modified couple stress theory (MCST), the energies and the work of external load and damping are formulated. Through use of Hamilton's principle, the coupled transverse-longitudinal equations governing the motion of the fluid-conveying viscoelastic microtube are developed. A weighted-residual-based discretisation method is applied to the continuous vibration model and the resultant reduced model is simulated via a continuation technique. The coupled fluid-structure dynamical characteristics of the fluid-conveying viscoelastic microtube are analysed by constructing the frequency-amplitude diagrams. It is shown that slight changes in the flow speed significantly affects the resonant response and modal interactions.

The influence of thermal aging on absorption phenomena in cross-linked polyethylene cable insulation

Absorption-controlled charge and discharge currents in cross-linked polyethylene (XPE) cable insulation before and after thermal aging have been measured. The experimental dependences were analyzed in terms of the equivalent Voigt scheme. Known parameters of the Voigt scheme were used to calculate the frequency dependences of relative dielectric permittivity, loss factor, and loss tangent of XPE films in the region of low frequencies (ω = 10–3–1 s–1) at high temperatures. Results of analysis of the absorption characteristics of XPE were applied to modeling of the process of thermal aging of cable insulation.

A deformation model of brittle failing composites with couple-stresses and disperse microdamages

A mathematical model for calculating the relation between macroscopic strains and stresses in brittle failing 3D composites upon their arbitrary deformation is suggested. The model is based on the Voigt scheme in a differential form corrected for the effect of couple-stresses arising in the matrix of composites due to relative rotation of reinforcing fibers. The nonlinearity of composites is derived as a consequence of the progressive accumulation of disperse microdamages in the material under deformation, which lead to degradation of the mechanical properties of the composites. As an example, a ±ψ/2 angle-ply structure is considered, and it is shown how the unknown constants for the materials of such a structure can be found from the uniaxial tension or compression curves.

Elasticity and anisotropy of dunite and bronzitite

Compressional and shear wave velocities in 13 directions at pressures to 10 kb were measured in dunite from the Twin Sisters peaks, Washington, and in bronzitite from the Stillwater Complex, Montana. Dunite is characterized by a strong preferred orientation of olivine grains, leading to anisotropy of velocity of 15% at 10 kb. The bronzitite is more nearly isotropic, the greatest difference of P wave velocities reaching 6%. The comparison of elasticity diagrams, obtained at pressures of 0.5 kb and 10 kb, shows that the system of pores, more open at low pressure, is of minor influence; anisotropy is controlled mainly by the preferred orientation of olivine and bronzite in both rocks. Most of the compressional and shear wave velocities, calculated according to Voigt's scheme on the basis of petrofabric determinations and published single-crystal data for olivine and bronzitite, are in good agreement with the ultrasonic velocities measured at 10 kb. The results confirm the possibility of using this procedure to determine anisotropic elasticity of simple aggregates and suggest a possibility of using ultrasonic measurements in petrostructural analysis.

Voigt and Reuss prediction of anisotropic elasticity of dunite

Aggregate anisotropic elastic constants were calculated for two nearly mono-minerallic dunites by both the Voigt and the Reuss averaging schemes. The average constants were obtained rigorously from petrofabric data, which provided precise orientation of a sample of 100 grains in each specimen, by using published values of olivine single-crystal constants. The resultant elastic constants were used to calculate P- and S-wave phase velocities in various directions for comparison with actual measurements made in the same specimens. Agreement between the predicted and observed velocities was within the observational error for compressional (pseudo-compressional) waves when using the Voigt scheme, with best agreement at pressures above 2 kb. The Reuss scheme also predicts the variation in velocity with direction quite well. Agreement of shear wave velocities is not so good, probably because of larger uncertainties in the measured data. The data suggest that the anisotropy of crystalline aggregates at hydrostatic pressures above a few kilobars is governed almost exclusively by crystal orientation.