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Low level radioactive liquid waste (LLW) is generated at different stages of operation of reprocessing as well as radioactive waste management. The LLW generated here is alkaline with high salt content. It contains different radioisotopes namely106Ru, 125Sb, 99Tc, 137Cs, 90Sr and traces of Pu. Presence of 99Tc in LLW is of great environmental concern due to its long half-life (T1/2: 2 × 105 years) and mobility. Hence it needs to be separated from LLW to maximum possible extent prior to discharge to environment. In this paper, study carried out for separation of 99Tc using the crown ether, Di-tert-Butyldibenzo-18-Crown-6 (DtBuDB18C6). The performance of the composite material was evaluated with respect to 99Tc uptake and the effect of various parameters like pH, salt concentration, time period and temperature on Kd value was studied.

The isolation of Am(III) ion from Ln(III) ions is very crucial for the safe disposal of nuclear wastes and thus, studies are being continuously pursued to accomplish this goal. In view of this, herein, a new conformationally rigid bitopic ligand, N,N,N′,N′-tetra(2-ethylhexyl)piperazine-di-methylenecarboxamide (PIPDA) has been synthesized and studied for the separation of Am(III) from Ln(III) ions. The effect of structural rigidification on the selectivity of Am(III) over Ln(III) was compared with an open chain flexible compound, namely, N,N,N′,N′-tetra(2-ethylhexyl)-3,6-(N′′,N′′′-dibutyl)diaza-octane-1,8-diamide (DADA). Two oxygen atoms of the diamide moiety seem to be responsible for controlling the metal ion extraction ability of PIPDA, whereas two nitrogen atoms of the piperazine moiety most probably dictate the separation factor between the Am(III) and Eu(III) ions in PIPDA. In addition, scalar relativistic density functional theory (DFT) in conjunction with Born–Haber thermodynamics was used herein to compliment the experimental selectivity. The experimentally observed preferential selectivity of PIPDA for Am(III) ion over the Ln(III) ion was corroborated by the computed extraction free energy, ΔGext. The covalent nature of bonding between the metal ions and the ligand was confirmed by analyzing the Mayer bond order and bond character analysis using the atom in molecule concept. Though the conformational rigidity of PIPDA gives stronger interaction than DADA, it does not offer a significant advantage over DADA in terms of the separation factor. The marginal increase in the separation factor for PIPDA over DADA might be attributed to the piperazine nitrogen and to the ligand architecture during complex formation.

This paper reports the result of process development studies on separation of Sr(II) from Eu(III) in 4 M nitric acid using supported liquid membrane (SLM). The process utilizes addition of 18-crown-6 for masking of Sr(II), followed by their transport across SLM with TEHDGA as carrier molecule. The optimized process shows complete transport of Eu(III) in about 60 min, leaving pure Sr(II) in the feed compartment. The Sr(II) and Eu(III), both in pure form are valuable in medical and industrial radiation technology applications.

A process is described for separation and recovery of uranium from low grade sodium diuranate (SDU) obtained from processing of phosphatic uranium with D2EHPA-TBP solvent. SDU containing impurities of rare earths mostly heavier fraction (Y, Dy, Er, Yb) and Fe, Al, Cr, Mn, Ca, etc. was dissolved in nitric acid and contacted with N,N-dihexyl octanamide (DHOA)/n-dodecane solvent for selective separation of uranium from rest of the impurities. The average separation factor of uranium with respect to the heavy rare earths and base metals was obtained was 30 and 1000 respectively. Effect of different experimental parameters like aqueous nitric acid concentration, DHOA concentration, uranium concentration, phase ratio of extraction, scrubbing and stripping was optimized to obtain high purity uranium product solution. The extraction of uranium by DHOA follows solvation mechanism, at low uranium loading the combining ratio of U to DHOA determined by slope analysis method suggests complex formation as [UO2(NO3)2·2DHOA]. A 8-stage counter current extraction of 70 g/L uranium feed solution obtained on dissolving SDU in 3 M HNO3 with 1 M DHOA/n-dodecane solvent at O/A = 1 and scrubbing with 80 g/L pure uranium solution in 3 M HNO3 at O/A = 4:1 was found appropriate to obtain uranium of purity above 99.9%.

A new bisglycolamide substituted calix-benzo-crown-6 (CBCBGA) ionophore has been synthesized and characterized by using 1H, 13C NMR, ESI-MS and elemental analysis. Detailed investigations on the effect of various parameters such as the aqueous phase acidity, ionophore concentration and nitrate ion concentration on extraction of cesium have been carried out. The new ionophore is found to be highly selective for Cs over other metal ions present in the simulated high level liquid waste solution. The complexing ability of this novel ionophore towards Cs+ and Na+ metal ions was further complimented by predicting the structure, extraction free energy and fraction of charge transfer using the B3LYP density functional employing a split-valence plus polarization (SVP) basis set in conjunction with the conductor like screening model. The unusually high selectivity of CBCBGA for Cs+ ion over Na+ ion was established by the calculated value of difference in the free energy, ΔΔG (ΔGext,Cs+ − ΔGext,Na+), −9.46 kcal mol−1, which is in good agreement with the experimentally determined value of −5.59 kcal mol−1. The calculated values of ρ and ∇2ρ at the bond critical point for the hydrated Na+ ion are found to be reduced during complexation with the CBCBGA, whereas for the hydrated Cs+ ion, though ρ remains same, the value of ∇2ρ is increased which seems to play a decisive role in the higher selectivity to Cs+ ion over Na+ ion of CBCBGA. The new CBCBGA ionophore shows promise for the selective removal of Cs+ ion over other metal ions present in the simulated high level liquid waste solution.

The extraction behavior of rare earth (RE) elements from thiocyanate medium by N,N,N’,N’-tetra(2-ethylhexyl) diglycolamide (TEHDGA), a neutral extractant, has been investigated and the optimum conditions for their separations were determined. Isodecyl alcohol was used as phase modifier and a concentration of 5%(v/v) was found sufficient to mitigate third phase formation under our experimental conditions. The extraction mechanism of RE with TEHDGA was established by analyzing distribution data with slope analysis technique and showed the formation of a neutral species, RE(SCN)3.2TEHDGA, in the organic phase. The extraction of rare earth decreased with increase in temperature indicating exothermic nature and the enthalpy change (ΔH) obtained for Y(III) was −14.27 kJ/mol. Among various stripping agents studied, oxalic acid was found to be efficient in quantitative stripping of rare earths from TEHDGA. The extraction efficiency for all the rare earths by TEHDGA was also investigated. High separation factor of...

Pluronics are considered as potential materials for the removal of tributyl phosphate (TBP) from nuclear fuel reprocessing plants. Recent studies showed that solubilization of TBP in aqueous solution of Pluronic L64 reduces its cloud point (CP) and in addition, induces a second CP at low temperature. In this manuscript we have attempted to understand the origin of this lower CP (LCP) by carrying out DLS, SANS, viscosity and fluorescence measurement studies on 10% aqueous L64 solutions containing 60 mM TBP. The studies show that on approaching both LCP (≈25 °C) and the conventional or upper CP (UCP ≈ 42.5 °C), the copolymer solution exhibits a large increase in light scattering intensity and apparent micellar radius. Detailed studies suggest that whereas the copolymer micelles undergo a progressive growth on heating to the UCP, they form a micellar cluster upon cooling down to the LCP due to the onset of an inter-micellar attractive interaction. Although such clusters are known to form in micellar solutions of non ionic surfactants on approaching the UCP, their formation upon cooling is the first of its kind for them. The observed unusual behavior has possibly been triggered by dehydration of micellar corona caused by relocation of TBP from micellar core to corona upon cooling down to the LCP.

This article deals with the transverse vibrations in a homogeneous isotropic, thermoelastic-diffusive thin beam based on the Euler–Bernoulli theory under clamped–clamped boundary conditions. The analytical expressions for deflection, thermal moment, mass moment, frequency shift, and damping due to thermoelastic-diffusion in the beam has been derived. The effects of mass diffusion, thermomechanical coupling, surface conditions, and beam dimensions on energy dissipation and other field quantities induced by thermoelastic-diffusion have been investigated. The analytical results have been numerically analyzed with the help of MATLAB software. The numerically computed results for deflection, temperature change, thermal moment, mass moment, damping factor, and frequency shift have been presented graphically. The computed values of effective flexural rigidity have been given in tabular form. The study may find applications in medical science, engineering, accelerometers, sensors, resonators, etc.

The 25,27-di(octyloxy)calix[4]arenebenzocrown-6 (CBC) in 1,3-alternate conformation was synthesized indigenously starting from its intermediates in good yield and purity. The extraction studies of CBC were carried out by using two different phase modifiers namely isodecyl alcohol and ortho-nitrophenyl hexyl ether. Detailed investigations on the effect of various parameters like, concentration of phase modifiers, aqueous phase acidity, ligand concentration, nitrate ion concentration and effect of temperature on extraction of cesium have been carried out. The concentration of phase modifiers was optimized to be 30 % in n-dodecane to ensure optimum extraction of cesium. Stoichiometry of the extracted complex determined by slope analysis method reveals 1:1:1 molar ratio for CsNO3:CBC:HNO3. The extraction process was found to be exothermic as determined from the plot of log K ex versus 1/T. The solvent system with a composition 0.01 M CBC/30 % phase modifier/n-dodecane was found to be effective for selective separation of cesium from simulated high level liquid waste solution.

The present study focuses on the analysis of free vibrations of axisymmetric functionally graded hollow spheres. The material is assumed to be graded in radial direction with a simple power law. Matrix Frobenious method of extended power series is employed to derive the analytical solutions for displacement, temperature, and stresses. The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollowsphere are derived in a compact form. In order to explore the characteristics of vibrations, the secular equations are further solved by using fixed point iteration numerical technique with the help of MATLAB software. The numerical results have been presented graphically for polymethyl methecrylate materials in respect of natural frequencies, frequency shift, inverse quality factor, displacement, temperature change, and radial stress. Open image in new window

A series of novel calix[4]arene-benzocrown-6 amide (CBCA) ligands in 1,3-alternate conformation having an amide group attached to the aromatic ring of the polyether ring network have been synthesized and evaluated for the extraction of cesium at varying concentrations of aqueous nitric acid. Amide substituted calix-crowns modified with isodecyl alcohol (IDA) and o-nitrophenylhexyl ether (o-NPHE) in n-dodecane have been used for the extraction of cesium and compared to their non-amide analogue viz. calix-benzocrown (CBC). It was observed that the presence of the amide group enhanced the uptake of cesium at high nitric acid concentrations as compared to CBC . This behavior may be attributed to an internal buffering effect of the amide group present in the calix-crowns.

In this work, the dynamic problem of elasto-thermodiffusion in infinite isotropic cylindrical cavity subjected to certain boundary conditions has been studied. Laplace transform technique is used to solve the problem. The interactions are supposed to be due to a constant step in radial stress, temperature and concentration applied to the boundary of the cavity, which is maintained at constant temperature or radial stress in respective cases. The distributions of displacement, temperature, concentration and stress have been displayed graphically and analytically.

In this paper an exact analysis of homogenous rigidly fixed vibrations of viscothermoelastic hollow sphere is presented. The basic governing partial differential equations have been reduced to ordinary differential equations by using Helmholtz decomposition equations. The uncoupled equation is taken for first class vibrations and remains independent of temperature variations, while coupled system of equations are taken for second class vibrations. Matrix Frobenious method of extended power series has been applied in the coupled system of differential equations to get displacements and temperature. Numerical results have been presented, giving lowest frequency, dissipation factor, displacements and temperature change.

A dynamic problem of an infinite isotropic cylinder of radius r subjected to boundary conditions of the radial stress, temperature, or concentration of the diffusing substance is studied by using the equations of state of a elastothermodiffusive solid with one relaxation time and the Laplace transform technique. The distributions of the displacement, temperature, and concentration are displayed graphically and analytically.

The aim of this article is to study the disturbance in a homogeneous, transversely isotropic (6 mm class), linear generalized piezothermoelastic, cylindrical continuum subjected to continuous mechanical and thermal point loads. A combination of integral transforms, Laplace and Hankel, has been employed to solve the model consisting of partial differential equations and boundary conditions. The transform technique reduces the system of partial differential equations to ordinary differential equations. The formal solution of the resulting system of coupled ordinary differential equations has been obtained by using the eigenvalue approach. A numerical technique for inverting the integral transforms along with Des Cartes’ procedure and the Gauss elimination method has been used to obtain the results in physical domain. The stresses, temperature change and electric displacement have been computed numerically from the relevant expressions and relations for PZT-5A material. The computer simulated results have be...

Smart materials with integrated sensing capabilities are now ubiquitous in many structures and devices manufactured from composite materials and they offer enhanced safety, reliability and efficiency in such smart devices. This paper explores the application of embedded sensors to components manufactured using additive layer manufacturing (ALM) technology. ALM offers the ability to create physical parts with little or no restriction in shape and complexity. In this paper, optical fiber sensors incorporating fiber Bragg gratings are embedded inside a component made by, and during a powder-bed-based, layer-by-layer, additive manufacturing process. A commercial EOS P730 system is used, where a laser is employed to sinter the polymeric powder into a 3D component. The fiber embedding approach is based upon insertion of a “fiber-carrier” component, which replaces a removable “place-holder” component during an interruption of the ALM build process. Tensile test specimens fabricated this way are subjected to extended cyclic tensile loading trials at low strain levels of up to 580 μe . The test specimens demonstrate stable and reproducible responses over a period in excess of 720 days and 311000 load cycles. Polyimide and acrylic jacketed fibers are trialled, and the resulting deformations of the component through internal stresses depending on the fiber jacket type are discussed.

The extraction properties of N,N,N',N'-tetra-(2-ethylhexyl) dithiodiglycolamide (DTDGA) have been evaluated for separation and recovery of palladium from simulated high-level liquid waste (SHLW) solution. Extraction of Pd was found to increase with increase in nitric acid concentration up to 4.0 M, above which the extraction remains almost constant. Acid uptake studies show 1:1 stoichiometry between DTDGA and HNO3 at nitric acid concentration above 3.0 M. The acid uptake constant (KH) was found to be 0.60 which could be due to the presence of two carbonyl groups of amidic moiety. DTDGA has shown very high extractability and selectivity for Pd over other metal ions present in SHLW. The separation factor (SF) for Pd over other metal ions was found to be more than 104. Almost complete back extraction of palladium from organic phase was achieved with 0.01 M thiourea in 0.1 M nitric acid. Reusability studies of the extractant indicate that DPd remains almost constant even after five successive cycles of extrac...

The extractant N,N,N′,N′-tetra-2-ethylhexyl diglycolamide (TEHDGA) has been evaluated for extraction of strontium from the raffinate solution of TEHDGA-actinide partitioning process. Actinide partitioning of HLW using 0.2 M TEHDGA + 30% isodecyl alcohol/n-dodecane, carried at our unit at engineering scale, selectively separates trivalent ‘f’ group elements from HLW leaving all the elements including strontium in the raffinate. Strontium from the raffinate was extracted using 0.3 M TEHDGA + 5% isodecyl alcohol/n-dodecane, isodecyl alcohol has been used as a phase modifier whose concentration was optimized to 5% (v/v) to obtain maximum extraction of strontium (D3.1–3.8 M = 23) without third phase formation in the given extraction conditions. The stoichiometry of the extracted complex was found to depend on initial aqueous nitric acid concentration and obtained as Sr(NO3)2(TEHDGA)2(HNO3)2. Fission products, such as Mo, Pd, and Zr, co-extracted during extraction process were scrubbed with 3.5 M nitric acid containing 0.2 M oxalic acid and 0.05 M HEDTA. Complete stripping of strontium was achieved with 0.01 M nitric acid. Quantitative recovery of strontium was obtained in a single contact of extraction, two contacts of scrubbing and two contacts of stripping each at O/A = 1.

The paper concentrates on the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor half-space underlying an inviscid liquid. The reflection and transmission coefficients varying with the incident angles are examined. Calculated results are verified by considering the quasilongitudinal ( 𝑞 𝑃 ) and quasitransverse ( 𝑞 𝑆 𝑉 ) waves. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection and transmission coefficients are carried out with the help of Gauss elimination method by using MATLAB programming software for silicon (Si) and germanium (Ge) semiconductors. The computer simulated-results have been plotted graphically for Si and presented in tabular form in case of Ge semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

The three-dimensional free vibrations in a simply supported homogeneous isotropic, thermally conducting, circular cylinder of finite length with an eccentrically located inner circular cavity have been studied. The surfaces of the cylinder are subjected to stress free and thermally insulated or isothermal boundary conditions. The three-dimensional linear theory of coupled thermoelasticity has been employed to model the problem. The displacement potential functions have been introduced to decouple purely shear and longitudinal motions. The purely transverse wave has been found to remain unaffected due to thermal field. The translation addition theorem for cylindrical wave functions along with orthogonal series expansions has been used to develop the exact solution. To illustrate the analytical results, the numerical solution of some relations and equations have been obtained to compute lowest frequency and dissipation factor versus eccentricities, for selected length to radius ratio and radius ratio of hol...

PurposeThe purpose of this paper is to analyze the free vibrations in a stress free and thermally insulated (or isothermal), homogeneous, transversely isotropic, solid cylinder based on three‐dimensional coupled thermoelasticity, which is initially undeformed and kept at uniform temperature.Design/methodology/approachThe displacement potential functions have been introduced in the equations of motion and heat conduction in order to decouple the purely shear and longitudinal motions. The system of governing partial differential equations is reduced to four second‐order coupled ordinary differential equations in radial coordinate by using the method of separation of variables. The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate. The convergence analysis of matrix Frobenius method has been successfully carried out.FindingsThe purely transverse mode is found to be independent of the rest of the motion and temperature change. The natural frequency, dissipation factor, inverse quality factor and frequency shift of vibrations in a stress free solid cylinder get significantly affected due to thermal variations and thermo‐mechanical coupling.Originality/valueA new procedure is used and compared to other methods available in the literature.

The aim of the paper is to study three-dimensional free vibrations in a homogeneous transversely isotropic, thermoelastic hollow cylinder, which is initially undeformed and at uniform temperature. The surfaces of the cylinder are subjected to stress free and thermally insulated or isothermal boundary conditions. The displacement potential functions have been introduced in the equations of motion and heat conduction to decouple purely shear and longitudinal motions. The purely transverse wave is not affected by thermal field. By using the method of separation of variables, the system of governing partial differential equations is reduced to four second-order coupled ordinary differential equations in radial coordinate. The Matrix Frobenius method of the extended power series is employed to obtain the solution in radial direction. To illustrate the analytic results, the numerical solution of various relations and equations has been carried out to compute the lowest frequency, frequency shift and damping fac...

The governing equations of flexural vibrations in a transversely isotropic thermoelastic beam are derived in closed form based on Euler–Bernoulli theory. The out-of- plane vibrations have been studied under different beam dimensions and boundary conditions. The analytical expressions for thermoelastic damping and frequency shift of vibrations are obtained. The damping and frequency shift of beam vibrations significantly depend on thermal relaxation time and surface conditions at resonance. The expressions for displacement and temperature fields in the beam resonator are obtained. Some numerical results with help of MATLAB software have been computed and presented graphically for silicon material beams.

The present paper deals with the propagation of body waves in a homogenous isotropic, rotating, generalized thermoelastic solid with voids. The complex quartic secular equation has been solved by employing Descartes’ algorithm and perturbation method to obtain phase velocities, attenuations and specific loss factors of four attenuating and dispersive waves, which are possible to exist in such media. These wave characteristics have been computed numerically for magnesium crystal and presented graphically. Statistical analysis has been performed to compare the obtained computer simulated result in order to have estimate on the suitability of the method to compute various characteristics of the waves. This work may find applications in geophysics and gyroscopic sensors.

In this paper the closed form expressions for the transverse vibrations of a homogenous isotropic, thermoelastic thin beam with voids, based on Euler–Bernoulli theory have been derived. The effects of voids, relaxation times, thermomechanical coupling, surface conditions and beam dimensions on energy dissipation induced by thermoelastic damping in (micro-electromechanical systems) MEMS/(nano-electromechanical systems) NEMS resonators are investigated for beams under clamped and simply supported conditions. Analytical expressions for deflection, temperature change, frequency shifts and thermoelastic damping in the beam have been derived. Some numerical results with the help of MATLAB programming software in case of magnesium like material have also been presented. The computer simulated results in respect of damping factor and frequency shift have been presented graphically.

The extraction properties of N,N,N′,N′-tetra(2-ethylhexyl)thiodiglycolamide T(2EH)TDGA have been evaluated for the separation and recovery of palladium from simulated high-level liquid waste (SHLW). T(2EH)TDGA has shown very high selectivity for Pd (II) over other metal ions present in SHLW. The separation factor (SF) for Pd (II) over other metal ions was found to be more than 105. Reusability studies of the extractant indicate that DPd remained almost constant even after five successive cycles of extraction and stripping. Palladium was quantitatively recovered from thiourea strip solution by treating it with ammonia and filtering the precipitate of palladium sulphide. The acid uptake constant (KH) was found to be 0.62 which could be due to the presence of two carbonyl groups of amidic moiety. To account for very high extractability of palladium with T(2EH)TDGA over other ‘S’ donor extractants, namely Bis-(2-ethylhexyl)sulphoxide (BESO), FTIR, as well as Raman studies were carried out. FTIR and Raman stud...

The present investigation is concerned with the study of extensional wave motion in an infinite homogenous isotropic, thermoelastic plate by using asymptotic method. The governing equation for the extensional wave motions have been derived from the system of three-dimensional dynamical equations of linear coupled theory of thermoelasticity. All coefficients of the differential operator are expressed as explicit functions of the material parameters. The velocity dispersion equation for the extensional wave motion is deduced from the three-dimensional analog of Rayleigh–Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity are also derived. The thermoelastic Rayleigh–Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established to that of asymptotic method. The dispersion curves for phase velocity and attenuation coefficient are shown graphically for extensional wave motion of the plates.

In this paper the asymptotic method has been applied to investigate propagation of generalized thermoelastic waves in an infinite homogenous isotropic plate. The governing equations for the extensional, transversal and flexural motions are derived from the system of three-dimensional dynamical equations of linear theories of generalized thermoelasticity. The asymptotic operator plate model for extensional and flexural free vibrations in a homogenous thermoelastic plate leads to sixth and fifth degree polynomial secular equations, respectively. These secular equations govern frequency and phase velocity of various possible modes of wave propagation at all wavelengths. The velocity dispersion equations for extensional and flexural wave motion are deduced from the three-dimensional analog of Rayleigh–Lamb frequency equation for thermoelastic plate. The approximation for long and short waves along with expression for group velocity has also been obtained. The Rayleigh–Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations and its equivalence established with that of asymptotic method. The numeric values for phase velocity, group velocity and attenuation coefficients has also been obtained using MATHCAD software and are shown graphically for extensional and flexural waves in generalized theories of thermoelastic plate for solid helium material.

The present work deals with the propagation of interfacial surface waves in a composite consisting of homogeneous, transversely isotropic, piezoelectric halfspace underlying a thin layer of non-piezoelectric semiconductor material. The mathematical model of the problem is depicted by partial differential equations of motion for the structure and boundary conditions to be satisfied at the interface and free surface of the composite. After obtaining formal wave solution of the model the secular equation that governs the propagation of surface waves in the considered composite structure has been derived in compact form. The numerical solution of secular equation is being carried out for the composites Si–CdSe, Ge–CdSe and Ge–PZT by employing functional iteration method along with irreducible Cardano method using MATLAB programming. The computer simulated results in respect of dispersion curves, attenuation coefficient and specific loss factor of energy dissipation are presented graphically for Si–CdSe composite to illustrate the analytical developments. We have extended our analysis to Ge–CdSe and Ge–PZT composites also. However, to avoid clustering of profiles and also to have clear understanding of the variations, the computer simulated values of phase velocity and attenuation coefficient are presented in tabular form for all three considered composite structures. This work may be useful for designing and construction of surface acoustic wave (SAW) devices and electronics industry.

The present investigation is concerned with the flexural and transversal wave motion in an infinite, transversely isotropic, thermoelastic plate by asymptotic method. The governing equations for the flexural and transversal motions have been derived from the system of three-dimensional dynamical equations of linear theory of coupled thermoelasticity. The asymptotic operator plate model for free vibrations; both flexural and transversal, in a homogenous thermoelastic plate leads to fifth degree and cubic polynomial secular equations, respectively, that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. All the coefficients of differential operator have been expressed as explicit functions of the material parameters. The velocity dispersion equations for the flexural and transversal wave motion have been deduced from the three-dimensional analog of Rayleigh–Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity have also been derived. The thermoelastic Rayleigh–Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established with that of asymptotic method. The dispersion curves for phase velocity, group velocity and attenuation coefficient of various flexural and transversal wave modes are shown graphically for aluminum-epoxy material elastic and thermoelastic plates.

The propagation of thermoelastic waves along circumferential direction in homogeneous, isotropic, cylindrical curved solid plates with voids has been investigated in the context of linear generalized theory of thermoelasticity. The plate is subjected to stress free or rigidly fixed, thermally insulated or isothermal boundary conditions. Mathematical modeling of the problem for the considered cylindrical curved plate with voids leads to a system of coupled partial differential equations. The model has been simplified by using the Helmholtz decomposition technique and the resulting equations are solved by using the method of separation of variables. The formal solution obtained by using Bessel’s functions with complex arguments is utilized to derive the secular equations which govern the wave motion in the plate with voids. The longitudinal shear motion and axially symmetric shear vibration modes get decoupled from the rest of the motion in contrast to non-axially symmetric plane strain vibrations. These modes remain unaffected due to thermal variations and presence of voids. In order to illustrate theoretical developments, numerical solutions have been carried out for a stress free, thermally insulated or isothermal magnesium plate and are presented graphically. The obtained results are also compared with those available in the literature.

The present paper deals with the propagation of body waves in a homogenous isotropic, rotating, generalized thermoelastic solid. The complex cubic secular equation has been solved by using Cardano’s and perturbation methods to obtain phase velocities, attenuations and specific loss factors of three attenuating and dispersive waves, which are possible to exist in such media. These wave characteristics have also been computed numerically for magnesium crystal and are presented graphically. Statistical analysis has been performed to compare the computer simulated results obtained by using both methods. This work may find applications in geophysics and gyroscopic sensors.

The present article is devoted to investigate the propagation of elasto-thermodiffusive (ETNP) surface waves in a homogeneous isotropic, thermally conducting semiconductor material of half-space with relaxation of heat and charge carrier fields. The secular equation, a more general functional relation, that governs the propagation of elasto-thermodiffusive (ETNP) surface waves in homogeneous isotropic, thermoelastic semiconductor material halfspace with relaxation of heat and charge carrier fields has been derived by solving a system of coupled partial differential equations. A hybrid numerical technique consisting of Descartes algorithm for solving complex polynomial characteristic equation along with functional iteration scheme has been successfully used to solve the secular equation in order to obtain dispersion curves, attenuation coefficient and specific loss factor of energy dissipation for p-type germanium (Ge) semiconductor. Some particular forms of the general secular equation governing the propagation of elasto-thermodiffusive (ETN/ETP), thermoelastic (ET), elastodiffusive (EP/EN) and thermodiffusive (TP/TN) surface waves have been also deduced and discussed. In order to illustrate the analytical development, the numerical solution of the secular equation and other relevant relations under different situations is also carried out for Ge semiconductor materials to characterize the elasto-thermodiffusive (ETP) and thermodiffusive (TP) surface waves. The computer simulated results have been presented graphically in respect of the dispersion curves, attenuation coefficient and specific loss factor.

The propagation of Lamb waves in a homogeneous, transversely isotropic (6 mm class), piezothermoelastic plate rotating with uniform angular velocity about normal to its boundary has been investigated. The generalized (non-classical) theories of thermoelasticity in contrast to Sharma and Pal [Sharma, J.N., Pal, M., 2004. Lamb wave propagation in transversely isotropic piezothermoelastic plate. J. Sound Vib. 270, 587–610] have been used to investigate the problem. The surfaces of the plate are subjected to stress free, thermally insulated/isothermal and electrically shorted boundary conditions. Secular equations for wave propagation modes in the plate are derived from a coupled system of governing partial differential equations of linear piezothermoelasticity. After obtaining the complex characteristic roots with the help of Descartes' algorithm, the transcendental secular equations have been solved by functional iteration numerical technique to compute phase velocity and attenuation coefficient. Finally, in order to illustrate the analytical development, numerical solution of secular equations is carried out for PZT-5A piezo-thermoelastic material. The corresponding simulated results of various physical quantities such as phase velocity, attenuation coefficients, specific loss factor of energy dissipation, thermo-mechanical coupling factor and relative frequency shifts have been presented graphically for both rotating and non-rotating plates for comparison purpose. There is a scope for extension of the present work to other classes of piezo/pyroelectric crystals. The study will be useful in design and construction of gyroscope, rotation sensors, temperature sensors and other pyro/piezoelectric surface acoustic wave (SAW) devices.

The present paper is aimed at to study the propagation of surface waves in a homogeneous isotropic, thermally conducting and elastic solid underlying a layer of viscous liquid with finite thickness in the context of generalized theories of thermoelasticity. The secular equations for non-leaky Rayleigh waves, in compact form are derived after developing the mathematical model. The amplitude ratios of displacements and temperature change in both media at the surface (interface) are also obtained. The liquid layer has successfully been modeled as thermal load in addition to normal (hydrostatic pressure) one, which is the distinctive feature of the present study and missing in earlier researches. Finally, the numerical solution is carried out for aluminum-epoxy composite material solid (half-space) underlying a viscous liquid layer of finite thickness. The computer simulated results for dispersion curves, attenuation coefficient profiles, amplitude ratios of surface displacements and temperature change have been presented graphically, in order to illustrate and compare the theoretical results. The present analysis can be utilized in electronics and navigation applications in addition to surface acoustic wave (SAW) devices.

The present article is aimed at an investigation of the propagation of elasto-thermodiffusive (ETN) surface waves in a homogenous isotropic, thermoelastic semiconductor material half-space underlying a viscous or inviscid fluid half-space or layer of finite thickness with varying temperature. The relaxation times of heat and charge carrier fields are also taken into consideration during the study. The secular equation that governs the propagation of elasto-thermodiffusive surface (interfacial) waves in the considered composite structures has been derived in compact form after obtaining the general wave solution of the model. Some particular forms of the general secular equation are also deduced and investigated. Numerical solution of secular equation and other relevant relations is carried out for silicon (Si) semiconductor material under different situations with the help of functional iteration numerical technique along with the irreducible case of Cardano's method. The computer-simulated results in res...

The present paper deals with the study of the propagation of Rayleigh surface waves in homogeneous isotropic, thermodiffusive elastic half-space. After developing the formal solution of the model, the secular equations for stress free, thermally insulated or isothermal, and isoconcentrated boundary conditions of the half-space have been obtained. The secular equations have been solved by using irreducible Cardano's method with the help of DeMoivre's theorem in order to obtain phase velocity and attenuation coefficient of waves under consideration. The motion of the surface particles during the Rayleigh surface wave propagation is also discussed and found to be elliptical in general. The inclinations of wave normal with the major axis of the elliptical path of a typical particle have also been computed. Finally, the numerically simulated results regarding phase velocity, attenuation coefficient, specific loss and thermo-mechanical coupling factors of thermoelastic diffusive waves have been obtained and presented graphically. Some very interesting and useful characteristics of surface acoustic waves have been obtained, which may help in improving the fabrication quality of optical and electronic devices in addition to construction and design of materials such as semiconductors and composite structures. Therefore, this work finds applications in the geophysics and electronics industry.

The present paper represents an analysis of Rayleigh surface waves in a homogeneous, transversely isotropic, generalized piezothermoelastic half-space rotating with uniform angular velocity about normal to its boundary and subjected to stress free, electrically shorted/charge free and thermally insulated/isothermal boundary conditions. The secular equations for stress free, generalized piezothermoelastic half-space in closed form and isolated mathematical conditions are derived. The characteristics of surface waves propagating in generalized piezothermoelastic solid half-space and their dependence upon various geometric and physical parameters have been investigated. Finally, in order to illustrate and compare the theoretical results, numerical solution of various secular equations and other relevant relations are derived for cadmium selenide (6 mm) class material by adopting functional iteration scheme after employing Descartes’ algorithm to compute the characteristic roots of coupled differential equation system. The corresponding simulated results of various physical quantities such as phase velocity, attenuation, specific loss, frequency shifts and electromechanical coupling have been presented graphically for rotation and non-rotation cases. The study will be useful in design and construction of gyroscope, rotation sensors, temperature sensors and other pyro/piezoelectric SAW devices.

Keeping in view the applications of diffusion processes in geophysics and electronics industry, the aim of the present paper is to give a detail account of the plane harmonic generalized thermoelastic diffusive waves in heat conducting solids. According to the characteristic equation, three longitudinal waves namely, elastodiffusive (ED), mass diffusion (MD-mode) and thermodiffusive (TD-mode), can propagate in such solids in addition to transverse waves. The transverse waves get decoupled from rest of the fields and hence remain unaffected due to temperature change and mass diffusion effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic diffusive waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. At low frequency mass diffusion and thermal waves do not exist but at high-frequency limits these waves propagate with infinite velocity being diffusive in character. Moreover, in the low-frequency regions, the disturbance is mainly dominant by mechanical process of transportation of energy and at high-frequency regions it is significantly dominated by a close to diffusive process (heat conduction or mass diffusion). Therefore, at low-frequency limits the waves like modes are identifiable with small amplitude waves in elastic materials that do not conduct heat. The general complex characteristic equation is solved by using irreducible case of Cardano's method with the help of DeMoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation of various modes. The propagation of waves in case of non-heat conducting solids is also discussed. Finally, the numerical solution is carried out for copper (solvent) and zinc (solute) materials and the obtained phase velocities, attenuation coefficients and specific loss factor of various thermoelastic diffusive waves are presented graphically.