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

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.

Automated summary

This work investigates the vibration characteristics of imperfect bi-directional functionally graded beams with arbitrary boundary conditions. Two types of geometrical imperfections, global and localized, are simulated using hyperbolic, exponential, and trigonometric functions. The energy equations of the beam are formulated based on the Timoshenko beam theory, and a domain decomposition method is used to divide the beam structure into several segments. The flexible couplings between the beam segments and the boundary constraints are modeled using an artificial spring technique. Modal characteristics are obtained using the Ritz method with Jacobi polynomials as admissible functions. Numerical simulations are performed to analyze the impact of geometric and material parameters on the vibration performance. Results show that imperfections can cause mode veering phenomena, and the type of mode veering is influenced by the material distribution pattern, boundary constraints, and geometrical imperfections.