A domain decomposition method based vibration analysis of BDFGs imperfect beams with arbitrary boundary conditions

Abstract

This work addresses the vibration characteristics of imperfect bi-directional functionally graded (BDFG) beams with arbitrary boundary conditions. Two kinds of geometrical imperfections including global and localized types are considered, which are simulated using hyperbolic, exponential and trigonometric functions. Energy equations of beam are formulated on basis of the Timoshenko beam theory, and the domain decomposition method in which the original beam structure is divided to several beam segments. The flexible couplings between beam segments and boundary constraints of beam are modeled employing artificial spring technique. By choosing the Jacobi polynomials as admissible functions, modal characteristics are acquired using the Ritz method. Convergence, stability and reliability of presented method are validated, and penalty technique for artificial springs is examined for the classic and general boundary conditions. Numerical simulations are performed to probe the impact mechanism of geometric and material parameters on vibration performance of BDFG beam. Results show that imperfection may cause appearance of mode veering phenomenon where modal features distort. The types of mode veering are dominated by material distribution pattern, boundary constraints and kinds of geometrical imperfection.