Bifurcation Study of Thin Plate with an All-Over Breathing Crack

An all-over breathing crack on the plate surface having arbitrary depth and location is assumed to be nonpropagating and parallel to one side of the plate. Based on a piecewise model, the nonlinear dynamic behaviors of thin plate with the all-over breathing crack are studied to analyze the effect of external excitation amplitudes and frequencies on cracked plate with different crack parameters (crack depth and crack location). Firstly, the mode shape functions of cracked thin plate are obtained by using the simply supported boundary conditions and the boundary conditions along the crack line. Then, natural frequencies and mode functions of the cracked plate are calculated, which are assessed with FEM results. The stress functions of thin plate with large deflection are obtained by the equations of compatibility in the status of opening and closing of crack, respectively. To compare with the effect of breathing crack on the plate, the nonlinear dynamic responses of open-crack plate and intact plate are analyzed too. Lastly, the waveforms, bifurcation diagrams, and phase portraits of the model are gained by the Runge-Kutta method. It is found that complex nonlinear dynamic behaviors, such as quasi-periodic motion, bifurcation, and chaotic motion, appear in the breathing crack plate

Advanced ODE Based Head Modelling for Chinese Marionette Art Preservation

Puppetry has been a popular art form for many centuries in different cultures, which becomes a valuable and fascinating heritage assert. Traditional Chinese marionette art with over 2,000 years history is one of the most representative forms offering a mixture of stage performance of singing, dancing, music, poem, opera, story narrative and action. Apart from a set of string rules which controls the dynamics, head carving skill is another important pillar in this art form. This paper addresses the heritage preservation of the marionette head carving by digitalizing the head models with a novel modelling technique using ordinary differential equations (ODEs). The technique has been specially tailored to suit the modelling complexity and the need of accurate description of shapes. It offers smoothly sewing ODE swept patches to represent the distinct features of a marionette head with sharp variance of local geometry. Such features otherwise are difficult to model and capture accurately, which may require a great effort and tedious hand-crafting of an experienced modeller, when using other representation forms like polygons