Based on the direct differentiation method, sensitivity analysis of transient responses with respect to local nonlinearity is developed in this paper. Solutions of nonlinear equations and time-domain integration are combined to compute the response sensitivities, which consist of three steps: firstly, the nonlinear differential equations of motion are solved using Newton–Raphson iteration to obtain the transient response; secondly, the algebraic equations of the sensitivity are obtained by differentiating the incremental equation of motion with respect to nonlinear coefficients; thirdly, the nonlinear transient response sensitivities are determined using the Newmark-β integration in the interested time range. Three validation studies, including a Duffing oscillator, a nonlinear multiple-degrees-of-freedom (MDOF) system, and a cantilever beam with local nonlinearity, are adopted to illustrate the application of the proposed method. The comparisons among the finite difference method (FDM), the Poincaré method (PCM), the Lindstedt–Poincaré method (LPM), and the proposed method are conducted. The key factors, such as the parameter perturbation step size, the secular term, and the time step, are discussed to verify the accuracy and efficiency. Results show that parameter perturbation selection in the FDM sensitivity analysis is related to the nonlinear features depending on the initial condition; the consistency of the transient response sensitivity can be improved based on the accurate nonlinear response when a small time step is adopted in the proposed method.
To accurately obtain the influence of geometric deviation on the vibration characters of the bladed disk. It is necessary to count the deviation characteristics of a large number of real bladed disks and establish the highfidelity structural analysis model. An automatic finite element model updating method of mistuned blade disks and characterization method of blade geometric deviation is proposed in this paper. The geometric mistuning blade finite element model is obtained by moving the finite element structured mesh nodes to the measured point cloud data. The proposed finite element model updating method includes bladed disk cloud processing, blade surface classification, blade node movement. The method can be applied to large deformed blades and damaged blades. The obtained geometric deviation can accurately distinguish the abnormal blade model. The surface measurement data of the blade is obtained by a blue light optical scanner. Compare with the blade modal experiments result, the updated highfidelity finite element calculation result error was less than 8‰.
Inevitable mistuning in cyclic bladed disk structures would cause vibration amplification phenomena that seriously reduce the reliability of the bladed disk. The ability to accurately and quickly predict the dynamic responses is critical to investigating the dynamic behavior of the mistuned system. However, it is still challenging because the mistuned responses are extremely sensitive to the random mistuning parameters. In this work, a novel mistuned system deep neural network model (MS-DNN) is presented to predict the dynamic responses of mistuned bladed disks through the mistuning parameters for both the lumped parameter model and the large-scale finite element (FE) model, which decouples the vibration equations of the mistuned system and uses a neural network to replace the coupling process. MS-DNN is divided into two levels, namely, the blade and the disk. The blade-level neural networks are used for forward and backward propagation of mistuning parameters in the different blades, and the disk-level neural network is used to replace the physical coupling process in the disk of multiple mistuning parameters from individual blades, with data transmission between the neural networks via blade–disk boundary nodes. The expected physical response of the blade tip is predicted through MS-DNN. All neural networks in MS-DNN show high prediction accuracy on both training sets and unknown test sets. For the FE model of the industrial bladed disk, the effect of the number of boundary nodes selected as the data interface between neural networks on the prediction accuracy is also investigated. The results show that, for unknown test data, the predicted response has an [Formula: see text] value of 0.998 versus the actual response with an amplification factor error of less than 0.388%.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.