An exact solution for coupled bending and torsion vibrations of uniform beams having single cross-sectional symmetry

Transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the Rayleigh-Ritz method

This paper investigates the nonlinear dynamic responses of the rotating blade with varying rotating speed under high-temperature supersonic gas flow. The varying rotating speed and centrifugal force are considered during the establishment of the analytical model of the rotating blade. The aerodynamic load is determined using first-order piston theory. The rotating blade is treated as a pretwist, presetting, thin-walled rotating cantilever beam. Using the isotropic constitutive law and Hamilton’s principle, the nonlinear partial differential governing equation of motion is derived for the pretwist, presetting, thin-walled rotating beam. Based on the obtained governing equation of motion, Galerkin’s approach is applied to obtain a two-degree-of-freedom nonlinear system. From the resulting ordinary equation, the method of multiple scales is exploited to derive the four-dimensional averaged equation for the case of 1:1 internal resonance and primary resonance. Numerical simulations are performed to study the nonlinear dynamic response of the rotating blade. In summary, numerical studies suggest that periodic motions and chaotic motions exist in the nonlinear vibrations of the rotating blade with varying speed.

Nonlinear vibrations of blade with varying rotating speed

Energy expressions and free vibration analysis of a rotating double tapered Timoshenko beam featuring bending–torsion coupling

Coupled bending-bending vibrations of pre-twisted cantilever blading allowing for shear deflection and rotary inertia by the Reissner method

Coupled bending-torsion vibrations of rotating blades of asymmetric aerofoil cross section with allowance for shear deflection and rotary inertia by use of the Reissner method

K.B. Subrahmanyam

Papers

Coupled bending-torsion vibrations of rotating blades of asymmetric aerofoil cross section with allowance for shear deflection and rotary inertia by use of the Reissner method