Research On Error Localization In Structural Dynamics Model With Modal Strain Energy Method

Model verification and validation of Structural dynamics is one of the key point in the modern areo-engine design process,and the model updating is most important step of model verification and validation.Due to the reasonable assumptions and errorunous of the structural dynamic finite element model,how to identify and locate the model errors becomes the most crucial problem,which could be used to guide the seletion strategy of updating parameters and has a great significance in engineering.Most of the model error localization methods are focus on the system identification using inverse method with the modal parameters and the localization results are not satisfying the requirements of the model updating in most cases.As a derived parameter from modal parameters,the modal strain energy is very sensitive to the change of model parameters and could be used as an effective tool for error localization.But,the accuracy and noise of measured mode shape makes the calculated modal strain energy differ from the requirements of model error localization.For this problem,the high fidelity and detailed 3D finite element model,which is also called as supermodel,is proposed and the modal parameters derived from the supermodel will be used for calculating the modal strain energy as an alternative of the measured modal parameters.Also,the model match between the updating model and the supermodel needs to be carefully considered.Especially for the updating model built with shell model,how to extract the rotational dofs component of the mode shape from the supermodel data still needs to be studied.In order to obtain the high accuracy modal strain energy and establish the corrected error indicator,there is still much works to be further studied.Aim at these issuses on the error localization method based on modal strain energy,several works should be finished and the whole procedure of model verification and validation will be developed to improve the ablility of structural dynamics design of aero-engine industry for national.The main work and contributions of this paper are as follows:(1)A new concept of equivalent modal strain energy is proposed and the methodology of error localization based on modal strain energy change are further developed.The sensitivity of the modal strain energy is derived theoretically and proves that the strain energy is sensitive to the local parameter change.Furthermore,the concept of equivalent modal strain energy and three kinds of error indicator is proposed,which is expressed as the change between the modal strain energy and equivalent modal strain energy or the change of the ratio of the modal strain energy and equivalent modal strain energy.Also,the weighted factor of error indicator using fractional modal strain energy,normalized and truncated method based on the 2σ confidence criteria are presented.Simulation results shows that these indicators could identify different types of errors accurately.(2)A high precision model matching technique is proposed to extract the equivalent mode shape from the high-confidence finite element model,which is called supermodel and can be used as an alternative of experimental results.The modeling technique and evaluation criterion of supermodel are presented.Because the nodes of supermodel and design model cannot match perfectly,the mapping relationships from nodes of design model and elements of supermodel are established based on node projection.On this basis,the accurate equivalent mode shape can be obtained using the shape function method.Simulation results prove that the equivalent modal strain energy using high precision model matching technique is accurate,while the results derived from traditional match methods are not.(3)The modeling of aero-engine casing structure using shell element is widely used in practice to reduce the dofs of whole engine model analysis.However,the equivalent mode shape of that contains the rotational dofs,while the supermodel cannot afford to provide them.A mode shape transformation method is proposed.Based on the assumption of shell element,virtual nodes along the normal direction of the shell element are obtained and form a virtual solid element.The equivalent mode shapes of these virtual nodes are extracted using the high precision matching technique.After that,the rotational dofs can be derived by the derivative of the shape function of the virtual element or linear interpolation.Simulation results show that the transformation method could be used for error localization of shell type design model based on supermodel.(4)Two kinds of modal rotational mode shape measurement methods are proposed based on continuously scanning lased doppler vibrometer technique,the dual sinusoidal scanning method and uniform rate scanning method.For the dual sinusoidal scanning method,the displacement mode shape is expressed as the high order polynomial functions.The polynomial coefficients are determined by the sidebands information of the measurement output signal.On this basis,the modal rotational could be derived using the first derivative of the polynomial functions against the orthogonal directions.However,the polynomial function fitted mode shape are smooth but cannot reflect the discontinuous features,which is caused by local anomaly.Based on that,the uniform rate scanning method is proposed.The measured displacement mode shapes using that method are obtained directly through output signal demodulation and the corresponding modal rotationals are derived using finite difference method.Method verification is performed with plate structures and a damage detection method based on uniform rate scanning method are proposed and validated using various crack plate.(5)The proposed error localization method is applied on a casing structure of rotor test-rig.The first step is evaluated the supermodel using test data and the correlation analysis results shows that it can be used to replace the test data.The design model with shell elements is established and error localization is performed using the error indicator.As the mode shape transformation method is worked within the elemental coordinate system,different sub-region nodes should be treated using different coordinate system.Indicator results show that the flange and fuel hole protrusion part are the model errors.Compared with the results using sensitivity analysis selection method,model updating results with these parameters based on error location are more accurate and full of physical meaning.