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Large flexible aircraft are often accompanied by large deformations during flight leading to obvious geometric nonlinearities in response. Geometric nonlinear dynamic response simulations based on full-order models often carry unbearable computing burden. Meanwhile, geometric nonlinearities are caused by large flexible wings in most cases and the deformation of fuselages is small. Analyzing the whole aircraft as a nonlinear structure will greatly increase the analysis complexity and cost. The analysis of complicated aircraft structures can be more efficient and simplified if subcomponents can be divided and treated. This paper aims to develop a hybrid interface substructure synthesis method by expanding the nonlinear reduced-order model (ROM) with the implicit condensation and expansion (ICE) approach, to estimate the dynamic transient response for aircraft structures including geometric nonlinearities. A small number of linear modes are used to construct a nonlinear ROM for substructures with large deformation, and linear substructures with small deformation can also be assembled comprehensively. The method proposed is compatible with finite element method (FEM), allowing for realistic engineering model analysis. Numerical examples with large flexible aircraft models are calculated to validate the accuracy and efficiency of this method contrasted with nonlinear FEM.

To improve the simulation efficiency of mistuned blisk, a method called receptance substructure component modal synthesis method (RSCMSM) is proposed to reduce its degrees of freedom (DOFs). The advantage of this method is that only the interface DOFs need to be solved, which observably enhances the computational efficiency. The modal frequencies, maximum modal shape and frequency response function are calculated via RSCMSM. It is seen that the smooth frequency band is governed by blade vibration and the steep frequency band is governed by disk or bladed-disk coupling vibration. In addition, a peak is observed for the tuned blisk but many peaks appear for the mistuned blisk and many small wave crests are observed near the peak. To verify validity of this method, the computational time of RSCMSM is compared with high fidelity finite element method (HFFEM) and classical substructure component modal synthesis method (CSCMSM), which manifests that the computational efficiency increases by 32.19 %–80.82 % than that of HFFEM when the mistuned level is 0 %~5 %. Moreover, computational efficiency of RSCMSM is increased by 0.85 %–7.56 % than that of CSCMSM. The validity of RSCMSM is verified for calculating the complex mechanical structure.

In this thesis, a new identification method for joint stiffness and damping has been developed by using the substructure synthesis method and finite element modeling. The substructure synthesis method is stated firstly, according to the substructures are connected by joints and the equilibrium and compatibility conditions at the joints have to be fulfilled, establishing identification equation through completely frequency response function. Then, finite element model is established, and update this model, make use of the update model to replace the experimental model, using an accurate finite element model to obtain the required data. In order to ensure the stability of the numerical calculation, translate inconsistent equation into the general solution through the principle of least squares, besides the introduction of the concept of weighted, makes the measured data can be fully utilized. Finally, the method is applied to a simulated example and good agreement is found between identified and true parameters.

In this paper, a new method of analysis of a complex nonlinear vibration system is presented. Combining substructure synthesis and perturbation methods the computation cost for large mechanical system is considerably reduced. The system is divided into components. Under the assumption that the mode shape does not change, these are approximately transformed to modal coordinate system with nonlinearity. Using perturbation method, the overall modal equations are derived and solved sequentially. These solutions are synthesized to the overall system. Solution of the overall system is obtained in the modal coordinate system and then, these are translated into the physical coordinate. This method is applied to a vibration analysis of a large mechanical structure system composed of the rotor-bearing and casing. In order to illustrate accuracy and computation time of the proposed method, the results are compared with those obtained by the finite element method.[PUBLICATION ABSTRACT]

In this work, the delta parallel manipulator (PM) was considered as a case study to present a system elastodynamic modeling of spatial PMs contain subclosed loops. The mechanism consisted of major substructures including proximal, short, and distal links. Each link was divided into elements to establish the body-to-body and body-to-ground constraint equations. The global independent generalized displacement coordinates (IGDC) of the mechanism were extracted with the theory of multi-point constraint elements. Besides, the global IGDC and substructure synthesis approach was used to obtain the complete elastodynamic modeling of the mechanism without supplementing constraint equations. The resulting configuration-dependent elastodynamic modeling had fewer degrees of freedom, different from thousands used in finite element model (FEM). The natural frequencies could be predicted at any configuration of the mechanism, and were compared against the values of FEM to assess the correctness of the modeling. The proposed modeling could predict the distribution of natural frequencies of the mechanism in the workspace with computational efficiency. Therefore, it could be used as a numerical twin to simulate the elastodynamic performance of PMs in the pre-design stage.

To acquire precise high-resolution cryo-electron tomography data from transmission electron microscopy, a parallel manipulator (PM) with flexure hinges is often used to support and manipulate the samples. The precision and stability of the PM’s motion are intricately associated with its dynamic characteristics. Thus, it is essential to predict and enhance the PM’s dynamic characteristics during the initial design phase. To achieve this goal, a simplified dynamic characteristic analysis method (SDCAM) for PMs is developed. This method is based on the mass–spring model and accounts for only the mass of the mobile platform and the stiffness of the legs. A typical 6-PSS PM is employed as a case study to evaluate the proposed method. Analysis of the associated stiffness, mass, and frequency matrices allows us to derive the natural frequencies and modal shapes of the PM. The validity of the proposed SDCAM is confirmed through comparisons with the finite element method and the substructure synthesis method. Finally, using the average and population standard deviation of the first six-order natural frequencies of the PM as evaluation criteria, a hybrid optimization algorithm based on the multi-island genetic algorithm and sequential quadratic programming is adopted to optimize the configuration parameters and improve the PM’s dynamic characteristics. The impact of load on dynamic characteristics and optimization is explored based on practical application scenarios of the PM. We find that the SDCAM can be used to estimate the natural frequencies of PMs with flexure hinges, and the hybrid optimization algorithm in conjunction with the SDCAM effectively enhances the dynamic characteristics of PMs, thus providing important guidance for early-stage design.

The folding wing, as a possible concept for designing morphing aircraft, has gained special attention. However, such a wing may encounter complex nonlinear aeroelastic effects with bilinear-hinge stiffnesses during the in-flight morphing process. This paper presents a novel parameterized nonlinear aeroelastic modeling methodology, based on the substructure synthesis of the folding wing with fictitious mass in hinge joints and piecewise-linear theory. The most attractive feature of the present methodology is that the nonlinear aeroelastic dynamics of the wing can be efficiently represented by piecewise, parameterized, linear subsystems using the parameterized fictitious mode method. To demonstrate the accuracy of the present method in representing the nonlinear dynamics of the morphing wing, a folding wing with bilinear stiffness in both fuselage-inboard and inboard-outboard hinges was selected as a numerical example. The numerical results demonstrate that the natural modes of each linear subsystem, as well as the limit-cycle oscillations of the folding wing at different folding angles, can be accurately predicted. In addition, a comparison between the time cost of the present parameterized method and the direct nonparameterized method was made. The comparison showed that the parameterized, nonlinear, aeroelastic modeling methodology provides an efficient way to analyze the nonlinear aeroelastic responses of a morphing wing with bilinear-hinge stiffness.

Structures can exhibit non-linear behavior due to the presence of free-play. To analyze this behavior, different numerical and analytical methods like the substructure synthesis method or the harmonic balance method are used. To determine the effect of non-linarites caused by free-play, descriptive functions must be identified. The restoring force approach is frequently used in systems where mass and stiffness matrices are known, such as finite element models. Another approach involves frequency response functions obtained through vibration tests. This article discusses the second approach, which involves extracting the free-play function using frequency response functions obtained from tests. The tests include a modal test with random excitation to determine the frequency response functions for the linear mode of the modes with low excitation amplitude. Additionally, sinusoidal excitation is used with increasing amplitude for the frequency response functions in the nonlinear state of the modes. The laboratory method used to determine the nonlinear modes involves increasing the amplitude of sinusoidal stimulation in the frequency range of each resonance. This article presents a practical method for analyzing the dynamic behavior of structures related to the folding wing of a flying system. Using simple techniques and vibration test results, it deals with extracting the free-play function of the structure.

This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been suggested to obtain a satisfactory size for the reduced systems. Although previous hybrid-level interface-reduction approaches have addressed major issues associated with conventional interface-reduction methods—in terms of accuracy and efficiency through considering partial substructure synthesis—this method can be applied to limited modeling conditions where interfaces and substructures are independently defined. To overcome this limitation, an interface localizing algorithm is developed to ensure an enhanced performance in the conventional hybrid-level interface-reduction method. The interfaces are discriminated through considering the Boolean operation of substructures, and the interface reduction basis is computed at the localized interface level, which is constructed by a partially coupled system. As a result, a large amount of computational resources are saved, achieving the possibility of efficient design modifications at the semi-substructural level.

This study presents a dynamic modeling and analysis methodology for the 3- P RS parallel mechanism. First, an improved reduced dynamic model of component substructures is proposed using the dynamic condensation technique and the rigid multipoint constraints at the joint/interface level, leading to a minimum set of generalized coordinates for external nodes. Next, the mapping between interface constraint stiffness and global stiffness is illustrated, resulting in an analytical stiffness model of joint substructures. Subsequently, the derived component and joint substructures are synthesized into the entire mechanism based on the Lagrange equation. Finally, a case study illustrates that the lower-order dynamic performances predicted within the proposed approach have the same trend as those obtained from a complete-order finite element model. The root mean square discrepancy of the lower-order natural frequencies between the two models is less than 5.92%, indicating the accuracy and effectiveness of the proposed model. The developed approach can highly and efficiently predict the dynamic performance distributions across the entire workspace and guide the optimal functional design under the virtual machine framework.