A new method is presented to generate two-directional (2D) grid multi-scroll chaotic attractors via a specific form of the sine function and sign function series, which are applied to increase saddle points of index 2. The scroll number in the x-direction is modified easily through changing the thresholds of the specific form of the sine function, while the scroll number in the y-direction is controlled by the sign function series. Some basic dynamical properties, such as equilibrium points, bifurcation diagram, phase portraits, and Lyapunov exponents spectrum are studied. Furthermore, the electronic circuit of the system is designed and its simulation results are given by Multisim 10.
In this paper, we report a new model in analysis of spherical thin-shell piezoelectric transducers for transient response, based on Fourier transform and the principle of linear superposition. We show that a circuit-network, a combination of a series of parallel-connected equivalent-circuits, can be used in description of a spherical thin-shell piezoelectric transducer. When excited by a signal with multiple frequency components, each circuit would have a distinctive radiation resistance and a radiation mass, arising from an individual frequency component. Each frequency component would act independently on the electric/mechanic-terminals. A cumulative signal-output from the mechanic/electric-terminals is measured as the overall acoustic/electric output. As a prototype example in testing the new model, we have designed two spherical shin-shell transducers, applied a gated sine electric-signal as the initial excitation, and recorded the experimental information. The transient response and the output signals are calculated based on the new model. The results of calculation are in good agreement with that of experimental observation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.