Vibration, linear elastic buckling and dynamic stability behaviors of a cracked cylindrical shell with time-varying rotating speed are analyzed. Finite element method is used to obtain the system mass and stiffness matrix, and Bolotin's method is applied to explore the dynamic stability region. The effects of constant rotating speed, crack length and orientation, and length-diameter ratio of the cylindrical shell on the free-vibration and buckling behaviors are investigated. The stability characteristics of the cracked shell are also researched and the influences of crack length, crack orientation, rotating speed basic value, steady load factor, dynamic load factor and damping ratio are considered. Numerical examples show that crack length and orientation can affect the vibration, buckling and dynamic stability behavior of cylindrical shell significantly.

Vibration, Buckling and Dynamic Stability of a Cracked Cylindrical Shell with Time-Varying Rotating Speed

Dynamic stability of a radially rotating beam subjected to base excitation

Parametric instability of spinning pretwisted beams subjected to sinusoidal compressive axial loads

An investigation on the non-linear aeroelastic behavior of a wind turbine blade with both external and internal resonances is presented. The external resonance is a primary resonance that appears at the first flapwise mode; it can cause severe damage to blade. The internal resonance happens at the first two flapwise modes; it can enhance the energy transfer between two modes, and change blade dynamics in primary resonance. Three aspects including blade behavior in pure primary resonance (abbr. PPR; only considering external resonance), blade behavior in combination resonance (abbr. CR; including both external and internal resonances), and the influence of internal resonance (i.e. modal interaction) on external resonance are examined. A simple Bernoulli–Euler beam model, in which geometric non-linearity and unsteady aerodynamic force are considered, is used to describe the flapwise motion of blade. The perturbation method is applied to the infinite-degree-of-freedom discrete system, which is obtained from the original continuous system via Galerkin׳s method, to get dynamic responses. Amplitude–frequency curves of resonance modes in CR and PPR are derived, and the stability of the steady state motion of blade is judged. The strongest modal interaction between two resonance modes is taken into account, and then effects of modal interaction, excitation amplitude, damping and non-linearity on non-linear vibration properties of blade are analyzed. Also, influences of three designing parameters (inflow ratio, setting angle and coning angle) and two detuning on the non-linear behavior of blade are discussed for a concrete downwind turbine.

G.T. Liou

Papers

Dynamic Response of a Rotating Blade with Time-Dependent Rotating Speed