Analyzing and Characterizing the Global Complexity of Bistable Structures Under Simple Harmonic Excitation

The paper aims to develop a method to analyze and characterize the complexity of periodic excited bistable structures.

An efficient method is developed based on the compute unified device architecture (CUDA) platform for analyzing the complexity of bistable systems in terms of the characteristics of their periodic response. Also, a new complexity metric, state entropy, is proposed by considering the complexity of both the basin of attraction and the attractor. This metric is well suited to be computed by exploiting the parallelism of the graphics processing unit (GPU).

The basins of attraction slices of the system in the three-dimensional state space are plotted by taking a preloaded von Mises truss as an example. Then, the existence of the safety response, steady-state stability, transient stability, and state entropy of the system is calculated for different excitation amplitudes and frequencies.

The proposed method allows an efficient global characterization of bistable systems subject to periodic excitation, and the proposed state entropy is suitable for quantitatively assessing the response complexity of bistable systems.