Mode Shape Transformation for Error Localization with Modal Strain Energy
Z Huang, CP Zang, GB Zhang & MI Friswell (Swansea University)
Journal of Sound and Vibration, Vol. 473, 12 May 2020, paper 115230
A modeling error location method based on modal strain energy is presented in this paper. Errors in the design model with shell elements are located by an error indicator which is based on changes between the equivalent modal strain energy and the modal strain energy of the design model. The equivalent modal strain energy is defined as a quadratic form using the stiffness matrix of the design model and the mode shape of the reference coming from the sophisticated and high fidelity finite-element model, called the supermodel, or the full-field measurement. The major obstacle to obtain the equivalent modal strain energy is how to match the mode shapes of a solid element and those of a shell element since each node of the solid element contains only three translation degrees of freedom (dofs) while each node of the shell element has six dofs, including three translation and three rotation components. In order to solve this problem, a mode shape transformation method from the solid element to the shell element is proposed using the shape functions or linear approximation. Using this approach, the errors in the design model can be determined and the updating parameters can be selected so that the updated model has physical meaning and can represent the dynamic characteristics of the real structure. The simulation of a simple plate is used initially to illustrate the effectiveness of the proposed method. Then, a rotor test rig casing is taken as an example for further investigation. A comparison of the updating parameters selected by the proposed method and the traditional sensitivity analysis technique is then undertaken. It is verified that the updating parameters selected based on error location have physical sense and represent the true errors in the design model through the updating results. The advantage of this technique is that only detailed mode shapes from the reference is required. The approach shows potential for further industrial engineering applications.
This material has been published in the Journal of Sound and Vibration, Vol. 473, 12 May 2020, paper 115230. Unfortunately the copyright agreement with Elsevier does not allow for the PDF file of the paper to be available on this website. However the paper is available from ScienceDirect - see the link below.
Link to paper using doi: 10.1016/j.jsv.2020.115230
Journal of Sound and Vibration on ScienceDirect