scholarly journals Simulation of an incomplete algebraic problem of eigenvalues and vectors by the method of frequency-dynamic condensation based on FEM in the form of the classical mixed method

2019 ◽  
Vol 15 (1) ◽  
pp. 62-68
Author(s):  
Alexander V Ignatyev ◽  
Artem V Chumakov ◽  
Vadim V Gilka
Keyword(s):  
Dynamic Analysis ◽  
Mixed Method ◽  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Frequency Equation ◽  
Practical Implementation ◽  
Algebraic Problem ◽  
Static Condensation ◽  
Dynamic Condensation ◽  
Reduction Methods

Relevance . Dynamic analysis of complex structures using numerical methods leads to the solution of the algebraic problem of eigenvalues and the corresponding eigenvectors of high orders. The solution of this problem for high order matrices is performed using reduction methods. One of the most effective methods is the method of sequential frequency-dynamic condensation, which allows partial consideration of the dynamic properties of the structure in the minor degrees of freedom. This allows for more accurate results compared to static condensation. Frequency-dynamic condensation is traditionally used to reduce frequency equations derived from the finite element method in the form of the displacement method or the force method. Methods. The authors have developed an algorithm for the frequency-dynamic condensation method for the frequency equation obtained on the basis of the FEM in the form of the classical mixed method. That allows to obtain not only the spectrum of the lower vibration frequencies, but also the corresponding vibration modes and the stress-strain state of the structure. Results . This article describes the algorithm and its practical implementation in the problem of dynamic analysis of a rectangular plate. The results of the numerical analysis of the problem are presented. An assessment of the accuracy of the method and recommendations for its use are given.

Selection of Degrees of Freedom for Dynamic Analysis

1987 ◽  
Vol 109 (1) ◽  
pp. 65-69 ◽  
Author(s):  
K. W. Matta
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
General Purpose ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Large Complex ◽  
Static Condensation ◽  
Basis Vectors ◽  
Selection Of

A technique for the selection of dynamic degrees of freedom (DDOF) of large, complex structures for dynamic analysis is described and the formulation of Ritz basis vectors for static condensation and component mode synthesis is presented. Generally, the selection of DDOF is left to the judgment of engineers. For large, complex structures, however, a danger of poor or improper selection of DDOF exists. An improper selection may result in singularity of the eigenvalue problem, or in missing some of the lower frequencies. This technique can be used to select the DDOF to reduce the size of large eigenproblems and to select the DDOF to eliminate the singularities of the assembled eigenproblem of component mode synthesis. The execution of this technique is discussed in this paper. Examples are given for using this technique in conjunction with a general purpose finite element computer program GENSAM[1].

scholarly journals Implementing model reduction to the JuliaFEM platform

2018 ◽  
Vol 51 (1) ◽  
pp. 36-54 ◽  
Author(s):  
Marja Liisa Rapo ◽  
Jukka Aho ◽  
Hannu Koivurova ◽  
Tero Frondelius
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Model Reduction ◽  
Open Source ◽  
Degrees Of Freedom ◽  
Mass Matrices ◽  
Dynamic Condensation ◽  
Dynamic Analyses ◽  
Reduction Methods ◽  
Large Model

JuliaFEM is an open source finite element method solver written in the Julia language. This paper presents an implementation of two common model reduction methods: the Guyan reduction and the Craig-Bampton method. The goal was to implement these algorithms to the JuliaFEM platform and demonstrate that the code works correctly. This paper first describes the JuliaFEM concept briefly after which it presents the theory of model reduction, and finally, it demonstrates the implemented functions in an example model. This paper includes instructions for using the implemented algorithms, and reference the code itself in GitHub. The reduced stiness and mass matrices give the same results in both static and dynamic analyses as the original matrices, which proves that the code works correctly. The code runs smoothly on relatively large model of 12.6 million degrees of freedom. In future, damping could be included in the dynamic condensation now that it has been shown to work.

Calculating Natural Frequencies With Extended Tuplin’s Method

1981 ◽  
Vol 103 (2) ◽  
pp. 379-386
Author(s):  
C. C. Wang
Keyword(s):  
Torsional Vibration ◽  
Degrees Of Freedom ◽  
Numerical Procedure ◽  
Basic Program ◽  
Frequency Equation ◽  
Lumped Mass ◽  
General Belief ◽  
Reduction Methods ◽  
Roots Of Polynomials ◽  
Vibration Problems

In this paper an efficient numerical procedure is described which yields the eigenvalue of a lumped mass torsional vibration directly from the frequency equation of the system. Special characteristics of Tuplin’s frequency equation allow all eigenvalues to be easily located and accurately evaluated from the frequency polynomial. In contrast to the general belief that extracting roots of polynomials is less efficient than matrix reduction methods, this paper demonstrates that the direct solution competes favorably with the modern eigenvalue routines such as QR and tridiagonal methods [15] [16] [17] [21] in torsional vibration problems. A BASIC program FUNG has been written based on the numerical concepts of this paper. The current version is able to solve multiple branch systems of many degrees of freedom subject to the restriction that no branch shall exceed 4 rotors and 4 shafts. The program has been tested for various examples and the output compared with the known results. Within the above range of applicability, this method beats the modern tridiagonal eigenvalue subroutines [16] [21] by a comfortable margin which ranges from 15 times to 120 times faster. The comparisons were made on the basis of solving the same problems on the same computer. FUNG assumes a tight tolerance of convergence for iteration (correct to approximately 14 significant digits).

scholarly journals Design, Fabrication, and Testing of a Novel 3D 3-Fingered Electrothermal Microgripper with Multiple Degrees of Freedom

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 444
Author(s):  
Guoning Si ◽  
Liangying Sun ◽  
Zhuo Zhang ◽  
Xuping Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Polyimide Film ◽  
Zebrafish Embryos ◽  
Multiple Degrees Of Freedom ◽  
Electrothermal Actuator ◽  
3D Space ◽  
Pick And Place

This paper presents the design, fabrication, and testing of a novel three-dimensional (3D) three-fingered electrothermal microgripper with multiple degrees of freedom (multi DOFs). Each finger of the microgripper is composed of a V-shaped electrothermal actuator providing one DOF, and a 3D U-shaped electrothermal actuator offering two DOFs in the plane perpendicular to the movement of the V-shaped actuator. As a result, each finger possesses 3D mobilities with three DOFs. Each beam of the actuators is heated externally with the polyimide film. The durability of the polyimide film is tested under different voltages. The static and dynamic properties of the finger are also tested. Experiments show that not only can the microgripper pick and place microobjects, such as micro balls and even highly deformable zebrafish embryos, but can also rotate them in 3D space.

scholarly journals Designing of Drive Systems in the Aspect of the Desired Spectrum of Operation

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2562
Author(s):  
Tomasz Dzitkowski ◽  
Andrzej Dymarek ◽  
Jerzy Margielewicz ◽  
Damian Gąska ◽  
Lukasz Orzech ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Dynamic Parameters ◽  
Synthesis Algorithm ◽  
Moments Of Inertia ◽  
Driving System ◽  
Six Degrees Of Freedom ◽  
Resonance Frequencies ◽  
Drive Systems ◽  
Power Component

A method for selecting dynamic parameters and structures of drive systems using the synthesis algorithm is presented. The dynamic parameters of the system with six degrees of freedom, consisting of a power component (motor) and a two-speed gearbox, were determined, based on a formalized methodology. The required gearbox is to work in specific resonance zones, i.e., meet the required dynamic properties such as the required resonance frequencies. In the result of the tests, a series of parameters of the drive system, defining the required dynamic properties such as the resonance and anti-resonance frequencies were recorded. Mass moments of inertia of the wheels and elastic components, contained in the required structure of the driving system, were determined for the selected parameters obtained during the synthesis.

Accelerometer correction for the dynamic analysis of damped multi-degree of freedom systems

1969 ◽  
Vol 59 (4) ◽  
pp. 1591-1598
Author(s):  
G. A. McLennan
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Exact Method ◽  
Three Degrees Of Freedom

Abstract An exact method is developed to eliminate the accelerometer error in dynamic response calculations for damped multi-degree of freedom systems. It is shown that the exact responses of a system can be obtained from the approximate responses which are conventionally calculated from an accelerogram. Response calculations were performed for two typical systems with three degrees of freedom for an assumed pseudo-earthquake. The results showed that the approximate responses may contain large errors, and that the correction developed effectively eliminates these errors.

Interface Reduction in Craig-Bampton Component Mode Synthesis by Orthogonal Polynomial Series

2017 ◽  
Author(s):  
Luigi Carassale ◽  
Mirko Maurici
Keyword(s):  
Degrees Of Freedom ◽  
Axial Compressor ◽  
Component Mode Synthesis ◽  
Reduction Techniques ◽  
Interface Reduction ◽  
Reduction Methods ◽  
Interface Displacement ◽  
Polynomial Series ◽  
Efficient Representation

The component mode synthesis based on the Craig-Bampton method has two strong limitations that appear when the number of the interface degrees of freedom is large. First, the reduced-order model obtained is overweighed by many unnecessary degrees of freedom. Second, the reduction step may become extremely time consuming. Several interface reduction techniques addressed successfully the former problem, while the latter remains open. In this paper we tackle this latter problem through a simple interface-reduction technique based on an a-priory choice of the interface modes. An efficient representation of the interface displacement field is achieved adopting a set of orthogonal basis functions determined by the interface geometry. The proposed method is compared with other existing interface reduction methods on a case study regarding a rotor blade of an axial compressor.

scholarly journals An Efficient Contact Model for the Simulation of Cargo Airdrop Extraction Phase

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Leiming Ning ◽  
Jichang Chen ◽  
Mingbo Tong
Keyword(s):  
Degrees Of Freedom ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Dynamics ◽  
Moving Frame ◽  
Contact Friction ◽  
Practical Implementation ◽  
Contact Formulation ◽  
Efficient Code ◽  
Extraction Phase

A high-fidelity cargo airdrop simulation requires the accurate modeling of the contact dynamics between an aircraft and its cargo. This paper presents a general and efficient contact-friction model for the simulation of aircraft-cargo coupling dynamics during an airdrop extraction phase. The proposed approach has the same essence as the finite element node-to-segment contact formulation, which leads to a flexible, straightforward, and efficient code implementation. The formulation is developed under an arbitrary moving frame with both aircraft and cargo treated as general six degrees-of-freedom rigid bodies, thus eliminating the restrictions of lateral symmetric assumptions in most existing methods. Moreover, the aircraft-cargo coupling algorithm is discussed in detail, and some practical implementation details are presented. The accuracy and capability of the present method are demonstrated through four numerical examples with increasing complexity and fidelity.

scholarly journals Novel analysis methods of dynamic properties for vehicle pantographs

2018 ◽  
Vol 180 ◽  
pp. 01005 ◽  
Author(s):  
Andrzej Wilk
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Simulation ◽  
High Speed ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Computer Software ◽  
Fem Analysis ◽  
Electrical Energy ◽  
Modern Approach ◽  
Static And Dynamic Analysis

Transmission of electrical energy from a catenary system to traction units must be safe and reliable especially for high speed trains. Modern pantographs have to meet these requirements. Pantographs are subjected to several forces acting on their structural elements. These forces come from pantograph drive, inertia forces, aerodynamic effects, vibration of traction units etc. Modern approach to static and dynamic analysis should take into account: mass distribution of particular parts, physical properties of used materials, kinematic joints character at mechanical nodes, nonlinear parameters of kinematic joints, defining different parametric waveforms of forces and torques, and numerical dynamic simulation coupled with FEM calculations. In this work methods for the formulation of the governing equations of motion are presented. Some of these methods are more suitable for automated computer implementation. The novel computer methods recommended for static and dynamic analysis of pantographs are presented. Possibilities of dynamic analysis using CAD and CAE computer software are described. Original results are also presented. Conclusions related to dynamic properties of pantographs are included. Chapter 2 presents the methods used for formulation of the equation of pantograph motion. Chapter 3 is devoted to modelling of forces in multibody systems. In chapter 4 the selected computer tools for dynamic analysis are described. Chapter 5 shows the possibility of FEM analysis coupled with dynamic simulation. In chapter 6 the summary of this work is presented.

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