Abstract:

The fracture mechanics theory posits that cracks induce strain energy concentration near their tips in structural components, generating localized flexibility that impedes crack propagation. Theoretically, cracks are represented as dimensionless, massless spring models, effectively capturing crack characteristics and cross-sectional properties at the crack location. Leveraging this spring-based representation, this study establishes an open-crack model for a one-dimensional (1D) piezoelectric semiconductor (PSC) curved beam under dynamic loading. This model enables the investigation of vibration characteristics in cracked structures. The analytical solutions for the electromechanical fields of the beam are derived using the differential operator method, and the natural frequencies together with the corresponding generalized mode shapes of the beam are determined analytically. Furthermore, the effects of the crack parameters on the natural vibration characteristics of the PSC curved beam are analyzed.

Key words: piezoelectric semiconductor (PSC), curved beam, vibration, crack, analytical solution