Reduction of Hybrid FE-SEA Model for the Mid-Frequency Vibration of Vibro-Acoustic Systems Using Dynamic Condensation Approach

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Ruxin Gao ◽  
Yahui Zhang ◽  
David Kennedy
Keyword(s):  
Present Method ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Fe Model ◽  
Dynamic Matrix ◽  
Acoustic Cavity ◽  
Hybrid Finite Element ◽  
Flexibility Matrix ◽  
Point Of Interest ◽  
Dynamic Condensation

In this paper, an improved hybrid finite element (FE)-statistical energy analysis (SEA) method is proposed for the mid-frequency vibration of vibro-acoustic systems. Within the framework of the hybrid FE-SEA method, the present method reduces the size of the total dynamic matrix of a vibro-acoustic system by employing dynamic condensation to reduce the order of the dynamic matrix of the acoustic cavity. A fast algorithm is introduced to obtain the dynamic flexibility matrix of the slave degrees-of-freedom (DOFs) of the acoustic cavity FE model, thereby avoiding the direct inverse computation of a large dynamic stiffness matrix at each frequency point of interest. The first numerical example illustrates the validity and efficiency of the present method, while the convergence and accuracy analysis of the proposed method is investigated numerically by the second example.

scholarly journals Study on Multi-Degree of Freedom Dynamic Vibration Absorber of the Carbody of High-Speed Trains

2021 ◽  
Author(s):  
Yu SUN ◽  
Jinsong Zhou ◽  
Dao Gong ◽  
Yuanjin Ji
Keyword(s):  
Vibration Control ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Degree Of Freedom ◽  
Vibration Absorber ◽  
High Speed Train ◽  
Dynamic Vibration Absorber ◽  
Multiple Degrees Of Freedom ◽  
Dynamic Vibration

Abstract To absorb the vibration of the carbody of the high-speed train in multiple degrees of freedom, a multi-degree of freedom dynamic vibration absorber (MDOF DVA) is proposed. Installed under the carbody, the natural vibration frequency of the MDOF DVA from each DOF can be designed as a DVA for each single degree of freedom of the carbody. Hence, a 12-DOF model including the main vibration system and a MDOF DVA is established, and the principle of Multi-DOF dynamic vibration absorption is analyzed by combining the design method of single DVA and genetic algorithm. Based on a high-speed train dynamics model including an under-carbody MDOF DVA, the vibration control effect on each DOF of the MDOF DVA is analyzed by the virtual excitation method. Moreover, a high static and low dynamic stiffness (HSLDS) mount is proposed based on a cam–roller–spring mechanism for the installation of the MDOF DVA due to the requirement of the low vertical dynamic stiffness. From the dynamic simulation of a non-linear model in time-domain, the vibration control performance of the MDOF DVA installed with nonlinear HSLDS mount on the carbody is analyzed. The results show that the MDOF DVA can absorb the vibration of the carbody in multiple degrees of freedom effectively, and improve the running ride quality of the vehicle.

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.

“Snapping” Torsional Response of an Anisotropic Radially Loaded Rotor

1997 ◽  
Vol 119 (2) ◽  
pp. 397-403 ◽  
Author(s):  
D. E. Bently ◽  
P. Goldman ◽  
A. Muszynska
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Dynamic Stiffness ◽  
Radial Force ◽  
Lateral Stiffness ◽  
Frequency Range ◽  
Torsional Response ◽  
Specific Shape ◽  
Lateral Resonance ◽  
Laterally Loaded

A rotor system with two orthogonal lateral and two angular (torsional) degrees of freedom is considered. The rotor has asymmetry of the lateral stiffness and is laterally loaded with a constant radial force and a rotating unbalance. Constant driving and load torques are applied to the rotor. The important part of the research includes an analysis of “snapping” action, when, during rotation, the rotor experiences a peak of torsional acceleration. This occurs when the “strong stiffness” axis of the anisotropic rotor passes under the axis of the sideload. The numerical simulation of the analytical model exhibits a snapping (accelerated) torsional response of the rotor at twice synchronous frequency (2×), and it is especially pronounced at 1× and 2× torsional resonances. The snapping response can initiate a rotor crack in the area of stress concentration, can stimulate existing crack propagation, and can be a cause of the coupling failure. The analytical results are obtained by the Averaging Method application. They confirm the numerical results and show the possibility of combination resonance occurrences. The synchronous dynamic stiffness for the frequency range around 1× lateral resonance is analytically obtained. The specific shape of the quadrature dynamic stiffness component can serve as a shaft crack indicator and can be used for early detection of a lateral crack on the rotor.

Research on the dynamic characteristic of semi-active hydraulic damping strut

2019 ◽  
Vol 234 (6) ◽  
pp. 1779-1791 ◽  
Author(s):  
Daoyong Wang ◽  
Wencan Zhang ◽  
Mu Chai ◽  
Xiaguang Zeng
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Maxwell Model ◽  
Friction Model ◽  
Damping Capacity ◽  
Frequency Range ◽  
Stiffness Model ◽  
Rubber Bushing

To reduce the vibration and shock of powertrain in the process of engine key on/off and vehicle in situ shift, a novel semi-active hydraulic damping strut is developed. The purpose of this paper is to study and discuss the dynamic stiffness model of the semi-active hydraulic damping strut. In this study, the dynamic characteristics of semi-active hydraulic damping strut were analyzed based on MTS 831 test rig first. Then, the dynamic stiffness model of semi-active hydraulic damping strut was established based on 2 degrees of freedom vibration system. In this research, a linear, fractional derivative and friction model was used to represent the nonlinear rubber bushing characteristic; the Maxwell model was used to describe the semi-active hydraulic damping strut body model; and the parameters of rubber bushing and semi-active hydraulic damping strut body were identified. The dynamic stiffness values were calculated with solenoid valve energized and not energized at amplitudes of 1 mm and 4 mm, which were consistent with experimental results in low-frequency range. Furthermore, the simplified dynamic stiffness model of the semi-active hydraulic damping strut was discussed, which showed that bushing can be ignored in low-frequency range. Then, the influence of equivalent spring stiffness, damping constant, and rubber bushing stiffness on the stiffness and damping capacity of the semi-active hydraulic damping strut were analyzed. Finally, the prototype of the semi-active hydraulic damping strut was developed and designed based on the vehicle in situ shift and engine key on/off situations, and experiments of the vehicle with and without semi-active hydraulic damping strut were carried out to verify its function.

scholarly journals Study of a Nonlinear Membrane Absorber Applied to 3D Acoustic Cavity for Low Frequency Broadband Noise Control

Materials ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1138 ◽  
Author(s):  
Jianwang Shao ◽  
Tao Zeng ◽  
Xian Wu
Keyword(s):  
Degrees Of Freedom ◽  
Noise Control ◽  
Normal Modes ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Nonlinear Normal Modes ◽  
Broadband Noise ◽  
Frequency Noise ◽  
Acoustic Cavity ◽  
Nonlinear Membrane

As a new approach to passive noise control in low frequency domain, the targeted energy transfer (TET) technique has been applied to the 3D fields of acoustics. The nonlinear membrane absorber based on the TET can reduce the low frequency noise inside the 3D acoustic cavity. The TET phenomenon inside the 3D acoustic cavity has firstly investigated by a two degrees-of-freedom (DOF) system, which is comprised by an acoustic mode and a nonlinear membrane without the pre-stress. In order to control the low frequency broadband noise inside 3D acoustic cavity and consider the influence of the pre-stress for the TET, a general model of the system with several acoustic modes of 3D acoustic cavity and one nonlinear membrane is built and studied in this paper. By using the harmonic balance method and the numerical method, the nonlinear normal modes and the forced responses are analyzed. Meanwhile, the influence of the pre-stress of the nonlinear membrane for the TET is investigated. The desired working zones of the nonlinear membrane absorber for the broadband noise are investigated. It can be helpful to design the nonlinear membrane according the dimension of 3D acoustic cavity to control the low frequency broadband noise.

Dynamic Characteristics of Spiral-Grooved Opposed-Hemisphere Gas Bearings

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Guangwei Yang ◽  
Jianjun Du ◽  
Weiping Ge ◽  
Tun Liu ◽  
Xiaowei Yang
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Translational Motion ◽  
Coupling Coefficients ◽  
Dynamic Coefficients ◽  
Large Eccentricity ◽  
The Stability ◽  
Stiffness And Damping ◽  
Gas Bearing

The traditional eight-coefficient bearing model only considers the translational motion of the bearings and neglects the tilting motion and coupling effects between them. In this paper, the dynamic characteristics of the spiral-grooved opposed-hemisphere gas bearing considering five degrees-of-freedom are studied, and 50 dynamic coefficients including the translational, tilting, and coupling components are completely calculated. The Reynolds equations and their perturbed equations are solved by the finite element method to obtain the dynamic stiffness and damping coefficients. The effects of the tilting motion on the dynamic coefficients and response are analyzed, respectively. The results show that the coupling coefficients between the translational and tilting motions, which have been neglected in most previous studies, are significant at large eccentricity ratio. But these coupling coefficients have little effect on the dynamic response. On the other hand, the influences of the tilting motion on the synchronous response and natural frequency are remarkable and will decrease the stability of the rotor bearing system.

Dynamic matrix control with input saturation constrained

2020 ◽  
Author(s):  
Rosana C. B. Rego ◽  
F. Josiran da Silva ◽  
Marcus V. S. Costa
Keyword(s):  
Degrees Of Freedom ◽  
System Modeling ◽  
Input Saturation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Dynamic Matrix Control ◽  
Rotating Beam ◽  
Dynamic Matrix ◽  
Beam System ◽  
Matrix Control

It is proposed, in this paper a dynamic matrix control (DMC) with an anti-windup (AW) based on linear matrix inequalities (LMI). The DMC-AW control is applied in the ballbeam system, in which the main purpose is to control the ball position on a rotating beam. System modeling was performed, which presented two degrees of freedom. For the mechanical system implementation a microcontroller, an ultrasonic sensor, and a servo motor were used. Theproposed control was implemented both numerically with the software MATLAB and with the microcontroller  ATmega328Pu. The simulation results validated the eciency of the proposed DMC-AW and showed that the approach improves the response of the system under input saturation.

scholarly journals Exact and Direct Modeling Technique for Rotor-Bearing Systems with Arbitrary Selected Degrees-of-Freedom

1994 ◽  
Vol 1 (6) ◽  
pp. 497-506 ◽  
Author(s):  
Shilin Chen ◽  
Michel Géradin
Keyword(s):  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Modeling Technique ◽  
Dynamic Stiffness Matrix ◽  
Global Dynamic ◽  
Combination Methods ◽  
Stiffness Matrices ◽  
Direct Modeling ◽  
Rotor Bearing

An exact and direct modeling technique is proposed for modeling of rotor-bearing systems with arbitrary selected degrees-of-freedom. This technique is based on the combination of the transfer and dynamic stiffness matrices. The technique differs from the usual combination methods in that the global dynamic stiffness matrix for the system or the subsystem is obtained directly by rearranging the corresponding global transfer matrix. Therefore, the dimension of the global dynamic stiffness matrix is independent of the number of the elements or the substructures. In order to show the simplicity and efficiency of the method, two numerical examples are given.

Output-Only Modal Analysis of an Internal Unreachable Module Embedded in a Space Electronic Equipment

2012 ◽  
Author(s):  
Lassaad Ben Fekih ◽  
Georges Kouroussis ◽  
David Wattiaux ◽  
Olivier Verlinden ◽  
Christophe De Fruytier
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Degrees Of Freedom ◽  
Transverse Direction ◽  
Mode Shapes ◽  
Fe Model ◽  
Fe Method ◽  
Numeric Model ◽  
Stiffness Matrices ◽  
Output Only

An approach is proposed to identify the modal properties of a subsystem made up of an arbitrary chosen inner module of embedded space equipment. An experimental modal analysis was carried out along the equipment transverse direction with references taken onto its outer housing. In parallel, a numerical model using the finite element (FE) method was developed to correlate with the measured results. A static Guyan reduction has led to a set of master degrees of freedom in which the experimental mode shapes were expanded. An updating technique consisting in minimizing the dynamic residual induced by the FE model and the measurements has been investigated. A last verification has consisted in solving the numeric model composed of the new mass and stiffness matrices obtained by means of a minimization of the error in the constitutive equation method.

INTASK—a program for postelastic dynamic analysis of three-dimensional structures

1987 ◽  
Vol 14 (1) ◽  
pp. 127-130
Author(s):  
Shing-Sham Lai ◽  
George T. Will
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Three Dimensional ◽  
Structural Response ◽  
Time Deformation ◽  
Inelastic Analysis ◽  
Orthogonal Components ◽  
History Of ◽  
Pertinent Information ◽  
Structural Configurations

An inelastic analysis program for three-dimensional structures subjected to static/gravity loads and (or) dynamic loads in the form of three translational and orthogonal components of base motions is described. Using incremental integration technique, the program computes structural response as a function of time. Deformation history of elements within the structure can be traced and pertinent information obtained via user element subroutines. Each node can possess up to six displacement degrees of freedom and can accommodate user elements with any specified nodes and degrees of freedom per node. The program is very flexible for modelling different structural configurations, and components like beam column elements, shear wall elements, slab elements, semirigid connection elements, and inelastic spring elements can be easily added to the base program. Key words: inelastic analysis, three-dimensional structures, earthquake, computer program, dynamic, stiffness matrix, base accelerations, unbalanced forces, element subroutines.

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