X.X. Hu

Fundamental vibration of rotating cantilever blades with pre-twist

Abstract A non-linear strain–displacement relationship of a pre-twisted conical shell on the general shell theory is utilized, and a method for vibration of a rotating cantilever conical shell with pre-twist is developed by the principle of virtual work and the Rayleigh–Ritz method. Firstly, deformation and stress resultants caused by rotation are analyzed. Secondly, an equilibrium of energy for vibration of a pre-twisted conical shell having the conditions achieved in the first process is given and then an eigenfrequency equation of a rotating cantilever conical shell with pre-twisted is formulated. The effects of parameters such as an angular velocity, a radius of a hub, a setting angle, a twist angle, a subtended angle and a tapered ratio of cross-section on the fundamental vibration are investigated.

Vibration of twisted laminated composite conical shells

Abstract A methodology for free vibration of a laminated composite conical shell with twist is proposed, in which a strain–displacement relationship of a twisted conical shell is given by considering the Green strain tensor on the general thin shell theory, the principle of virtual work is utilized, and the governing equation is formulated by the Rayleigh–Ritz procedure with algebraic polynomials in two elements as admissible displacement functions. The convergence, the accuracy and the validity of the methodology are verified by comparisons. As a result of the vibration frequencies and mode shapes, the effects of the laminated constructional and the geometric parameters, such as the number of laminae, the fiber orientation angles, the twist angle, the subtended angle and the taper ratio, on the vibration characteristics are studied by the present methodology.

Vibration analysis of rotating twisted and open conical shells

Abstract Based on a non-linear strain–displacement relationship of a non-rotating twisted and open conical shell on thin shell theory, a numerical method for free vibration of a rotating twisted and open conical shell is presented by the energy method, where the effect of rotation is considered as initial deformation and initial stress resultants which are obtained by the principle of virtual work for steady deformation due to rotation, then an energy equilibrium of equation for vibration of a twisted and open conical shell with the initial conditions is also given by the principle of virtual work. In the two numerical processes, the Rayleigh–Ritz procedure is used and the two in-plane and a transverse displacement functions are assumed to be algebraic polynomials in two elements. The effects of characteristic parameters with respect to rotation and geometry such as an angular velocity and a radius of rotating disc, a setting angle, a twist angle, curvature and a tapered ratio of cross-section on vibration performance of rotating twisted and open conical shells are studied by the present method.

Vibration analysis of twisted conical shells with tapered thickness

Abstract Considering twisted conical shells with tapered thickness, a numerical method for analyzing free vibration is developed, where an exact strain–displacement relationship of twisted conical shells is derived based on the shell theory, the equation of energy equilibrium for free vibration is formulated by the principle of virtual work, and the governing equation is obtained by the Rayleigh–Ritz procedure. The convergent property is investigated in view of the assumed displacement functions, and the comparison between the present and the available previous results for several typical conical shells is carried out in order to demonstrate the practicability and the accuracy. The effects of the tapered thickness in two directions, the twist angle, the subtended angle and the taper ratio of cross-section on the vibration behavior are discussed through the frequencies and corresponding mode shapes.

Vibration analysis of laminated cylindrical thin panels with twist and curvature

Abstract Using the principle of virtual work and the Rayleigh–Ritz method with two dimensional algebraic polynomial displacement functions, the governing equation of vibration for a laminated cylindrical thin panel with twist and curvature is presented. The practicability and effectiveness of the method is verified by comparing the numerical results with those obtained by other researchers using experimental and other numerical methods. The effects of twist, curvature, characteristics of material, the number of layers, stacking sequence and fiber orientation on vibration frequency parameters of a laminated cylindrical thin panel with twist and curvature are studied, and some vibration mode shapes are also plotted to explain the variations of the vibration caused by them.