Snap-through behaviors of bistable composite panel in centrifugal environments

Abstract

In this paper, a cross-well dynamics model of bistable composite panels in centrifugal environments is proposed. The external excitation applied at the four corners is assumed to be a uniformly distributed harmonic acceleration. Nonlinear equations are derived by combining geometric nonlinearity, thermal stresses, and centrifugal effects with the first-order shear deformation theory, and are expressed in terms of curvature. Additionally, the maximum Lyapunov exponent is used to classify vibration types. Observations of periodic and chaotic snap-throughs are categorized into vibration type domains. To facilitate understanding, bifurcation diagrams, phase portraits, time histories, and Poincaré maps are presented for representative operating conditions. The effects of centrifugal environments, external excitation amplitude, and frequency on snap-through behavior are thoroughly investigated. The results show that there exists a critical static angular velocity, beyond which the panel cannot maintain bistability, and indicate that snap-through behavior in bistable panels is caused by negative stiffness due to residual thermal stresses. Bistable composite panels exhibit both forward and backward bouncing. Furthermore, three types of frequencies are identified: upper Stable I frequency, lower Stable II frequency, and snap-through frequency. It is also noted that the impact of angular velocity on these frequencies is not uniform. When the external excitation frequency approaches one stable state frequency, it can destabilize the configuration, causing vibrations to occur in the other configuration.