Degree Of Freedom Method Research Articles

Numerical simulation study of the effect of porous media passive flow control on the propulsion performance of airfoils in kármán vortex streets

This study investigates the influence of porous media on the propulsion performance of airfoils in eddy currents. The passive motion of the airfoil was simulated using overlapping grid technology and the six degrees of freedom method. Research has found that porous media reduces the traction of fixed airfoils and reduces surface turbulence intensity. In the released state, the porous airfoil horizontal movement is slower and the lateral displacement decreases. Combining the two results in a longer forward distance for the NACA0024 thick airfoil, but the effect depends on the release time. This study may inspire the design of underwater robots.

Effect of blade chord length on startup performance of H-type tidal current turbine rotor

This study aims to reveal the effect of the blade chord length on the startup performance of the lift rotor that converts the kinetic energy of tidal currents. The computational fluid dynamics technique was used to simulate unsteady flows around the rotor. The six degrees of freedom method was adopted to model the correlation between the rotational speed of the rotor and influential torques acting on the rotor. A comparative analysis of transient flows, rotational speed, and output torque was implemented at different initial azimuthal angles. The results show that as the rotor starts up at the minimum torque, the time required to attain the maximum rotational speed is longer than that associated with the maximum torque. As the maximum rotational speed is reached, low-pressure elements are produced in the area enclosed by the rotor blades, which is insensitive to the initial setting angle. A large area of low pressure is responsible for low output torque. During the startup process, the rotational speed experiences stages of sharp increase, fluctuating decrease, and moderate fluctuation, as is common at different blade chord lengths. As the chord length increases from 0.16 to 0.24 m, the startup process is extended by 0.63 s, and the average rotational speed in the stabilization stage decreases.

Numerical investigation of a reduced scale Lenz wind turbine model for aerodynamic tunnel applications

Renewable energy sources represent efficient and reliable energy solutions for the modern world, as they are eco-friendly alternatives to fossil fuels or nuclear power plants. The technologies available nowadays allow researchers to perform in-depth computational fluid dynamics analysis for systems that can generate green energy. The wind energy industry developed considerably as classic wind turbine models (horizontal axis wind turbines and vertical axis wind turbines) are constantly optimized and new configurations are studied in order to asses better performances. This paper presents the numerical investigation campaign of a reduced scale Lenz wind turbine model. The Lenz model has three blades that are attached directly on a vertical shaft. For the numerical simulations of the model, the ANSYS Fluent software is employed. For the evaluation of its self-starting behaviour the six degree of freedom method was employed and the configuration was studied for different moments of inertia. Furthermore, the chosen range of inlet velocities allowed the investigation of the influence of high Reynolds numbers on the proposed Lenz model and the vorticity magnitude contours were computed for different azimuth angles. Future work includes the validation of the numerical results with experimental data obtained during a wind tunnel testing campaign.

Damage Detection of Truss Structures by Reduction of Degrees of Freedom Using the Serep Method

Damage detection of bridge structures during their operating lifetime is essential. In this paper, two approaches, All Degrees of Freedom and Reduction of the Degrees of Freedom methods, are used to detect the damages in structures. The first method considers All Degrees of Freedom of the structure and the second method, Reduction of the Degrees of Freedom. Since the sensors are installed only on a few degrees of freedom, the responses are available for some of them. The Degrees of Freedom must be reduced and System Equivalent Reduction Expansion Process method is one of the most efficient ways to solve the problem. This research aimed to identify the damage of structures using the Modal Strain Energy method by reducing the structural degree of freedom. Two standard examples are used and the results compared to different damage cases to examine the efficiency of the mentioned method. The results illustrated the proper performance of the Reduction of the Degrees of Freedom method to identify the damage in truss structures. By increasing the number of modes, Reduction of the Degrees of Freedom method detects considerably more accurate the damaged elements, especially when the noise is considered. Also, based on the outcomes to identify damaged elements, it is possible to consider more modes instead of more sensors.

Modal analysis of an aerostatic spindle system for ultra-precision machine tools at different spin speeds

The dynamic properties of aerostatic spindle systems vary with the spindle speed and have a significant impact on the processing quality of ultra-precision machine tools. In this article, using the ICEM CFD, the structured grid model of a large-span scale gas film is built under the condition in which the ratio of the spindle gas film length to the gas film thickness is 13,100. Integral calculation model of spindle and thrust is established and CEL expressions are compiled based on dynamic meshing technique to acquire trajectory of aerostatic spindle system. The degree of freedom method is used to obtain flow field of spindle system. Considering the spindle system as an elastomer, the influence of rotational speed on natural frequencies is studied under the flow field boundary. The results indicate that the former four-order natural frequencies of the aerostatic spindle system will clearly increase as the rotational speed increases. The increase in the fifth- to seventh-order natural frequencies is small, and the eighth-order natural frequency is almost invariable. The flow field has little influence on the mode shapes of the aerostatic spindle system. The former four-order natural frequencies of spindle system decrease considering rotation effects. Rotational speed and rotation effects mainly impact the tilting motion natural frequencies of spindle and thrust.

Dynamic Response of RC Cantilever Beam by Equivalent Single Degree of Freedom Method on Elastic Analysis – A Review on Transformation Factors and Dynamic Magnification Factors

The response of multi-degree-of-freedom (MDOF) structure can be correlated to the response of an equivalent single-degree-of-freedom (SDOF) system, implying that the response is controlled by a single, unchanged mode shape. This equivalent SDOF method is eminent as an approximate method of dynamic analysis. In this study, equivalent SDOF method analysis is carried out on RC cantilever beam subjected to dynamic blast loading to review the transformation factors (TFs) provided by TM5-1300 code.

Heteroscedasticity in One Way Multivariate Analysis of Variance

This work aimed at developing an alternative procedure to MANOVA test when there is problem of heteroscedasticity of dispersion matrices and compared the procedure with an existing multivariate test for vector of means. The alternative procedure was developed by adopting SatterthwaiteA¢Â€Â™s approach of univariate test for unequal variances. The approach made use of approximate degree of freedom method in one way MANOVA when the dispersion matrices are not equal and unknown but positive definite. The new procedure was compared by using simulated data when it is Multivariate normal, Multivariate Gamma and real life data. The new procedure performed better in terms of power of the test and type I error rate when compared with Johanson procedure.

Integrated procedure for vibration characterization of a magnetic bearing supported rotor delevitation system

This paper considers an integrated procedure to verify and validate (V&V) the rotordynamic analyses of a magnetic bearing supported rotor delevitation system (RDS). Rotor-AMB (active magnetic bearing) systems in general have complex geometries which make accurate modelling thereof a difficult task. For this purpose, simple rotordynamic analyses methods, practical measurements, and finite element method (FEM) models are applied in an integrated framework to characterize the natural vibration frequencies of the system. First, a numerical model (Rayleigh’s energy method) and an experimental modal analysis of the rotor-only are utilized to V&V the bending natural frequency estimates of a rotor FEM simulation model. Thereafter, an analytical model (two degree of freedom method) and a modal analysis of the integrated rotor-AMB system are employed to V&V the rigid body natural frequency estimates of a rotor-AMB FEM simulation model. Adjustments of the FEM models are realized using feedback to fine-tune the geometric, material, and operating properties of the discs, the rotor, and the AMBs. A practical case study of a RDS successfully demonstrates application of the integrated procedure, which ultimately facilitates improved correlation between FEM simulation and experimental results.

Numerical investigation of solid particle penetration into liquid droplet

Computational fluid dynamics (CFD) model is developed to study the penetration behaviour of a solid particle into a liquid droplet with respect to the production of metal‐matrix‐composite (MMC) particles. In contrast to existing theoretical models, the computational fluid dynamics model properly describes the multiphase flow situation (gas‐droplet‐particle) by means of Navier‐Stokes equations coupled with Volume of Fluid method, Six Degrees of Freedom method, and dynamic mesh technique, respectively. The comparison with experimental data indicates that the computational fluid dynamics model can give accurate descriptions of the particle penetration behaviour by taking into account the penetration‐induced droplet deformation and the cavity formation behind the penetrating particle. In the case of a cubic particle penetrating a droplet, two typical outcomes observed in simulations are: 1) the particle partially penetrates into the droplet and then is ejected by the droplet surface; 2) the particle completely penetrates into the droplet. The outcomes are categorized with Weber number (We) and Reynolds number (Re) in a regime map. The variation of the regime boundary is investigated by varying solid‐liquid contact angle, particle/droplet size ratio, particle orientation, and particle‐droplet collision direction. It is found that the critical velocity required for complete penetration increases rapidly with increasing solid fraction in semi‐solid droplets.

Singularity analysis and detection of 6-UCU parallel manipulator

6-UCU kind Gough-Stewart platform (GSP) has been used extensively in practice. The singularity of GSP has been studied by many scholars, but their works mainly focused on finding the methods to divide the cases of singularity or searching the solutions with Jacobian matrices. On the other hand, this paper studies the singularities of 6-UCU parallel manipulator caused by not only the active joints but also passive universal joints. Two types of singularity are derived based on a degree of freedom method by using screw theory. Singularity detection is essential to certify the absence of singularity within a prescribed workspace or a reachable workspace for a practical use of the 6-UCU parallel manipulator. Algorithms are proposed by using evolutionary strategy to detect the singularity in the desired or reachable workspace of the 6-UCU parallel manipulator. Case studies are presented to demonstrate the effectiveness of the proposed singularity detection methods.

Research on Modal Identification of Structures Using Robust Second-Order Blind Identification Technique

The paper discusses the basic principle of blind source separation algorithm applying in structural modal identification. By improving the signal-whitening method, a robust second-order blind identification (RSOBI) algorithm is established on the basis of second-order statistics. The modal responses and mode shapes can be obtained using the RSOBI algorithm from the observed data of structures in time domain. Frequency and damping are estimated from the modal responses by traditional single degree of freedom methods. The simulation results show that the RSOBI algorithm has good performance in modal identification of structures.

Study on Applicability of Equivalent Single Degree of Freedom Methods for Single Column Pier with Uniform Cross Section

Applicability of the simplified method based on equivalent single-degree-of-freedom (ESDOF) for single-column pier with uniform cross-section is investigated in this paper. The modal participating mass ratio of pier’s fundamental mode is taken as an index to evaluate the applicability of the simplified method. Based on the fundamental mode shape functions selected deliberately in the first step, equations to evaluate the modal participating mass ratio of pier fundamental mode is obtained. Using the proposed equations, it is convenient to evaluate applicability of the simplified method with the height of the pier and the ratio of the linear mass along the column to the dumped mass at the top of the pier. Finally, the index is verified in the different nonlinear range of piers.

Blast Simulator Testing of Structures: Methodology and Validation

The blast simulator at the University of California, San Diego is a unique tool for conducting full-scale testing of blast effects on structures without the use of explosive materials. This blast simulator uses high speed hydraulic actuators to launch specially designed modules toward the specimen, thereby imparting impulse in a blast-like manner. This method of testing offers numerous advantages over field tests with actual explosives, including cost, turn-around time, repeatability, and a clear view of the progression of damage in the specimen. The viability of this method is established by comparing results obtained in the blast simulator with results obtained with actual explosives. The process by which the impulse is imparted to the specimen is then described by a detailed model based on the equivalent single degree of freedom method. Impulse calculated by the model is found to be in good agreement with the experimentally recorded values. Calculated impulse is found to be relatively insensitive to assumptions made about the specimen's resistance function (often not well known before a test) implying that the model can be used with confidence in designing an experimental study.

Flutter control effect and mechanism of central-slotting for long-span bridges

The flutter control effect and mechanism of central-slotting, which have gradually been adopted in the design and construction of long-span bridges as an effective flutter controlling measure, were investigated with theoretical analysis and wind tunnel test. Five basic girder cross-sections representing five typical aerodynamic configurations were selected and central-slotted with two different slot widths. Then, a series of sectional model tests and theoretical analyses based on the two-dimensional three-degrees-of-freedom coupling flutter analysis method (2 dimension-3 degrees of freedom method, 2d-3DOF method) were carried out to investigate the aerody namic performance, flutter mechanism and flutter modality of the five basic sections and their corresponding central-slotted sections. The results show that central-slotting can not always improve the aerodynamic stability of bridge structure. The control effect of central-slotting depends on the aerodynamic configuration of the original girder section and the corresponding central-slotting width. If the original section is inappropriate or the slot width is unsuitable, central-slotting will even deteriorate the structural flutter performance. Theoretical investigations indicated that the differences in flutter control effects come from the different formation and evolution of aerodynamic damping, and flutter modality especially the participation level of heaving motion also has a significant influence on the control effect of central-slotting.

ON A TWO DEGREE OF FREEDOM GENERALIZED MINIMUM VARIANCE CONTROL

This paper presents a servo strategy of Generalized Minimum Variance Control (GMVC) with a two degree of freedom. If GMVC fasts the transient response by tuning the control signal weight of the cost function, a large overshoot remains. This paper introduces the two degree of freedom GMVC. The two degree of freedom function curbs the overshoot, while the satisfactory transient characteristic holds. This paper presents two type methods for two degree of freedom: One is setting a reference signal filter in the feedforward part of the closed loop systems, the other is setting a rational function into the cost function. This paper recommends two degree of freedom method with the rational function for the simplification.

Finite element modelling of fatigue crack growth of surface cracked plates: Part III: Stress intensity factor and fatigue crack growth life

Stress intensity factors (SIFs) and fatigue crack growth lives, obtained by a numerical simulation technique which is based on a multiple degree of freedom model, are presented. The results include those for both semi-elliptical static cracks and propagating cracks that are not necessarily semi-elliptical. Comparisons are made between the present results and the predictions from a two degree of freedom model based on the Newman and Raju closed-form SIF equation. The results show that the widely used Newman and Raju equation might be of relatively worse accuracy for cracks whose depth is larger than 90% of the plate thickness; that the present SIF predictions during crack growth are generally in good agreement with those obtained by the two degree of freedom method; and that most of the cracks approach, but cannot subsequently maintain, an iso- K profile because of the presence of both the front and back surfaces of the plate, or the bending component of the load. The free surface correction is also considered in both the multiple and two degree of freedom methods. The results show that the free boundary correction seems to have little influence on fatigue crack growth curves; and that agreement between the fatigue crack growth curves estimated from the present technique and the Newman and Raju ‘two-point plus semi-ellipse’ method, assuming the relation of C C =0.9 m C A , is excellent for pure tension, while it becomes slightly worse for pure bending.

Asymptotic equivalence of an expansion test and an approximate degrees of freedom test

Suppose that Y is an n x 1 observable random vector, normally distributed, with mean XfB and dispersion D(F1, ..., Fk), where X is an n x q matrix of known constants, ,B is a q x 1 vector of unknown parameters, Fj = ((ojtu)), say, is an unknown p x p symmetric positive-definite matrix for j = 1, ..., k, and D(F1, ..., Fk) is an n x n symmetric positivedefinite matrix which is a known linear function of the vector of -kp(p + 1) parameters ojtu (j = 1, ..., k; t ) u). In addition, suppose that there are observable p x p random matrices Si (j = 1, ..., k), with Y, S1, ..., Sk mutually independent, such that nj Sj Wp(nj, F), where Wp(n, F) denotes the Wishart distribution of size p with n degrees of freedom and associated dispersion F. Suppose that we are interested in testing the hypothesis Ho: H,B = h versus H1: H/I * h where H is an r x q matrix of known constants with rank r such that H/I is estimable and h is an r x 1 vector of known constants in the column space of H. The problem is to test Ho, the probability of type I error to be approximately oc for all values of the unknown parameters. In the literature, two methods of obtaining a test in particular examples and in general have been tractable. One is an expansion method following Welch (1947) for the Behrens-Fisher problem, James (1951) for the one-way classification, James (1956) for the common mean problem and James (1954) for the problem in general. The other is an approximate degrees of freedom method following Welch (1947) for the Behrens-Fisher problem, Welch (1951) for the one-way classification, Meier (1953) for the common mean problem and Johansen (1980) for the problem in general. Welch (1947) showed that the approximate degrees of freedom test and the expansion test in the Behrens-Fisher problem are equivalent to terms of order nj-'. Welch (1951) showed that the approximate degrees of freedom test of Welch (1951) and the expansion test of James (1951) for the one-way classification are equivalent to terms of order nj-l. Johansen (1980) stated that it is difficult to compare his approximate degrees of freedom test with the expansion test of James (1954). It is the purpose of this paper to show that equivalence to terms of order n-' holds between the general solutions of Johansen (1980) and James (1954) by deriving the approximate degrees of freedom test of Johansen using the methods of James and by deriving a simpler version of the expansion test.