scholarly journals A Truncated Low Approach of Intrinsic Linear and Nonlinear Damping in Thin Structures

2006 ◽  
Vol 129 (1) ◽  
pp. 32-38
Author(s):  
Yves Gourinat ◽  
Victorien Belloeil
Keyword(s):  
Experimental Data ◽  
Damping Ratio ◽  
Vibrational Analysis ◽  
Nonlinear Damping ◽  
Thin Structures ◽  
Adaptive Approach ◽  
Equivalent Damping ◽  
Linear And Nonlinear ◽  
Algebraic Representations

An adaptive approach of vibrating thin structures is proposed here. The method consists in applying an equivalent adimensional damping ratio to each potential resonance. This ratio is deduced from experimental data obtained in vacuum facility, in relation with frequencies, for several structural technologies. Consequently, it is possible to calculate the structure in a linear nondissipative context, valid out of resonance bands, and truncated in those bands. Thus, the equivalent damping ratio is directly used to define adimensional resonance truncation bandwith and level. The contribution consists in tested and applied modal methodology and algebraic representations of damping including several dissipations—viscous and internal microfrictions—inducing a nonmonotonous model. The here aim is to provide realistic recommendations for simple vibrational analysis of aerospace thin structures—panels and stiffeners.

Beneficial performance of a quasi-zero stiffness vibration isolator with generalized geometric nonlinear damping

2020 ◽  
pp. 095745652097238
Author(s):  
Chun Cheng ◽  
Ran Ma ◽  
Yan Hu
Keyword(s):  
Damping Ratio ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Equivalent Damping ◽  
Frequency Responses ◽  
Geometric Nonlinear ◽  
Resonant Region ◽  
Force Transmissibility ◽  
Isolation Performance ◽  
Force And Displacement Transmissibility

Generalized geometric nonlinear damping based on the viscous damper with a non-negative velocity exponent is proposed to improve the isolation performance of a quasi-zero stiffness (QZS) vibration isolator in this paper. Firstly, the generalized geometric nonlinear damping characteristic is derived. Then, the amplitude-frequency responses of the QZS vibration isolator under force and base excitations are obtained, respectively, using the averaging method. Parametric analysis of the force and displacement transmissibility is conducted subsequently. At last, two phenomena are explained from the viewpoint of the equivalent damping ratio. The results show that decreasing the velocity exponent of the horizontal damper is beneficial to reduce the force transmissibility in the resonant region. For the case of base excitation, it is beneficial to select a smaller velocity exponent only when the nonlinear damping ratio is relatively large.

A Method for the Optimal Design of Split Ring Dampers for Aviation Gears

2017 ◽  
Author(s):  
Hang Ye ◽  
Yanrong Wang ◽  
Xianghua Jiang
Keyword(s):  
Damping Ratio ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Forced Response ◽  
Design Parameters ◽  
Dissipated Energy ◽  
Vibration Energy ◽  
Equivalent Damping ◽  
Important Approach ◽  
Energy Dissipated

In order to reduce the resonance of aviation bevel gears, designing frictional interfaces for gear systems is an important approach through dissipate vibration energy. One emerging technology uses ring dampers, which are ring-like substructures constrained to move inside a groove at the rim of the gear. Ring dampers are in contact with the rim of the gear due to centrifugal force, and they create nonlinear dissipation by relative motion between the ring and the gear. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. In this paper an efficient methodology to predict the effect of the ring damper based on energy method, predicting the dissipated energy by friction force, converting into equivalent damping and to identify the main design parameters affecting the damper performance is proposed. The approach is based on expressing the vibration energy dissipated by nonlinear forces per vibration cycle as equivalent nonlinear damping ratio. This method avoids computing the forced response of the gear with ring damper in the frequency domain, that can increase the efficiency of the ring damper design. The methodology is applied to an aviation bevel gear. The effect of the principal design parameters of the ring damper is identified.

scholarly journals Estimation of Additional Equivalent Damping Ratio of the Damped Structure Based on Energy Dissipation

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Xiuyan Hu ◽  
Qingjun Chen ◽  
Dagen Weng ◽  
Ruifu Zhang ◽  
Xiaosong Ren
Keyword(s):  
Energy Dissipation ◽  
Damping Ratio ◽  
Theoretical Concept ◽  
Estimation Methods ◽  
External Excitation ◽  
Single Degree Of Freedom ◽  
Equivalent Damping ◽  
Seismic Motion ◽  
Practical Engineering ◽  
Energy Dissipation Capacity

In the design of damped structures, the additional equivalent damping ratio (EDR) is an important factor in the evaluation of the energy dissipation effect. However, previous additional EDR estimation methods are complicated and not easy to be applied in practical engineering. Therefore, in this study, a method based on energy dissipation is developed to simplify the estimation of the additional EDR. First, an energy governing equation is established to calculate the structural energy dissipation. By means of dynamic analysis, the ratio of the energy consumed by dampers to that consumed by structural inherent damping is obtained under external excitation. Because the energy dissipation capacity of the installed dampers is reflected by the additional EDR, the abovementioned ratio can be used to estimate the additional EDR of the damped structure. Energy dissipation varies with time, which indicates that the ratio is related to the duration of ground motion. Hence, the energy dissipation during the most intensive period in the entire seismic motion duration is used to calculate the additional EDR. Accordingly, the procedure of the proposed method is presented. The feasibility of this method is verified by using a single-degree-of-freedom system. Then, a benchmark structure with dampers is adopted to illustrate the usefulness of this method in practical engineering applications. In conclusion, the proposed method is not only explicit in the theoretical concept and convenient in application but also reflects the time-varying characteristic of additional EDR, which possesses the value in practical engineering.

scholarly journals Near-surface frequency-dependent nonlinear damping ratio observation of ground motions using SMART1

2021 ◽  
Vol 147 ◽  
pp. 106798
Author(s):  
Chun-Hsiang Kuo ◽  
Jyun-Yan Huang ◽  
Che-Min Lin ◽  
Chun-Te Chen ◽  
Kuo-Liang Wen
Keyword(s):  
Ground Motions ◽  
Damping Ratio ◽  
Nonlinear Damping ◽  
Frequency Dependent ◽  
Near Surface

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

Comparison of Linear and Nonlinear Damping Effects on a Ring Vibration Isolator

2020 ◽  
pp. 13-22
Author(s):  
Ze-Qi Lu ◽  
Dong-Hao Gu ◽  
Ye-Wei Zhang ◽  
Hu Ding ◽  
Walter Lacarbonara ◽  
...  
Keyword(s):  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Linear And Nonlinear ◽  
Damping Effects

Symmetry Coordinates and Tentative Force Field Analysis of a PMo12O40 Model with the Keggin Structure

1976 ◽  
Vol 31 (12) ◽  
pp. 1589-1600 ◽  
Author(s):  
Lennart Lyhamn ◽  
S. J. Cyvin ◽  
B. N. Cyvin ◽  
J. Brunvoll
Keyword(s):  
Experimental Data ◽  
Force Field ◽  
Force Constant ◽  
Raman Spectra ◽  
Vibrational Analysis ◽  
Field Analysis ◽  
Infrared And Raman Spectra ◽  
Symmetry Coordinates ◽  
Force Field Analysis ◽  
Complex Ion

Abstract A complete vibrational analysis is performed for the 53 atomic PMo12O40 model of Td symmetry. The symmetry coordinates are classified into those of (a) ligand vibrations, (b) framework-ligand couplings, (c) framework vibrations, and (d) interligand vibrations. Simple valence force fields are estimated, and the influence of inclusion of redundancies on the calculated frequencies and symmetry force constants is investigated. Comments are made on calculated symmetry force constant values up to 345 mdyne/Å. Vibrational frequencies are calculated for the Mo3O7 and Mo3O13 units and for the PMo12O403- complex ion. For the latter compound the calculated values are compared with experimental data from infrared and Raman spectra.

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