Vibration Mode Analysis of Frames by the Method of Reverberation Ray Matrix

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
F. X. Miao ◽  
Guojun Sun ◽  
Y. H. Pao
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Coefficient Matrix ◽  
Mode Analysis ◽  
System Matrix ◽  
Governing Equations ◽  
Unit Impulse ◽  
Impulse Load ◽  
The Difference

The method of reverberation ray matrix (MRRM) has been developed by (Pao et al. 1999, “Dynamic Response and Wave Propagation in Plane Trusses and Frames,” AIAA J., 37(5), pp. 594–603) recently based on the theory of wave propagation for transient analysis of truss or frame structures. In this study, the MRRM is employed to obtain the frequency response function (FRF) of displacement of a frame under the action of a unit impulse load. The natural frequencies of the frame are determined from the FRF, since the curve of FRF has peak when a resonant frequency is approached. The vibration mode is retrieved from the adjoint matrix of the coefficient matrix of the governing equations of MRRM. The MRRM has advantage over numerical methods, such as finite element method (FEM), since in MRRM the frame is treated as an assembly of multiconnected beams, and exact solutions to the beam differential equations are employed to yield the system matrix of the frame. The vibration mode obtained is therefore exact. A planar frame made of 17 aluminum bars is analyzed. The vibration modes, as well as natural frequencies obtained from MRRM, coincide accurately with those obtained from FEM of ANSYS for the first a few modes; however, the difference of the frequencies between the two methods becomes a bit obvious when high order modes are examined.

Modal Analysis of Laminated Composite Beams Based on Elastic Wave Theory

2012 ◽  
Vol 151 ◽  
pp. 275-280 ◽  
Author(s):  
Xue Jing Shen ◽  
Jiao Xia Lan ◽  
Xiao Rong Yang ◽  
Fang Ji
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Laminated Composite ◽  
Wave Theory ◽  
Coefficient Matrix ◽  
Governing Equations ◽  
Laminated Beam ◽  
Unit Impulse ◽  
Impulse Load ◽  
Laminated Composite Beams

The reverberation ray matrix method (MRRM) for analyzing dynamic response of elastic trusses is extended and used to solve the natural frequency and vibration mode of laminated beams. In this study, the MRRM is employed to obtain the frequency response function (FRF) of displacement of a laminated beam under the action of a unit impulse load. The natural frequencies are determined from the peak of the curve of FRF when a resonant frequency is approached. And the mode is retrieved from the ad joint matrix of the coefficient matrix of the governing equations of MRRM. The accuracy of result of MRRM is verified by a simply supported symmetrically laminated beam compared with the analytical solution of classical theory, which is also proved by finite element method (FEM).

Free Vibrations of Beams on Viscoelastic Pasternak Foundations

2015 ◽  
Vol 744-746 ◽  
pp. 1624-1627
Author(s):  
Li Peng ◽  
Ying Wang
Keyword(s):  
Natural Frequencies ◽  
Free Vibrations ◽  
Mode Analysis ◽  
Analysis Method ◽  
Governing Equations ◽  
Complex Mode ◽  
Transverse Vibrations ◽  
Quadrature Methods ◽  
Foundation Parameters ◽  
Good Agreement

This paper investigates free transverse vibrations of finite Euler–Bernoulli beams resting on viscoelastic Pasternak foundations. The differential quadrature methods (DQ) are applied directly to the governing equations of the free vibrations. Under the simple supported boundary condition, the natural frequencies of the transverse vibrations are calculated, and compared with the results of the complex mode analysis method. The numerical results obtained by using the DQ and the complex mode methods are in good agreement for the first seven order natural frequencies, but with the growth of the orders, the small quantitative differences between them increase. The effects of the foundation parameters on the natural frequencies are also studied in numerical examples.

scholarly journals Wave Equations of Porous Media Saturated With Two Immiscible Fluids Based on the Volume Averaging Method

2021 ◽  
Vol 9 ◽  
Author(s):  
Fansheng Xiong ◽  
Jiawei Liu ◽  
Zhenwei Guo ◽  
Jianxin Liu
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Wave Propagation ◽  
Wave Equations ◽  
Coefficient Matrix ◽  
Immiscible Fluids ◽  
Original Model ◽  
Governing Equations ◽  
Improved Model ◽  
Dispersion And Attenuation

Simulating and predicting wave propagation in porous media saturated with two fluids is an important issue in geophysical exploration studies. In this work, wave propagation in porous media with specified structures saturated with two immiscible fluids was studied, and the main objective was to establish a wave equation system with a relatively simple structure. The wave equations derived by Tuncay and Corapcioglu were analyzed first. It was found that the coefficient matrix of the equations tends to be singular due to the inclusion of a small parameter that characterizes the effect of capillary stiffening. Therefore, the previously established model consisting of three governing equations may be unstable under natural conditions. An improved model based on Tuncay and Corapcioglu’s work was proposed to ensure the nonsingularity of the coefficient matrix. By introducing an assumption in which one fluid was completely wrapped by the other, the governing equation of the wrapped fluid was degenerated. In this way, the coefficient matrix of wave equations became nonsingular. The dispersion and attenuation prediction resulting from the new model was compared with that of the original model. Numerical examples show that although the improved model consists of only two governing equations, it can obtain a result similar to that of the original model for the case of a porous medium containing gas and water, which simplifies the complexity of the calculations. However, in a porous medium with oil and water, the predictions of dispersion and attenuation produced by the original model obviously deviate from the normal trend. In contrast, the results of the improved model exhibit the correct trend with a smooth curve. This phenomenon shows the stability of the improved model and it could be used to describe wave propagation dispersions and attenuations of porous media containing two immiscible fluids in practical cases.

The Analysis on Different Circular Saw Structures for Reducing Saw Noise

2010 ◽  
Vol 145 ◽  
pp. 551-556
Author(s):  
Xiao Ling Wang ◽  
Yong Zhang
Keyword(s):  
Noise Level ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Mode Analysis ◽  
Response Analysis ◽  
Vibration Modes ◽  
Harmonic Response ◽  
Circular Saw ◽  
Harmonic Response Analysis ◽  
Circular Saws

In this paper, we carry out dynamic theoretical and numerical simulation on several differently designed structures of circular saw. Our goal is to improve the vibration property and reduce the noise level of circular saws. We obtain natural frequencies and vibration modes of differently designed saw structures by vibration mode analysis and harmonic response analysis. From our analytical results we prove the effectiveness of these differently designed circular saw structures in reducing the vibration and the noise level.

Support Placement for Machine Tools Using Stiffness Model

2015 ◽  
Vol 9 (6) ◽  
pp. 680-688 ◽  
Author(s):  
Kotaro Mori ◽  
◽  
Daisuke Kono ◽  
Iwao Yamaji ◽  
Atsushi Matsubara
Keyword(s):  
Finite Element Analysis ◽  
Machine Tools ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Vibration Modes ◽  
Element Analysis ◽  
Machining Center ◽  
Stiffness Model ◽  
The Difference ◽  
Rocking Vibration

The support stiffness model and the stiffness tuning technique are applied to a practical situation. The support stiffness model is integrated with finite element analysis (FEA) to simulate the rocking vibration mode. The support stiffness of a machining center prototype is calculated based on the support stiffness model. The stiffness tuning technique is used to determine the placement of support structures in the simulation. The calculated support stiffness is integrated into a three dimensional model as springs. Rocking vibration modes are obtained from simulations by using the support stiffness model. To compare the results, a simulation without the support stiffness model is conducted. An experiment is also conducted on the same machining center that is used in the simulation. Without the support stiffness model, the difference between the experimental and simulation natural frequencies was above 19%. In contrast, the difference is under 10% when the support stiffness model is included. The experimental and the simulation results were in good agreement with respect to the rocking vibration modes. These results demonstrate that incorporating the support stiffness model into finite element analysis increases the calculation accuracy of the rocking-vibration-mode natural frequencies. Consequently, the support stiffness model and the stiffness tuning technique are effective for designing the support systems of machine tools.

Modal Experiment Research on Fluid-Solid Coupling Vibration of Hydraulic Long-Straight Pipeline of Shield Machine

2011 ◽  
Vol 105-107 ◽  
pp. 286-293 ◽  
Author(s):  
Jing Hua Xie ◽  
Ke Tian ◽  
Li He ◽  
Tian Ren Yang ◽  
Xiang Heng Zhu
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Vertical Plane ◽  
Low Frequency ◽  
Pipeline System ◽  
Experiment Research ◽  
Coupling Vibration ◽  
The Difference ◽  
Shield Machine

The hydraulic long-straight pipeline system of the shield machine is to be studied in this paper. Modal parameters of the hydraulic long-straight pipeline whose length is 8m under three kinds of spans (single span, double spans and four spans) were measured and analyzed. Considering the inherent vibration characteristics of the shield machine, we limited the natural frequency of the multi-span long straight pipeline studied within the range of 0~ 200Hz.What the experiment shows is as follows: Firstly, the natural frequency of the hydraulic long-straight pipeline is densely distributed mainly in the low frequency; Secondly, the natural frequencies of vibration in the horizontal plane are slightly higher than those of corresponding orders in the vertical plane, although the difference is little; In addition, by increasing the number of supports, pipeline span can be reduced and the natural frequencies of pipeline can be significantly increased, but this will make the vibration mode change irregularly.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

scholarly journals Impact of Geometrical Imperfections on Estimation of Buckling and Limit Loads in a Silo Segment Using the Vibration Correlation Technique

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 567
Author(s):  
Łukasz Żmuda-Trzebiatowski ◽  
Piotr Iwicki
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Mode Shapes ◽  
Correlation Technique ◽  
Limit Loads ◽  
Linear Buckling ◽  
Geometrical Imperfections ◽  
Linear Problems ◽  
Formed Channel ◽  
Corrugated Wall

The paper examines effectiveness of the vibration correlation technique which allows determining the buckling or limit loads by means of measured natural frequencies of structures. A steel silo segment with a corrugated wall, stiffened with cold-formed channel section columns was analysed. The investigations included numerical analyses of: linear buckling, dynamic eigenvalue and geometrically static non-linear problems. Both perfect and imperfect geometries were considered. Initial geometrical imperfections included first and second buckling and vibration mode shapes with three amplitudes. The vibration correlation technique proved to be useful in estimating limit or buckling loads. It was very efficient in the case of small and medium imperfection magnitudes. The significant deviations between the predicted and calculated buckling and limit loads occurred when large imperfections were considered.

Elimination of outlier measurements for damage detection of structures under changing environmental conditions

2021 ◽  
pp. 147592172199847
Author(s):  
William Soo Lon Wah ◽  
Yining Xia
Keyword(s):  
Damage Detection ◽  
Multiple Regression ◽  
Natural Frequencies ◽  
Detection Method ◽  
Detection Methods ◽  
Structure Model ◽  
Bridge Structure ◽  
Beam Structure ◽  
Dependent Variables ◽  
The Difference

Damage detection methods developed in the literature are affected by the presence of outlier measurements. These measurements can prevent small levels of damage to be detected. Therefore, a method to eliminate the effects of outlier measurements is proposed in this article. The method uses the difference in fits to examine how deleting an observation affects the predicted value of a model. This allows the observations that have a large influence on the model created, to be identified. These observations are the outlier measurements and they are eliminated from the database before the application of damage detection methods. Eliminating the outliers before the application of damage detection methods allows the normal procedures to detect damage, to be implemented. A multiple-regression-based damage detection method, which uses the natural frequencies as both the independent and dependent variables, is also developed in this article. A beam structure model and an experimental wooden bridge structure are analysed using the multiple-regression-based damage detection method with and without the application of the method proposed to eliminate the effects of outliers. The results obtained demonstrate that smaller levels of damage can be detected when the effects of outlier measurements are eliminated using the method proposed in this article.

Axial Wave Propagation in Infinitely Long Periodic Curved Panels

2003 ◽  
Vol 125 (1) ◽  
pp. 24-30 ◽  
Author(s):  
C. Pany ◽  
S. Parthan
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Propagation Constant ◽  
Infinite Length ◽  
Approximate Methods ◽  
Bending Vibration ◽  
Element Analysis ◽  
Curved Panel ◽  
Propagation Of Waves ◽  
Curved Panels

Propagation of waves along the axis of the cylindrically curved panels of infinite length, supported at regular intervals is considered in this paper to determine their natural frequencies in bending vibration. Two approximate methods of analysis are presented. In the first, bending deflections in the form of beam functions and sinusoidal modes are used to obtain the propagation constant curves. In the second method high precision triangular finite elements is used combined with a wave approach to determine the natural frequencies. It is shown that by this approach the order of the resulting matrices in the FEM is considerably reduced leading to a significant decrease in computational effect. Curves of propagation constant versus natural frequencies have been obtained for axial wave propagation of a multi supported curved panel of infinite length. From these curves, frequencies of a finite multi supported curved panel of k segments may be obtained by simply reading off the frequencies corresponding to jπ/kj=1,2…k. Bounding frequencies and bounding modes of the multi supported curved panels have been identified. It reveals that the bounding modes are similar to periodic flat panel case. Wherever possible the numerical results have been compared with those obtained independently from finite element analysis and/or results available in the literature.

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