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The structural stability of clamped-free beam-columns resting on a two-parameter foundation under a nonconservative force is investigated. The higher-order beam theory is developed by considering the warping of the cross-section, rotary inertia, and axial force's direction. The characteristic equation of dynamic stability of rectangular/circular cantilevers on a Winkler-Pasternak foundation is obtained for a generalized follower force. Critical loads for divergence instability and flutter instability are evaluated. The influences of foundation stiffness, cross-sectional warping shape, the tangency coefficient on the critical loads are analyzed. The load-frequency interaction-curves are given for different directions of the follower force. The normal/shear stiffness of foundation on divergence and flutter loads has different effects. The normal stiffness increases the first divergence load but decreases the flutter load, reducing to the Herrmann–Smith paradox for Euler columns. The rise of shear stiffness enlarges the first divergence load and lowers the flutter loads. The effects are more sensitive for short beam-columns. Different warping shapes slightly affect the critical loads and the natural frequencies. The exponential warping shape gives the smallest critical divergence loads and the fundamental frequencies. The results of Haringx hypothesis are larger than those of Engesser hypothesis. For shorter columns, the classical results are overestimated and the higher-order beam theory is necessary. [ABSTRACT FROM AUTHOR]

For a thickness-wise functionally graded (FG) beam, the midplane does not coincide with its physical neutral plane. This paper presents a consistent shear beam theory that guarantees the warping of the cross-section with vanishing shear stress on the surfaces and maximal shear strain/stress at the physical neutral plane. The governing equation of the free vibration of FG beams is derived. For typical end conditions, the characteristic equations are obtained exactly. The numerical natural frequencies are calculated and verified for special cases by comparing the existing solutions. Effects of the exponential gradient of material properties on the natural frequencies are elucidated. [ABSTRACT FROM AUTHOR]

This paper presents a novel higher‐order shear deformation beam theory for analyzing the stability and free vibration of functionally graded (FG) sandwich beams with emphasis on the effect of higher‐order moment (HOM) and cross‐sectional warping. The governing equation of axially loaded FG sandwich beams is derived from three‐dimensional equations of the theory of elastic waves in bodies with homogeneous initial stresses. The characteristic equations for typical end conditions are obtained exactly. The numerical results of the natural frequencies and critical loads are calculated and verified for special cases by comparing them with the existing solutions. The effects of gradient index, core thickness, HOM, and warping shapes on the natural frequencies and critical buckling loads are elucidated for different slenderness ratios and end constraints. [ABSTRACT FROM AUTHOR]

In this paper, the thermoviscoelastic response of skin tissue, as a typical class of viscoelastic biological tissue, subject to thermal shock is studied based on the fractional Kelvin-Voigt model and fractional Pennes bioheat conduction. A time-fractional biothermoviscoelastic governing equation is derived and initial-boundary value conditions are given for monolayer skin tissue of finite thickness. The temperature change and thermal stress of viscoelastic skin tissue are obtained by the Laplace transform and its inversion using matlab software. The influences of viscosity coefficient, relaxation times, fractional-order viscosity/heat parameter, and blood perfusion rate of skin tissue on the temperature distribution and the elastic displacement are analyzed. The numerical results show that fractional-order viscosity does not affect temperature, whereas fractional-order heat flow does. Moreover, fractional-order heat flow affects the sensitivity of blood perfusion rate to the thermodynamic response. [ABSTRACT FROM AUTHOR]

This paper studies a class of nonlinear problems of convective longitudinal fins with temperature-dependent thermal conductivity and heat transfer coefficient. For thermal conductivity and heat transfer coefficient dominated by power-law nonlinearity, the exact temperature distribution is obtained analytically in an implicit form. In particular, the explicit expressions of the fin temperature distribution are derived explicitly for some special cases. An analytical expression for fin efficiency is given as a function of a thermogeometric parameter. The influences of the nonlinearity and the thermogeometric parameter on the temperature and thermal performance are analyzed. The temperature distribution and the fin efficiency exhibit completely different behaviors when the power-law exponent of the heat transfer coefficient is more or less than negative unity. Key words: exact solution, temperature-dependent thermal conductivity, temperature-dependent heat transfer coefficient, nonlinear fin problem. Nous etudions une classe de problemes non lineaires touchant des ailettes longitudinales convectives avec une conductivite thermique et un coefficient de transfert de chaleur dependants de la temperature. Pour une conductivite thermique et un coefficient de transfert de chaleur en loi de puissance, nous obtenons une expression exacte analytique sous forme implicite. En particulier pour certains cas speciaux, nous derivons une forme explicite de la distribution en temperature de l'ailette. Nous trouvons une expression analytique pour l'efficience de l'ailette en fonction d'un parametre thermo-geometrique et nous analysons l'influence de la non linearite et du parametre thermo-geometrique sur la temperature et le transfert thermique. La distribution en temperature et l'efficience de l'ailette ont un comportement tres different selon que l'exposant de la loi de puissance du coefficient de transfert de chaleur est plus grand ou plus petit que moins un. [Traduit par la Redaction] Mots-cles: solution exacte, conductivite thermique dependante de la temperature, coefficient de transfert de chaleur dependant de la temperature, probleme non lineaire d'une ailette., 1. Introduction Heat transfer is a typical phenomenon encountered frequently in both engineering applications and daily life, and it has a long history of research [1]. Great progress in this [...]