Iterative Coordinate Reduction Algorithm of Flexible Multibody Dynamics Using a Posteriori Eigenvalue Error Estimation

Coordinate reduction has been widely used for efficient simulation of flexible multibody dynamics. To achieve the reduction of flexible bodies with reasonable accuracy, the appropriate number of dominant modes used for the reduction process must be selected. To handle this issue, an iterative coordinate reduction strategy is introduced. In the iteration step, more dominant modes of flexible bodies are selected than the ones in the previous step. Among the various methods, the conventional frequency cut-off rule is here considered. As a stop criterion, a novel a posteriori error estimator that can evaluate the relative eigenvalue error between full and reduced flexible bodies is proposed. Through the estimated relative eigenvalue error obtained, the number of dominant modes is automatically selected to satisfy the error tolerance up to the desired mode range. The applicability to the automation process is verified through numerical examples. It is also evaluated that efficient and accurate flexible multibody dynamics simulation is available with the reduced flexible body, generated by the proposed algorithm.

Floating Frame of Reference formulation for modeling flexible multi-body systems in premise operational conditions

The Floating Frame of Reference (FFR) formulation is a well-established and reliable method for modeling flexible multi-body systems. The FFR formulation has been adopted for dynamic systems that are characterized by large rotations with relatively small deformations. Many scientific papers have pointed out these characteristics with the scrutiny of the simulation results and comparisons with other modeling techniques. However, the FFR is still enclosed in the theoretical aspects and simulation work and faces difficulties when being applied to practical systems. The crucial point in these difficulties centers on coordinate reduction and the associated mapping between nodal and modal coordinates. The process of selecting the necessary modes may be theoretically simple, but the situation is different when applied in a real operational environment. The strategy developed in this work combines the Operational Modal Analysis, specifically the Frequency Domain Decomposition (FDD) approach, and the FFR formulation to build a suitable model of practical multi-body systems. The output model has been validated experimentally. The results show that the proposed FFR-FDD method can be efficiently used to construct multi-body models for those systems that work in premise operational conditions.

The Weakest Point Evaluation Method for the Control Range of the Sound Velocity Profile Station

Sound velocity measurement is an important part of multi-beam sounding, and its accuracy directly affects the coordinate reduction of sounding points. Because of the variability of seawater sound velocity in time and space, the layout density of acoustic section stations directly affects the accuracy of multi-beam sounding. Over-dense layout wastes resources and causes inefficiency; over-sparse layout is not accurate enough to control the entire survey area. Based on the constant gradient acoustic ray tracing algorithm, this paper constructs the accuracy evaluation model of the weakest water depth point of acoustic profile station control, and analyses whether the existing multi-beam acoustic profile station layout scheme can satisfy the accuracy requirements of multi-beam sounding through an example calculation, which provides a theoretical basis for adjusting the layout scheme of acoustic profile station for field surveyors.

Ergative–Absolutive Patterns in Tongan: An Overview

Tongan (Polynesian) shows ergative-absolutive (ERG-ABS) patterns in morphology as well as syntax, but the ERG-ABS pattern is not consistent throughout the language. Noun morphology shows a split between clitic pronouns and other types of nouns. In syntax, three phenomena show an ERG-ABS contrast: (a) relativization using the gap strategy is limited to ABS and ERG-relatives require resumption; (b) coordinate reduction applies only if the gap and the antecedent are in the same case, be it ABS or ERG; and (c) only ABS, but not ERG, can serve as the antecedent of the null SE anaphor. No single factor can account for all three of these phenomena and at least two of the three patterns are shown to be better viewed as PF-phenomena. The data suggest that syntactic ergativity should be understood as a construction-specific phenomenon rather than a language-specific property.

Dynamic Analysis of a Calibration Mechanism

In order to verify the reliability of a calibration mechanism including a motion component used in the satellite, the dynamic analysis for this mechanism is conducted with modal coordinate reduction method. Firstly, FEM software ABAQUS is employed to calculate the eigenfrequency and mode shapes of this mechanism. Then, the transfer function at some key points can be acquired by coordinate transformation from its original format in modal coordinate. Finally, the power spectral density at the key points are obtained and compared with the results of random vibration experiments to prove the dynamics analytical validity.

Periodic Steady State Response of Complex Vehicle Models Using Multi-Level Substructuring

A systematic methodology is presented for investigating long term ride dynamics of large order vehicle models in a computationally efficient way. First, the equations of motion for each of the main structural components of the vehicle are set up by applying the finite element method. As a consequence of the geometric complexity of these components, the number of the resulting equations is so high that the classical coordinate reduction methodologies become numerically ineffective to apply. In addition, the composite model possesses strongly nonlinear characteristics. However, the method applied overcomes some of these difficulties by imposing a multi-level substructuring procedure, based on the sparsity pattern of the stiffness matrix. In this way, the number of the equations of motion of the complete system is substantially reduced. Subsequently, this allows the application of appropriate numerical methodologies for predicting response spectra of the nonlinear models to periodic road excitation. Results obtained by direct integration of the equations of motion are also presented. Where possible, the accuracy and validity of the applied methodology is verified by comparison with results obtained for the original models.