Structural Dynamic Modification Based on Combined Approximations Method

Structural dynamic modification plays an important role in structural dynamic design. This paper presents an algorithm for dynamic modification of the structure, which is based on the Combined Approximations (CA) approach, sensitivity analysis, Taylor series expansion and the least square method. The feasibility of the algorithm is verified by a numerical example and the results show that the algorithm is accurate enough and easy to be implemented.

Reanalysis Method for Second Derivatives of Static Displacement

The reanalysis method to obtain the second derivatives of static displacement is innovatively proposed in this paper. This method is based on the combined approximations method. The reanalysis formulations of the second derivative of static displacement are derived to provide a programmatic procedure of formulations construction. Besides, the normalized error and the number of algebraic operations are considered to evaluate the accuracy and efficiency, respectively. Finally, three typical numerical results verify the accuracy and robustness of the proposed method.

A Contribution to the Reduced-Order Analysis of Bladed Disks Using Combined Approximations for Quick Campbell Diagrams Assessment

This paper proposes an original approach to the reduced-order modelling of integrally bladed disks. It is proposed to build a reduction basis which is independent from the rotational speed, from only one modal, cyclic-symmetry calculation performed at rest, and a few static computations. Based on previous works, a polynomial expansion is used which leads to a parametric approximation of the stiffness matrix for the entire operating range. Furthermore, the Kirsch Combined Approximation (KCA) method is used for building the final reduction basis. This method is based on successive approximations of the negative binomial expansion applied to the reanalysis eigenproblem. After giving a general overview of the main theoretical aspects, the paper focuses on the reanalysis problem based on the combined approximations method. Finally, the application of the extended reduction method to the case of a real bladed disk is presented. It is shown that the use of combined approximations provides a very accurate estimation of a Campbell diagram, and allows substantial computational time savings.