Robustly identifying nonlinear mechanical systems is generally a challenging task, and this is particularly true when the structure under test exhibits nonlinear behaviors related to both stiffness...

Accurately determining system order plays a vital role in system identification directly related to the accuracy of identification results, especially for nonlinear system identification. Due to the need for human subjective judgment, the traditional sequence determination method easily causes uncertainty in the results; and the phenomenon of the virtual mode or omission occurs. An automatic nonlinear subspace identification method is proposed to address the aforementioned problems. When the eigenvalue decomposition of the constructed Hankel matrix is performed, the calculation range of the modal order of the system is estimated. The similarity coefficient and distance function are introduced to cluster the identified modal results, the poles of the false modes are removed to obtain the cluster stabilization diagram, and the best order of the system is received. Then, the modal parameters and nonlinear coefficients are obtained. Simulation examples are carried out to verify the effectiveness and robustness of the proposed method. An experimental study is carried out on a multilayer building with nonlinear characteristics. Compared with the traditional stabilization graph, the accuracy of the automatic order determination proposed in this paper is proven.

The sensitivity analysis plays a significant role in structural optimization, and repetitive calculations are necessary for the analysis procedure. A reanalysis approach of frequency response funct...

Model updating plays an important role in dynamics modeling with high accuracy, which is widely used in mechanical engineering. In this paper, a model updating method using frequency response function (FRF) is proposed based on Sherman–Morrison formula, in which only the initial FRFs and parameter perturbations are employed to calculate the sensitivity avoiding repeated finite element (FE) analyses and improving the computational efficiency. Firstly, the sensitivity of FRFs to the design parameters is calculated by Sherman–Morrison formula based on the QR decomposition of the system dynamic stiffness matrix variation after parameter perturbations, then the influence of damping on the amplitude of FRFs is considered to select an appropriate frequency range, and finally conduct the model updating according to the sensitivity of the FRFs. By employing simulation examples of a truss and a solar wing and the experiment of an aluminum frame, the updating error is still within ±1.00% in the condition of 5% random white noise, which shows the proposed method has high accuracy and a certain anti-noise capability. When only a few numbers of frequency points are selected near the resonance peak of the FRFs, the result shows that selecting the appropriate frequency range and points can reduce the computational cost. The results of the experiment study show that the proposed method can effectively identify the structural parameters. The above results verify the feasibility and effectiveness of proposed model updating method using FRFs.

Modal parameter identification is adversely affected by the mass loading of the transducer in experiments, especially when multi-transducers are arranged on the lightweight structure. In order to remove the coupling effects of transducers on each measurement point, a hierarchical multi-transducers eliminations method based on Sherman–Morrison theory is investigated. The method consists of two steps: (1) Decomposition: multiple elimination is decomposed into multi-levels, the relationship of the frequency response functions between each level is illustrated in the tree diagram; (2) Elimination: according to the relationship between each level, the measured frequency response functions are modified level by level. Numerical simulation is conducted by employing a three-degrees-of-freedom spring-mass system and the robustness is verified in the noise case. Experimental investigations are undertaken by employing a lightweight cantilever beam: Laser Doppler vibrometer is adopted to obtain measured frequency response functions without transducer mass loading effect, which are regarded as the target data. The initial frequency response functions are obtained in the case, in which multi-accelerometers are arranged and the effects should be removed. The result shows that the method can effectively decouple the frequency response functions due to transducers. In the elimination process, it is necessary to delete duplicate information (frequency response functions), which can greatly reduce the amount of calculation. And the effects of multi-transducers mass can be removed and the corrected frequency response functions are in quite good agreement with the target values.