A quadratic inverse eigenvalue problem in damped structural model updating

•We present a quadratic inverse eigenvalue problem with incomplete measured data arising from damped model updating.•We analyze the existence of solution to the problem, and give the solvability condition for the problem.•We propose a numerical method for solving the problem.•We provide two numerical examples to illustrate the effectiveness and the application of the proposed method.

A quadratic inverse eigenvalue problem arising from damped structural model updating is presented in this paper. The existence of solution to the problem is analyzed. A new model updating method for damped structural systems is proposed. The new approach can update directly the damped model using the spatially incomplete modes without using model reduction or eigenvector expansion techniques. Numerical examples show that the proposed method is efficient.