T. Sakiyama

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.

A method for vibration analysis of a tapered timoshenko beam with constraint at any points and carrying a heavy tip body

Abstract An approximate method is developed to study the bending vibration of a tapered Timoshenko beam with constraint at any points and carrying a heavy tip body. The solutions are obtained by transforming the ordinary differential equations into integral equations and integrating them numerically. As applications of this method, some numerical examples are shown.

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.

An approximate method of shallow shells with variable thickness

Abstract An approximate method is developed to study the static bending of shallow shells with variable thickness. The solutions are obtained by transforming the partial differential equations into the integral equations and applying the numerical integrations. Some numerical examples are shown together with other solutions, and as an application of this method, the results of shallow shell with variable thickness are shown.

A Fatigue Crack Driving Force Parameter

Most of the previous parameters that utilized as a crack driving force were established in modifying the parameter Kop in Elber’s effective SIF range (ΔKeff = Kmax –Kop ). This paper focuses on the physical meaning of compliance changes caused by plastic deformation at the crack tip, the test was carried out for structural steel under constant amplitude loading, and differences of several parameter ΔKeff in literature are analyzed quantificationally. The effect of actual stress amplitude at the crack tip on fatigue crack growth is investigated, and improved two-parameter driving force model ΔKdrive (=Kmax )n (ΔK^ )1−n ) has been proposed. Experimental data for several different types of materials taken from literature were used in the analyses. Presented results indicate that the parameter ΔKdrive is equally effective or better than ΔK(=Kmax -Kmin ), ΔKeff (=Kmax -Kop ) and ΔK* (=(Kmax )α (ΔK+ )1−α ) in correlating and predicting the R-ratio effects on fatigue crack growth rate.Copyright

Evaluation of propagation considering elasto-plastic behavior at fatigue crack tip

Publisher Summary The chapter discusses the evaluation of propagation considering the elasto-plastic behavior on a fatigue crack tip. It emphasizes on the generation of the tensile and compressive plastic zones near the crack tip during fatigue propagation. The relationships between generation and acceleration and deceleration and crack stop phenomena are investigated respectively. The role of each zone of the hysteresis loop denoting the relationship between loads and strains near the crack tip on fatigue propagation is studied by the fatigue crack propagation tests and the Kth test. The chapter clarifies that the elasto-plastic behavior at the crack tip has a great influence on the fatigue crack propagation because the crack closure phenomenon during the cyclic loading is confirmed. The chapter aims to consider the hysteresis loop at the crack tip in detail and clarify the physical role of each zone of the loop.

An approximate method for analyzing tapered mindlin plates

Abstract An approximate method is developed to study the static bending of tapered Mindlin plates. The solutions are obtained by representing the partial differential equations into the ordinary differential equations by means of the Fourier series and by transforming the ordinary differential equations into integral equations and applying the numerical integrations. Some numerical examples are shown together with other analytical solutions, and as an application of this method, the results of tapered Mindlin plate are shown.

Geometrical nonlinear analysis of rectangular mindlin plates

Abstract An approximate method is developed to study the geometrical nonlinear analysis of the rectangular plates. The solutions are obtained by transforming the partial differential equations into the integral equations and applying the numerical integrations. The nonlinear problem is solved by the iteration and the load incremental procedure. The results are compared with FE-solutions.