Free vibration analysis of a debonded curved sandwich beam

• Free vibration response of a debonded curved sandwich beam is studied.
• A high order theory is developed for curved sandwich beams.
• Debonding is modeled using “with contact” and “without contact” models.
• The curvature angle strongly affects the vibration response of curved beams.
• The effect of curvature angle is in conjunction with boundary conditions.

In this paper, a high order theory is developed to study the free vibration response of a debonded curved sandwich beam. Since the real contact condition at the debonded region is nonlinear, two linear “with contact” and “without contact” models are employed. The Lagrange's principle and the Rayleigh-Ritz method are employed to derive and solve the governing equations. The model regards the radial and circumferential rigidities of the core. For this purpose, quadratic polynomial distributions across the core's height are proposed for its displacement components. The high order model is validated by finite element simulation in ANSYS Workbench. It will be shown that the quadratic distributions can effectively be used for a debonded curved beam comparing to other possible distributions such as a linear pattern which has been previously suggested for an undamaged beam. The analyses demonstrate that curvature angle and boundary conditions play important roles in the vibration response of a curved beam. Also, the results show that the debond effect on natural frequencies is approximately identical for flat and curved beams.