Efficient Procedures of Sensitivity Analysis for Structural Vibration Systems with Repeated Frequencies

Algorithm 1

The produce of the proposed method.

(1) Introduce the relaxation factor and transform the eigenequations into equivalent equations.

(2) Compute eigenvector 𝝍₁.

(3) The eigenvectors 𝜽_𝑖(𝑖=2,3,…,𝑁) can be expressed by the basis vectors 𝜽_𝑖^𝐵(𝑖=2,3,…,𝑁)

  and coefficients vectors  𝐲_𝑖(𝑖=2,3,…,𝑁).

(4) Compute 𝜕𝜽_𝑖/𝜕𝑑=(𝜕𝜽_𝑖^𝐵/𝜕𝑑)𝐲_𝑖+𝜽_𝑖^𝐵(𝜕𝐲_𝑖/𝜕𝑑),  𝑖=1,2,…,𝑁.