Optimal Method for Determination of Rayleigh Damping Co-efficients for Different Materials using Modal Analysis

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
B. Rahul ◽  
J. Dharani ◽  
R. Balaji
Keyword(s):  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Modal Analysis ◽  
Degrees Of Freedom ◽  
Damping Ratio ◽  
Optimal Method ◽  
Multiple Degrees Of Freedom ◽  
Rayleigh Damping ◽  
Damping Matrix

Rayleigh damping co-efficients are the essential parameters to determine the damping matrix of a system in dynamic analysis. For the systems with multiple degrees of freedom, it is difficult to arrive for suitable Rayleigh damping co-efficients. This paper represents a simple and effective method for the determination of Rayleigh co-efficients α and β for the system with multiple degrees of freedom. An unrealistic constant damping ratio for all modes is assumed to get rational value of α and β, which leads the determination of progressively varying damping ratio for all modes. By comparing the damping ratio arrived from assumed α and β with assumed unrealistic damping ratio, the suitable and most precise values are determined. This method is implemented for different materials with different boundary conditions by considering different significant modes and the effect of above parameters on α and β values are also discussed.

scholarly journals Control of the boundary conditions of a dynamic knee simulator

2015 ◽  
Vol 6 (2) ◽  
pp. 7 ◽  
Author(s):  
Jan Tiré ◽  
Jan Victor ◽  
Patrick De Baets ◽  
Matthias Verstraete
Keyword(s):  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Ankle Joint ◽  
Hip Joint ◽  
Degrees Of Freedom ◽  
Muscle Forces ◽  
Inverse Dynamic ◽  
Human Knee ◽  
Inverse Dynamic Analysis ◽  
Knee Simulator

At Ghent University a dynamic knee simulator to analyse the kinematics of a human knee has been developed. The rig is designed to perform tests on a mechanical hinge or on a human knee (with or without a prosthesis). The rig has one degree of freedom in a hip joint and four degrees of freedom in an ankle joint. There is currently one actuator that simulates the quadriceps forces. Two additional actuators are proposed in this paper to simulate the hamstrings forces. The magnitude and phase of the forces varies significantly during the movement (e.g. cycling or squatting). Literature indicates that the maximum muscle forces do not exceed 2000 N. An inverse dynamic analysis, using the musculoskeletal software AnyBody, is proposed to determine the evolution of these forces during the studied movements.

scholarly journals Modal analysis of support structure of cylindrical container

2020 ◽  
Vol 310 ◽  
pp. 00032
Author(s):  
Lubomir Prekop
Keyword(s):  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Modal Analysis ◽  
Support System ◽  
Seismic Analysis ◽  
Road Maintenance ◽  
Cylindrical Container ◽  
Support Structure ◽  
Internal Forces ◽  
Winter Road

The paper deals with dynamic analysis of a container. The analyzed structure consists of a steel support structure and a cylindrical container. The container is used for storage of road salt and other spreading materials during winter road maintenance. Three variants of support system of a structure have been analyzed. These have been introduced into the model as different boundary conditions. The modal analysis was performed, whose results are eigenfrequencies and eigenshapes of the structure. In the final part, the results obtained from the seismic analysis of the structure (displacements and internal forces) have been presented.

Dynamic Analysis of Elastic Structures on Spreadsheet

2012 ◽  
Author(s):  
J.-M. Rambach
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Modal Analysis ◽  
Safety Assessment ◽  
Degrees Of Freedom ◽  
Vertical Plane ◽  
Design Stage ◽  
Margin Assessment ◽  
Sensitivity Studies ◽  
Stick Model

It is recalled the interest of modal analysis of heavy structures on stick model with reduced number of degrees-of-freedom (DOF), at every age of the structure: at the presizing stage, at the design stage, for assessing the results given by large tridimensional Finite Element (FE) models, and at every further seismic review (Seismic Margin Assessment studies, Seismic Probabilistic Safety Assessment studies). This article indicates a practical means for a simple programing of a modal analysis based FE code on spreadsheet able to handle up to 50 DOF. The beams, of Timoshenko’s type, are supposed moving along a vertical plane, with 2 DOF per node: the horizontal translational DOF and the rotational DOF around the horizontal axis perpendicular to the vertical plane. The analysis follows the classical steps of any FE code. The programing of such dynamic modal analysis on a spreadsheet is besides quite easy and provides a very convenient tool i) for the intimate understanding of the dynamic behavior of structures ii) for any accurate modal analysis and iii) for any sensitivity studies.

scholarly journals Computation of Rayleigh damping coefficient of a rectangular submerged floating tunnel (SFT)

2020 ◽  
Vol 2 (5) ◽  
Author(s):  
Md. Hafizur Rahman ◽  
Chhavi Gupta
Keyword(s):  
Dynamic Analysis ◽  
Modal Analysis ◽  
Fundamental Frequency ◽  
Significant Role ◽  
Analytical Study ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Damping Coefficients ◽  
Rayleigh Damping ◽  
Submerged Floating Tunnel

Abstract The dynamic behaviors of the submerged floating tunnel, a buoyant structure of high slenderness, are a matter of concern since it is surrounded by the huge hazardous effects called hydrodynamic, seismic and functional action. Modal analysis and Rayleigh damping coefficients play a significant role in dynamic analysis, but it is not sufficiently simple to predict the reasonable damping coefficients named α and β. The present paper outlines the modal analysis and the calculation of Rayleigh damping coefficients that provide the natural frequencies, mode shapes, mode’s motion as well as coefficients α and β. To compute the Rayleigh damping coefficients, 2–10% damping to the critical damping has been assumed for this analytical study. For the analysis, an FEA-based software ANSYS is utilized successfully. It has been seen that the fundamental frequency and Rayleigh damping coefficients (α = 0.946 and β = 0.00022) of the SFT are reasonably high and it is under noticeable damping.

Modified joint connectivity approach for identification of topological characteristics of planar kinematic chains

2011 ◽  
Vol 225 (11) ◽  
pp. 2700-2717 ◽  
Author(s):  
G S Bedi ◽  
S Sanyal
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Kinematic Chains ◽  
Multiple Degrees Of Freedom ◽  
Preferred Frame ◽  
Topological Characteristics ◽  
Synthesis Stage ◽  
Different Levels ◽  
Selection Of

In a kinematic chain, the links are connected to each other through joints. The connectivity of a joint indicates the number of joints to which it is connected. The connectivity level of a joint indicates the distance by which it is separated from the adjacent joints. The concept of joint connectivity and its application to detect isomorphism among kinematic chains and their inversions has been already reported by authors. The method utilizes the connectivity of joints at different levels to detect isomorphism and inversions among planar kinematic chains. The method is applied to eight-, nine-, and ten-link planar kinematic chains. The results so obtained are in agreement with those available in the literature. In this study, the method is further improved by incorporating the type of joint to make it more effective for the detection of isomorphism and distinct inversions. A joint connectivity table completely representing the kinematic chain is proposed. The application of the method is extended for the determination of additional topological characteristics of chains such as categorization of kinematic chains and selection of preferred frame, input and output links for function and path generation. The concept of ‘Motion Transfer Ability’ is introduced and utilized to develop numerical measures for comparing and categorizing the chains at the synthesis stage of mechanism design for a specific application. The method was successfully tested on planar kinematic chains with single and multiple degrees of freedom and the results for eight- and nine-link kinematic chains are appended.

scholarly journals Computation of Rayleigh Damping Coefficients for the Seismic Analysis of a Hydro-Powerhouse

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Zhiqiang Song ◽  
Chenhui Su
Keyword(s):  
Seismic Response ◽  
Seismic Analysis ◽  
Damping Ratio ◽  
Least Square Method ◽  
Least Square ◽  
Dynamic Responses ◽  
Damping Coefficients ◽  
Rayleigh Damping ◽  
Damping Matrix ◽  
Fundamental Frequencies

The mass and stiffness of the upper and lower structures of a powerhouse are different. As such, the first two vibration modes mostly indicate the dynamic characteristics of the upper structure, and the precise seismic response of a powerhouse is difficult to obtain on the basis of Rayleigh damping coefficients acquired using the fundamental frequencies of this structure. The damping ratio of each mode is relatively accurate when the least square method is used, but the accuracy of the damping ratios that contribute substantially to seismic responses is hardly ensured. The error of dynamic responses may even be amplified. In this study, modes that greatly influence these responses are found on the basis of mode participation mass, and Rayleigh damping coefficients are obtained. Seismic response distortion attributed to large differences in Rayleigh damping coefficients because of improper modal selection is avoided by using the proposed method, which is also simpler and more accurate than the least square method. Numerical experiments show that the damping matrix determined by using the Rayleigh damping coefficients identified by our method is closer to the actual value and the seismic response of the powerhouse is more reasonable than that revealed through the least square method.

Dynamic and Modal Analysis of a Snake like Robot

2020 ◽  
Vol 896 ◽  
pp. 203-210
Author(s):  
Leonard Marius Ciurezu-Gherghe ◽  
Nicolae Dumitru ◽  
Ionuţ Daniel Geonea ◽  
Cristian Copiluși
Keyword(s):  
Dynamic Analysis ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Time Frequency

In this paper a modal and dynamic analysis of a snake like robot is performed. Modal analysis consist in determination of own vibration modes and natural frequencies. The proposed dynamic analysis was performed in order to determine the variation time/frequency laws for the cinematic and dynamics parameters.

scholarly journals Model Updating for Systems with General Proportional Damping Using Complex FRFs

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xinhai Wu ◽  
Huan He ◽  
Yang Liu ◽  
Guoping Chen
Keyword(s):  
Model Updating ◽  
Damping Ratio ◽  
Viscous Damping ◽  
Rayleigh Damping ◽  
Damping Matrix ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Updating Procedure ◽  
Damping Model

In this paper, we propose a model updating method for systems with nonviscous proportional damping. In comparison to the traditional viscous damping model, the introduction of nonviscous damping will not only reduce the vibration of the system but also change the resonance frequencies. Therefore, most of the existing updating methods cannot be directly applied to systems with nonviscous damping. In many works, for simplicity, the Rayleigh damping model has been applied in the model updating procedure. However, the assumption of Rayleigh damping may result in large errors of damping for higher modes. To capture the variation of modal damping ratio with frequency in a more general way, the diagonal elements of the modal damping matrix and relaxation parameter are updated to characterize the damping energy dissipation of the structure by the proposed method. Spatial and modal incompleteness are both discussed for the updating procedure. Numerical simulations and experimental examples are adopted to validate the effectiveness of the proposed method. The results show that the systems with general proportional damping can be predicted more accurately by the proposed updating method.

Study on Equivalent Damping Ratio of Shenzhen Baoan International Airport T3 Terminal

2012 ◽  
Vol 446-449 ◽  
pp. 871-877
Author(s):  
Yu Chen Yang ◽  
Lei Gu ◽  
Zhong Yi Zhu ◽  
Kai Qin ◽  
Lin Zhang
Keyword(s):  
Modal Analysis ◽  
Damping Ratio ◽  
Earthquake Response ◽  
Structural System ◽  
Equivalent Damping ◽  
Damping Matrix ◽  
Modal Damping ◽  
Modal Coupling ◽  
Response Equation ◽  
Energy Theory

Today, the structures constituted by different materials, increase more and more, especially the lower part is concrete, the upper is steel. For this type of structural system, modal damping matrix is non-diagonal matrix, the earthquake response equation is coupled on the modal damping matrix, the modal coupling of the non-proportional damping system leads to the traditional real modal analysis methods not be directly applied. For such structure, the changes of the damping ratio are analyzed in this article. Finally, the equivalent damping ratio of Shenzhen Airport is obtained using the energy theory.

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