FLUID-CONVEYING DAMPED RAYLEIGH-TIMOSHENKO BEAMS IN TRANSVERSE VIBRATION ANALYZED BY USE OF AN EXACT FINITE-ELEMENT .1. THEORY

An exact finite element method is advanced for studying free and forced nonsynchronous harmonic linear vibrations of piecewise uniform straight beam structures supported by a Winkler-type ambient medium and conveying a piecewise constant-speed plug flow of material along the deflected beam axis. Hysteretic and viscous damping in the beam material and ambient medium are considered. Large static axial loads may act on the beam and the fluid calling for use of a second-order theory. An exact complex-valued nonsymmetric stiffness matrix is established for a uniform beam element based on a generalized second-order Rayleigh-Timoshenko beam theory. This transcendentally frequency-dependent stiffness matrix allows for an exact analysis of assembled nonproportionally damped continuous beam structures thus avoiding spatial discretization and eliminating truncation errors. Exact member stiffness matrices are also found for Euler-Bernoulli beams (with infinite shear stiffness) and strings (with zero bending stiffness). Numerical examples are given in a companion paper. © 1990 Academic Press Limited.