scholarly journals Dynamics of Structures with Distributed Gyroscopes: Modal Discretization Versus Spatial Discretization

2019 ◽  
Vol 10 (1) ◽  
pp. 160
Author(s):  
Xiao-Dong Yang ◽  
Bao-Yin Xie ◽  
Wei Zhang ◽  
Quan Hu
Keyword(s):  
Numerical Methods ◽  
Natural Frequencies ◽  
Computational Time ◽  
Discretization Method ◽  
Spatial Discretization ◽  
Gyroscopic Effect ◽  
Discretization Methods ◽  
Irregular Structures ◽  
Complex Modes ◽  
Base Structure

In this study, two discretization numerical methods, modal discretization and spatial discretization methods, were proposed and compared when applied to the gyroscopic structures. If the distributed gyroscopes are attached, the general numerical methods should be modified to derive the natural frequencies and complex modes due to the gyroscopic effect. The modal discretization method can be used for cases where the modal functions of the base structure can be expressed in explicit forms, while the spatial discretization method can be used in irregular structures without modal functions, but cost more computational time. The convergence and efficiency of both modal and spatial discretization techniques are illustrated by an example of a beam with uniformly distributed gyroscopes. The investigation of this paper may provide useful techniques to study structures with distributed inertial components.

A New Global Spatial Discretization Method for Calculating Dynamic Responses of Two-Dimensional Continuous Systems With Application to a Rectangular Kirchhoff Plate

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
K. Wu ◽  
W. D. Zhu
Keyword(s):  
Boundary Conditions ◽  
Continuous System ◽  
Dynamic Responses ◽  
Kirchhoff Plate ◽  
Continuous Systems ◽  
Discretization Method ◽  
Two Dimensional ◽  
Spatial Discretization ◽  
Arbitrary Boundary ◽  
Discretization Methods

A new global spatial discretization method (NGSDM) is developed to accurately calculate natural frequencies and dynamic responses of two-dimensional (2D) continuous systems such as membranes and Kirchhoff plates. The transverse displacement of a 2D continuous system is separated into a 2D internal term and a 2D boundary-induced term; the latter is interpolated from one-dimensional (1D) boundary functions that are further divided into 1D internal terms and 1D boundary-induced terms. The 2D and 1D internal terms are chosen to satisfy prescribed boundary conditions, and the 2D and 1D boundary-induced terms use additional degrees-of-freedom (DOFs) at boundaries to ensure satisfaction of all the boundary conditions. A general formulation of the method that can achieve uniform convergence is established for a 2D continuous system with an arbitrary domain shape and arbitrary boundary conditions, and it is elaborated in detail for a general rectangular Kirchhoff plate. An example of a rectangular Kirchhoff plate that has three simply supported boundaries and one free boundary with an attached Euler–Bernoulli beam is investigated using the developed method and results are compared with those from other global and local spatial discretization methods. Advantages of the new method over local spatial discretization methods are much fewer DOFs and much less computational effort, and those over the assumed modes method (AMM) are better numerical property, a faster calculation speed, and much higher accuracy in calculation of bending moments and transverse shearing forces that are related to high-order spatial derivatives of the displacement of the plate with an edge beam.

scholarly journals Tripod-Supported Offshore Wind Turbines: Modal and Coupled Analysis and a Parametric Study Using X-SEA and FAST

2019 ◽  
Vol 7 (6) ◽  
pp. 181 ◽  
Author(s):  
Pasin Plodpradit ◽  
Van Nguyen Dinh ◽  
Ki-Du Kim
Keyword(s):  
Wind Turbines ◽  
Natural Frequencies ◽  
Offshore Wind ◽  
Computational Time ◽  
Coupled Analysis ◽  
Physical Interaction ◽  
Support Structures ◽  
Coupled Models ◽  
Support Structure ◽  
Offshore Wind Turbines

This paper presents theoretical aspects and an extensive numerical study of the coupled analysis of tripod support structures for offshore wind turbines (OWTs) by using X-SEA and FAST v8 programs. In a number of site conditions such as extreme and longer period waves, fast installation, and lighter foundations, tripod structures are more advantageous than monopile and jacket structures. In the implemented dynamic coupled analysis, the sub-structural module in FAST was replaced by the X-SEA offshore substructure analysis component. The time-histories of the reaction forces and the turbine loads were then calculated. The results obtained from X-SEA and from FAST were in good agreement. The pile-soil-structure interaction (PSSI) was included for reliable evaluation of OWT structural systems. The superelement concept was introduced to reduce the computational time. Modal, coupled and uncoupled analyses of the NREL 5MW OWT-tripod support structure including PSSI were carried out and the discussions on the natural frequencies, mode shapes and resulted displacements are presented. Compared to the uncoupled models, the physical interaction between the tower and the support structure in the coupled models resulted in smaller responses. Compared to the fixed support structures, i.e., when PSSI is not included, the piled-support structure has lower natural frequencies and larger responses attributed to its actual flexibility. The models using pile superelements are computationally efficient and give results that are identical to the common finite element models.

Optimality Criterion Techniques Applied to Mechanical Design

1978 ◽  
Vol 100 (2) ◽  
pp. 319-327 ◽  
Author(s):  
M. R. Khan ◽  
W. A. Thornton ◽  
K. D. Willmert
Keyword(s):  
Natural Frequencies ◽  
Optimality Criterion ◽  
Mechanical Design ◽  
Minimum Weight ◽  
Computational Time ◽  
Minimum Weight Design ◽  
Linear Approach ◽  
Nonlinear Mathematical Programming ◽  
Programming Techniques ◽  
Weight Design

Presented are two optimality criterion techniques for the minimum weight design of mechanical and structural systems subject to limitations on stresses and natural frequencies. The results, based on their application to several examples, are compared with those obtained by other researchers and with standard nonlinear mathematical programming techniques, as well as with a special linear approach. It is shown in all cases that the optimality criterion methods are capable of locating the optimal design and are far superior to other methods in terms of computational time.

Vibration Characteristics of Bladed Disc Assemblies

1973 ◽  
Vol 15 (3) ◽  
pp. 165-186 ◽  
Author(s):  
D. J. Ewins
Keyword(s):  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Complex Modes ◽  
Modes Of Vibration ◽  
Excitation Conditions

A study is made to establish the basic vibration characteristics of bladed disc assemblies. An analysis is presented and used to predict the natural frequencies and mode shapes of uniform bladed discs. It is found that there are many more natural frequencies than those indicated by a study of the blade cantilever modes. The effects of blade detuning are studied and found to give rise to irregular and complex modes of vibration. Consideration of the vibration characteristics under typical operating excitation conditions shows that a detuned system is susceptible to many more resonances than is an equivalent tuned system.

scholarly journals A DISCRETIZATION METHOD BASED ON MAXIMIZING THE AREA UNDER RECEIVER OPERATING CHARACTERISTIC CURVE

2013 ◽  
Vol 27 (01) ◽  
pp. 1350002 ◽  
Author(s):  
MURAT KURTCEPHE ◽  
H. ALTAY GÜVENIR
Keyword(s):  
Roc Curve ◽  
Naive Bayes ◽  
Characteristic Curve ◽  
Naïve Bayes ◽  
Machine Learning Algorithms ◽  
Discretization Method ◽  
Operating Characteristics ◽  
Discretization Methods ◽  
Real World Datasets ◽  
Receiver Operating

Many machine learning algorithms require the features to be categorical. Hence, they require all numeric-valued data to be discretized into intervals. In this paper, we present a new discretization method based on the receiver operating characteristics (ROC) Curve (AUC) measure. Maximum area under ROC curve-based discretization (MAD) is a global, static and supervised discretization method. MAD uses the sorted order of the continuous values of a feature and discretizes the feature in such a way that the AUC based on that feature is to be maximized. The proposed method is compared with alternative discretization methods such as ChiMerge, Entropy-Minimum Description Length Principle (MDLP), Fixed Frequency Discretization (FFD), and Proportional Discretization (PD). FFD and PD have been recently proposed and are designed for Naïve Bayes learning. ChiMerge is a merging discretization method as the MAD method. Evaluations are performed in terms of M-Measure, an AUC-based metric for multi-class classification, and accuracy values obtained from Naïve Bayes and Aggregating One-Dependence Estimators (AODE) algorithms by using real-world datasets. Empirical results show that MAD is a strong candidate to be a good alternative to other discretization methods.

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