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The purpose of this paper is to present a model to analyze free vibrations in a transradially isotropic, thermoelastic hollow sphere subjected to stress free, thermally insulated or stress free, isothermal and rigidly fixed, thermally insulated or rigidly fixed, isothermal boundary conditions.

The potential functions along with spherical wave solution have been used to reduce the system of governing partial differential equations to a coupled system of ordinary differential equations in radial coordinates after employing non-dimensional quantities. Matrix Frobenius method of extended power series has been employed to obtain accurate solution of coupled differential equations in terms of radial coordinates. The mathematical model of the considered problem has been solved analytically to obtain the characteristics equations after imposing the appropriate boundary conditions at the outer and inner surfaces of the hollow sphere. The characteristic equations which govern various types of vibration modes expected to exist have been derived in the compact form. The special cases of spheroidal and toroidal modes of vibrations have been deduced from the characteristic equations and discussed.

The toroidal mode has been found to be independent of temperature change. The magnitude of lowest frequency and damping factor are significantly affected in the presence of thermal field and increase with an increase in the spherical harmonics in addition to geometry of the structure.

The matrix Frobenius method has been used to develop analytical solutions and functional iteration technique to carry out numerical simulations of such structures for the first time. The simulated results are presented graphically and compared with the available literature.

The purpose of this manuscript is to study the vibration characteristics of the spherically symmetric solid and hollow spheres poised of a homogeneous thermoelastic material, based on the three dimensional coupled thermoelasticity.

In this paper, matrix Fröbenius series solution is used to derive the frequency equations, for the field functions. Results have been applied on rigidly fixed boundary conditions.

The main finding of this paper is that the frequency of vibration of spherically symmetric sphere (structure is independent of theta and phi) increases with the increase of radius, for solid spheres and for hollow spheres with thickness to mean radius ratio. Deformation in the given materials increases with thickness to mean radius ratio of the hollow sphere.

A numerical simulation has been done with the help of functional iteration method for solid and hollow thermoelastic spheres made of zinc and poly methyl meth acrylate materials for different boundary conditions. The computer simulated results in contempt of frequency, damping of vibration modes and displacement have been obtained graphically and compared with the existed results.

It is well known that precision of mass unbalance measurement of sphere is determined by perturbing moments in contactless suspension systems. Therefore, estimating perturbing moment level in those systems is important and necessary to meet the requirements of a specified precision of mass unbalance measurement.

In this paper, probability‐theoretic method is employed to determine probability characteristics of the perturbing moments in both electrostatic suspension system and gas suspension system by statistically estimating of the quality of sphere surface. As a result, the relationship between probability characteristics of the perturbing moment and statistical estimates of the quality of sphere surface is established. It is expressed as a simple formula by specifying the correlation function of random field of sphere surface.

Numerical experiments of the perturbing moment calculation in the two suspension systems show that for sphere with small correlation coefficient α, it is better to use gas suspension system for mass unbalance measurement. While for sphere with large correlation coefficient α, electrostatic suspension system is more suitable for its perturbing moment are less than gas suspension system.

Knowledge of this relationship is of great theoretic and practical importance, since the probabilistic depiction of the perturbing moments, and hence the accuracy of the mass unbalance measurement systems can be estimated without a detailed roundness measurement of the sphere surface.

Thermal insulation is important to achieve energy efficiency in a buildings’ lifespan while maintaining comfort. Traditionally, the majority of insulation in buildings is man-made petroleum based products with limited or no-end life usage. However, from an environmental and economic sustainability perspective, they are not sustainable as natural resources are finite and in danger of run-out. Furthermore, they are also highly influenced by the increasing price and the ongoing scarcity of fossil fuel oils. The paper aims to discuss these issues.

This paper introduces soap based insulation from recycled materials as a sustainable alternative to petroleum counterparts. The methodology is lab based experimentation and iterative tests. The phased based research process for the incremental development of the soap based thermal insulation is explained.

Findings reveal that soap based insulation can be one possible way forward in the quest for natural and sustainable thermal insulation from recycled products to preserve and conserve the sustainable environment.

Thus, the paper provides a unique environmentally friendly approach as an alternative to those existing petroleum counterparts for thermal insulation in buildings.

Two sets of dual magnetodynamic and magnetostatic finite element formulations taking thin conducting magnetic shells into account are proposed. The abstraction of the thin region from the computational domain is performed by an appropriate treatment of the surface integral terms arising in the weak formulations. Results are presented for two three‐dimensional test‐problems.

Titanate coupling agents have been described for the past decade. What they will do and how they are used has been summarised in an article by Monte, Sugerman, and Seeman [Modern Paint & Coatings, 67, July (1977) p. 27]. Thus the authors point out that the titanate coupling agents, which are basically organotitanium compounds whose structures are shown in the article, can make possible the formulation of metal oxides, pigments, and extenders into organic systems to produce coatings with improved physical properties, higher solids, and advantages from the points of view of manufacturing and application. In other words the organotitanium compound will couple a pigment or related material with the vehicle by forming chemical bonds. Thus, the authors propose that metal chromates may be replaced in corrosion‐resistant coatings with silica extenders if these silica extenders are coupled to the vehicle with an organopyrophosphatotitanate.

Metal matrix composites (MMCs) are commonly used in many aerospace and industrial applications. MMCs possess significantly improved properties including high specific strength, specific modulus, damping capacity and good wear resistance compared to unreinforced alloys. The purpose of this paper is to describe the tribological studies of Al-Si alloy–fly ash composites manufactured using powder metallurgy technique.

Al-Si (12 Wt.%) alloy–fly ash composites were developed using powder metallurgy technique. Al-Si alloy powder was used as matrix material, and the fly ash was used as reinforcement. The particle size of Al-Si alloy powder was in the range of 75-300 μm, and the fly ash was in the range of 1-15 μm. The friction and wear characteristics of the composites were studied using a pin-on-disc set up. The test specimen was mated against cast iron disc, and the tests were conducted with the loads of 10, 20 and 30 N, sliding speeds of 0.5, 1 and 1.5 m/s for a sliding distance of 2,000 m.

The effects of load and sliding speed on tribological properties of the base alloy and Al-Si alloy–fly ash composites pins on sliding with cast iron disc are evaluated. The wear rate of Al-Si alloy–fly ash composites is lower than that of base alloy, and it increases with increasing load and sliding speed. The coefficient of friction of Al-Si alloy–fly ash composites is increased as compared with base alloy.

The development of Al-Si alloy–fly ash composites produced by powder metallurgy technique will modernize the automobile and other industries because near net shape at low cost and good mechanical properties are obtained.

There are few papers available on the development and tribological studies of Al-Si alloy–fly ash composites produced by powder metallurgy technique.

Related even more closely to the coatings industry's technology are printing inks. Like coatings, inks comprise a combination of vehicles, pigments, and small percentage additives Inks do not serve a protective function in the same way that coatings do but they must, on the other hand, adhere to the substrate and they must certainly frequently be decorative. Conversely, practically all inks are applied in a “factory”, analogous to factory‐applied or industrial coatings. The analogy goes even further in that the application is done by highly automated equipment at rapid speeds, although it must be pointed out that inks are applied much more rapidly than most coatings.

This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of heat generation.

Constant internal temperature and convective external conditions in hollow bodies along with internal heat generation with a combination of outer convective conditions in solid bodies are investigated individually. The effect of the heat convection coefficient on solid bodies is additionally discussed. The variation of the FGM properties in the radial direction is adapted to the Mori–Tanaka homogenization schemes, which produces irregular and two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method.

It has been shown that the selection of the mixtures of FGMs has to be made correctly to keep the thermal and mechanical loads acting on objects at low levels.

In this study, both solid and hollow functionally graded cylinders and spheres for different boundary conditions that are as their engineering applications are examined with the proposed method. The results have demonstrated that the pseudospectral Chebyshev method has high accuracy, low calculation costs and ease of application and can be easily adapted to such engineering problems.