Dynamic Thermoelastic Response of Cylindrical Shells

Abstract

The dynamic, thermoelastic response of cylindrical shells to suddenly applied and rotating thermal inputs is investigated. Fully coupled, dynamic, thermoelastic cylindrical shell equations are derived using Galerkin’s method. Identical results were obtained independently using a variational theorem. Analytical solutions to these equations are formulated for finite-length and infinite-length cylinders. Numerical results for the response of infinite-length cylindrical shells to suddenly applied and rotating longitudinal lines of heat flux are presented. It is shown that for many thermoelastic problems involving moving thermal inputs that the maximum ratio of dynamic to quasi-static deflection can be much greater than two, that dynamic effects can be important for all thicknesses within the realm of thin shell theory, and that semicoupled theory gives incorrect results in some cases for which a fully coupled theory is required.

Coupled thermoelasticity of functionally graded cylindrical shells

“…(14) and the resulting residue Re(T) is made orthogonal with respect to 1, and z. This yields two independent equations for T 0 , and T 1 , as (McQuillen and Brull, 1970…”

“…The first law of thermodynamics for heat conduction equation in the assumed cylindrical functionally graded shell, when the temperature distribution is assumed to be a function of time and thickness direction, is (McQuillen and Brull, 1970) qðzÞcðzÞD…”

Coupled Thermoelastic Theory for Dynamic Stability of Composite Plates

“…(for an isotropic plate C$ = E/(1-v 2 ) and AT = Ea/(l-v)) (6) in which Cij are elastic constants, ai the thermal expansion coefficients, and where To is a reference temperature (T = To will correspond here to the unstressed-unstrained state).…”

Exact closed-form solution of the dynamic coupled thermoelastic response of a functionally graded Timoshenko beam

“…Using (10), the residue, Res., of the energy equation may be made orthogonal with respect to dz and z dz to provide two independent equations for two independent functions θ 1 and θ 2 as [McQuillen and Brull 1970]…”

“…McQuillen and Brull [1970] presented an analytical solution for the dynamic thermoelastic response of cylindrical shells using the variational theorem. The coupled thermally induced vibrations of the Euler-Bernoulli and Timoshenko beams with one-dimensional heat conduction are investigated in [Seibert and Rice 1973].…”