Analytical dynamic model modification using acceleration and displacement feedback

Abstract

a b s t r a c tAn efficient numerical method for updating finite element models with incomplete modal measured data using acceleration and displacement feedback technique is developed. By the method, the required control gain matrices of acceleration and displacement feedback are determined, and thus the optimal approximation mass matrix and stiffness matrix which satisfy the required orthogonality relation and eigenvalue equation are found under the Frobenius norm sense. The procedure of this method is very simple and easy to realize and the solution of this problem have a compact expression. The numerical examples show that the modal measured data are better incorporated into the updated model.

Structural model updating study in consideration of complex pre-stress distribution

“…where K r 0 e is the addition stiffness matrix caused by the pre-stress distribution, G is the strain transformation matrix, and S is the pre-stress transformation matrix. The transformation matrix S can be written as Substituting equations (9) and (10) into equation 8, then the differential function can be expressed as…”

“…7,8 In the structural model updating, such as natural frequencies, mode shapes, and dynamic response parameters, are initially more interesting than the utilization of other parameters used in the structural model updating because such an approach allows a convenient model interpretation. 9,10 The structural model updating problem is essentially a structural optimization problem and it involves minimizing the given objective function under certain constraints condition, and it is necessary to define the corresponding optimization strategies in the structural model updating. [11][12][13] The pre-stress (initial stress) often exists in the structures before undertaking the external loading, which includes welding residual stress, structural manufacturing defects, material thermal effects, static loading, and so on, these types of pre-stress are defined as complex pre-stress.…”

“…7 , 8 In the structural model updating, such as natural frequencies, mode shapes, and dynamic response parameters, are initially more interesting than the utilization of other parameters used in the structural model updating because such an approach allows a convenient model interpretation. 9 , 10 The structural model updating problem is essentially a structural optimization problem and it involves minimizing the given objective function under certain constraints condition, and it is necessary to define the corresponding optimization strategies in the structural model updating. 11 – 13…”