• Nonlinear Functional Analysis and Applications
• /
• v.26 no.2
• /
• pp.237-272
• /
• 2021

The main purpose of the present paper is to study the asymptotic behavior near the origin of radial solutions of the equation 𝚫_p u(x) + u^q(x) + f(x) = 0 in ℝ^N\{0}, where p > 2, q > 1, N ≥ 1 and f is a continuous radial function on ℝ^N\{0}. The study depends strongly of the sign of the function f and the asymptotic behavior near the origin of the function |x|^λf(|x|) with suitable conditions on λ > 0.

• Structural Engineering and Mechanics
• /
• v.72 no.5
• /
• pp.597-615
• /
• 2019

The paper studies the dispersion of the axisymmetric longitudinal wave propagating in the "hollow cylinder + surrounding medium" system with inhomogeneous initial stresses caused by the uniformly distributed radial compressional forces acting at infinity. Up to now in the world literature, there exist only a few investigations related to the wave dispersion in a hollow cylinder with inhomogeneous initial stresses. Therefore, this paper is one of the first attempts in this field in the sense of the development of investigations for the case where the cylinder is surrounded with an infinite medium. The three-dimensional linearized theory of elastic waves is used for describing the considered wave propagation problem and, for a solution to the corresponding mathematical problem, the discrete-analytical solution method is developed and employed. The corresponding dispersion equation is obtained and this equation is solved numerically and, as a result of this solution, the dispersion curves are constructed for the first and second modes. By analyzing these curves, the character of the influence of the inhomogeneous initial stresses on the dispersion curves is established. In particular, it is established that as a result of the inhomogeneity of the initial stresses both new dispersion curves and the "band gap" for the wave frequencies can appear.

• Structural Engineering and Mechanics
• /
• v.56 no.1
• /
• pp.137-156
• /
• 2015

In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.