A new higher-order shell theory for vibration and acoustic scattering from bare and viscoelastically-coated circular cylindrical shells

This work presents a theoretical investigation of the free and forced vibration of bare and viscoelastically-coated infinite cylindrical shells by means of arbitrary-order Ritz expansions for displacement components. Such expansions, which are based on a set of related Legendre polynomials of the thickness coordinate multiplied by an irrational radial factor, allow analytic integration of strain and kinetic energy over the thickness. Sinusoidal functions are used for the circumferential dependence. For harmonic motion, Hamilton's principle leads to expressions for mass and stiffness matrices.; These matrices allow convergent approximations of natural frequencies and mode shapes. The natural frequencies agree with results based on analytic solution of the elasticity equations for the entire range of shell thickness, from a thin shell to a solid cylinder. Modal displacement variation across the thickness and contributions to modal strain energy yield qualitative conclusions regarding the failure of several conventional shell theories. These theories fail even for geometrically thin shells (h/a {dollar}ll{dollar} l) when the circumferential wavelength approaches the shell thickness.; Vibration of coated shells is modelled by employing independent Ritz expansions in the shell and coating. Explicit enforcement of displacement continuity at the shell-coating interface takes the form of a matrix transformation that eliminates constrained generalized coordinates. Natural frequencies of a shell coated with a vibration damping material match results from elasticity solutions. The modal strain energy method is used to estimate the damping effectiveness as a function of coating thickness and circumferential harmonic number. Calculations of response to a harmonic radial point force confirm conclusions drawn from the modal strain energy method. As a final application, the theory is applied to plane wave scattering from a steel shell with an acoustic decoupling coating. The backscattered farfield form function agrees with published experimental results and calculations based on elasticity solutions. A conventional coated shell theory is found to be inappropriate for this model.