The purpose of this work is to investigate the influences of viscosity and the variation of thermal conductivity on the thermoelastic vibrations in a very thin hollow cylinder. The generalized thermal model has been developed using the Moore Gibson-Thompson (MGT) equation by adding relaxation time in the developed Fourier law according to Green-Naghdi theories. In addition to the initial conditions, some boundary conditions have been taken into consideration on the inner and external surface of the hollow solid cylinder. Unlike many problems in which the coefficient of thermal conductivity is assumed to be constant, it has been taken into account that it is variable and depends on the change of temperature. By applying the Laplace transform method, the numerical solutions are assigned to the studied physical quantities. The studied quantities have been presented graphically and in tabular form to compare the outcomes for various models of thermoelasticity and to illustrate the influences of changing thermal properties and viscosity on the physical fields.

In this work, a modified viscoelastic model of initially stressed microbeam on the base of the Winkler foundation under the effect of ultrafast laser heating and axial stress has been proposed. Viscosity effects are taken into account following the Kelvin–Voigt model. The governing equation for the thermoelastic vibration of the microbeam is obtained when the thermal field effect is defined by the non-Fourier Moore–Gibson–Thompson (MGT) heat equation. The microbeam is seen as an Euler–Bernoulli beam that is exposed to varying sinusoidal heat. An analytical solution to the problem has been presented on the basis of the Laplace transform in addition to applying a numerical method to find inverse transformations. A numerical illustration is organized in the discussion section which discusses the impact of different effective parameters both on the vibrational behavior of a microbeam system and on the field variables. The viscous damping coefficient, laser pulse duration, and axial load greatly affect the deflection and temperature responses. The results obtained are verified and compared with the literature.

In this article, we are applying the competing risks model of product from two different lines of production. So, the comparative life test is done under type-II censoring scheme with consideration of only two independent causes of failure. The statistical analysis procedures are developed considering joint sample of production and its life distributed with the Rayleigh lifetime distribution. The point estimation and the corresponding asymptotic confidence interval of the model parameters under maximum likelihood are constructed. Two bootstrap confidence intervals, bootstrap- p p , and bootstrap- t t , are discussed. Also, Bayesian approach to estimate point and credible interval is constructed. The estimation results are discussed through data set analyses. The validity of theoretical results is assessed and compared through Monte Carlo study. Finally, some of the points are reported as a brief comment.

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