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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.

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.

This paper focuses on optimization of the geometrical parameters of peripheral milling tools by taking into account the dynamic effect. A substructure synthesis technique is used to calculate the frequency response function of the tool point, which is adopted to determine the stability lobe diagram. Based on the Taguchi design method, simulations are first conducted for varying combinations of tool overhang length, helix angle, and teeth number. The optimal geometrical parameters of the tool are determined through an orthogonal analysis of the maximum axial depth of cut, which is obtained from the predicted stability lobe diagram. It was found that the sequence of every factor used to determine the optimal tool geometrical parameters is the tool overhang length, teeth number, and helix angle. Finally, a series of experiments were carried out as a parameter study to determine the influence of the tool overhang length, helix angle, and teeth number on the cutting stability of a mill. The same conclusion as that obtained through the simulation was observed.

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.

This paper proposed an elastodynamic modeling method combined with independent displacement coordinates and substructure synthesis technology. Firstly, the connecting rod was discretized, and the elastodynamic control equation for each element was established. The multipoint constraint element theory, linear algebra, and singularity analysis were used to identify the globally independent displacement coordinates of the manipulator. On this basis, the elastodynamic model using the substructure synthesis for the 3-PRS parallel manipulator (PM) was developed, with its natural frequencies distribution in the regular workspace discussed. The comparison with the finite-element results showed that the maximum error of the first three-order natural frequencies was within 1.03%, which verified the correctness of the analytical model. The proposed elastodynamic model included all the kinematic constraints of the manipulator without increasing the Lagrangian multiplier. The method is computationally efficient and assesses the dynamic behaviors of the mechanism at the predesign phase.

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.

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.

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.

Journal bearing has been widely used in the wide range of rotating machineries to support large loads and to add significant damping to the system. Conventionally, its fluid film force is represented by the linear model of spring and damper around its equilibrium position in the vibration analysis of the rotor system. However, the fluid film force of the journal bearing is essentially nonlinear, and it is necessary to consider its nonlinearity to expect the characteristics of the limit cycle at around the instability point. This paper investigated the order reduction and bifurcation analysis of a flexible rotor system supported by a full circular journal bearing. The fluid film force is derived under the conditions of both infinitesimal length approximation and half-Zommerfeld boundary condition, and its polynomial function approximation expression is used. Order reduction in the FEM rotor model retaining the nonlinearity of the journal bearing was performed by utilizing the substructure synthesis method. Then, its bifurcation phenomena at around the instability point are investigated by applying the center manifold theory and using the normal form theory. The influences of various parameters, such as kinematic viscosity, bearing length, and the disk position, on the bifurcation phenomena at around the instability point were investigated and explained. Furthermore, the validity of the derived analytical observation was confirmed by numerical simulation and experiment. By invoking these analytical techniques and obtained results, the bifurcation characteristics can be expected theoretically at the design stage of the journal bearing and rotor system.

This paper reviews the research theory of domestic and foreign hybrid modeling dynamic substructure and frequency response, and then introduces the basic principle of Jetmundsen, Ren substructure synthesis method, mechanical impedance admittance method, mechanical admittance method of interchange-ability and FBS substructure method. In the end, the scope and limitations of the method are compared and analyzed, and a new direction of hybrid modeling of dynamic substructure theory is put forward.