A New Damping Model for Non-Linear Stiffness Systems With Variable Preload Displacements and Constant Amplitude Decay Ratios

1992 ◽  
Author(s):  
T. Xu ◽  
G. G. Lowen
Keyword(s):  
Energy Loss ◽  
Mathematical Description ◽  
Damping Coefficient ◽  
Constant Amplitude ◽  
Damping Force ◽  
Non Linear ◽  
Linear Damping ◽  
Damping Model ◽  
Good Agreement

Abstract This study of the behavior of non-linear stiffness systems with variable preload displacements and constant amplitude decay ratios showed that the energy loss per cycle is dependent on these preload displacements. By introducing a non-linear damping force, which is a function of both displacement and velocity, the associated work per cycle can be made approximately the same function of the preload displacement as is the case for the energy loss. In this manner, it becomes possible to make the resulting damping coefficient essentially independent of the preload displacement. This new damping model was incorporated into the mathematical description of an over-running sprag clutch. Confirming experimentation showed very good agreement with computed results.

A New Damping Model for Nonlinear Stiffness Systems With Variable Preload Displacements and Constant Amplitude Decay Ratios

1994 ◽  
Vol 116 (1) ◽  
pp. 257-263 ◽  
Author(s):  
T. Xu ◽  
G. G. Lowen
Keyword(s):  
Energy Loss ◽  
Mathematical Description ◽  
Nonlinear Damping ◽  
Damping Coefficient ◽  
Nonlinear Stiffness ◽  
Constant Amplitude ◽  
Damping Force ◽  
Damping Model ◽  
Good Agreement

This study of the behavior of nonlinear stiffness systems with variable preload displacements and constant amplitude decay ratios showed that the energy loss per cycle is dependent on these preload displacements. By introducing a nonlinear damping force, which is a function of both displacement and velocity, the associated work per cycle can be made approximately the same function of the preload displacement as is the case for the energy loss. In this manner, it becomes possible to make the resulting damping coefficient essentially independent of the preload displacement. This new damping model was incorporated into the mathematical description of an over-running sprag clutch. Confirming experimentation showed very good agreement with computed results.

The Analysis of Automotive Door Seal Energy Consumption

2011 ◽  
Vol 80-81 ◽  
pp. 714-718
Author(s):  
Yun Kai Gao ◽  
Da Wei Gao
Keyword(s):  
Energy Consumption ◽  
Elastic Force ◽  
Bernoulli Equation ◽  
Analysis Model ◽  
Damping Force ◽  
Total Energy Consumption ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Damping ◽  
Simplified Analysis

The seal deformation of automotive door is caused by the door compression forces, including non-linear elastic force and non-linear damping force. The working principles of them are analyzed and a new simplified analysis model is built. Based on the Bernoulli equation and the law of conservation of mass, the mathematical models are established to calculate energy consumption of the seal system. According to the analysis results, the energy consumption of non-linear elastic force and non-linear damping force are respectively 84% and 16% of the total energy consumption of the seal system. At last, the calculation data is compared with the test data and the error is less than 5%, so the calculation method proposed in this paper is observed to be accurate.

A Nonlinear Leg Damping Model for the Prediction of Running Forces and Stability

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Ian Abraham ◽  
ZhuoHua Shen ◽  
Justin Seipel
Keyword(s):  
Ground Reaction Force ◽  
Reaction Force ◽  
Energetic Cost ◽  
Ground Reaction Forces ◽  
Slip Model ◽  
Damping Force ◽  
Reaction Forces ◽  
Linear Damping ◽  
The Stability ◽  
Damping Model

Despite the neuromechanical complexity underlying animal locomotion, the steady-state center-of-mass motions and ground reaction forces of animal running can be predicted by simple spring-mass models such as the canonical spring-loaded inverted pendulum (SLIP) model. Such SLIP models have been useful for the fields of biomechanics and robotics in part because ground reaction forces are commonly measured and readily available for comparing with model predictions. To better predict the stability of running, beyond the canonical conservative SLIP model, more recent extensions have been proposed and investigated with hip actuation and linear leg damping (e.g., hip-actuated SLIP). So far, these attempts have gained improved prediction of the stability of locomotion but have led to a loss of the ability to accurately predict ground reaction forces. Unfortunately, the linear damping utilized in current models leads to an unrealistic prediction of damping force and ground reaction force with a large nonzero magnitude at touchdown (TD). Here, we develop a leg damping model that is bilinear in leg length and velocity in order to yield improved damping force and ground reaction force prediction. We compare the running ground reaction forces, small and large perturbation stability, parameter sensitivity, and energetic cost resulting from both the linear and bilinear damping models. We found that bilinear damping helps to produce more realistic, smooth vertical ground reaction forces, thus fixing the current problem with the linear damping model. Despite large changes in the damping force and power loss profile during the stance phase, the overall dynamics and energetics on a stride-to-stride basis of the two models are largely the same, implying that the integrated effect of damping over a stride is what matters most to the stability and energetics of running. Overall, this new model, an actuated SLIP model with bilinear damping, can provide significantly improved prediction of ground reaction forces as well as stability and energetics of locomotion.

The Periodic and Chaotic Vibration of Dynamical System With Elastic Pendulum

2006 ◽  
Author(s):  
Danuta Sado
Keyword(s):  
Linear Elasticity ◽  
Vertical Direction ◽  
System Response ◽  
Main Body ◽  
Bifurcation Diagrams ◽  
Damping Force ◽  
Chaotic Vibration ◽  
Non Linear ◽  
Linear Damping ◽  
Elastic Pendulum

The nonlinear damping effect on response of coupled three degree-of-freedom autoparametric vibration system with elastic pendulum attached to the main mass is investigated numerically. It was assumed that the main body is suspended by an element characterized by non-linear elasticity and non-linear damping force and is excited harmonically in the vertical direction. The elastic pendulum characterized also by -linear elasticity and non-linear damping. Solutions for the system response are presented for specific values of the uncoupled normal frequency ratios and the energy transfer between modes of vibrations is observed. Curves of internal resonances for free vibrations and external resonances for exciting force are shown. In this type system one mode of vibration may excite or damp another one, and except different kinds of periodic vibration there may also appear chaotic vibration. Various techniques, including chaos techniques such as bifurcation diagrams and: time histories, phase plane portraits, power spectral densities, Poincare` maps and exponents of Lyapunov, are used in the identification of the responses. These bifurcation diagrams show many sudden qualitative changes, that is, many bifurcations in the chaotic attractor as well as in the periodic orbits. The results show that the system can exhibit various types of motion, from periodic to quasi-periodic to chaotic, and is sensitive to small changes of the system parameters.

Estimation of Non-Linear Damping Parameters in a Normal Triangular Array Subject to Fluidelastic Instability

2006 ◽  
Author(s):  
Craig Meskell ◽  
Petr Eret
Keyword(s):  
Experimental Data ◽  
Limit Cycle ◽  
Triangular Array ◽  
Working Fluid ◽  
Structural Damping ◽  
Non Linear ◽  
Fluidelastic Instability ◽  
Linear Damping ◽  
Predicted Values ◽  
Good Agreement

The non-linear damping parameters associated with a coupled fluidelastic system have been extracted using the non-linear decrement method. The response of a single flexible tube in a five row normal triangular tube array (P/d = 1.32) was recorded over a range of freestream velocities with air as the working fluid. The structural damping has been set so as to avoid fluidelastic instability. The linear and cubic fluidelastic damping parameters have been obtained. Using these identified quantities, the limit cycle amplitudes for the system at lower structural damping levels have estimated. Good agreement between the predicted values and the experimental data is achieved.

On the experimental validation of a non-linear shaft damping model

2002 ◽  
Vol 216 (10) ◽  
pp. 1031-1035 ◽  
Author(s):  
L D MacLennan
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Experimental Validation ◽  
Viscous Damping ◽  
Signal Component ◽  
Non Linear ◽  
Linear Damping ◽  
Damping Model

This paper presents an experimental validation of a proposed non-linear damping model for shaft torsional vibration studies, compared to the linear viscous damping model. Nine different shaft configurations were used. The deflection of each shaft exhibiting free vibration was measured for a period of one minute and the signal component at the natural frequency of torsion was found. The experiments showed that the internal shaft damping was highly non-linear. The damping tended to be not only stiffness related but also depended on the material used.

scholarly journals Displacement Transmissibility Characteristics of Harmonically Base Excited Damper Isolators with Mixed Viscous Damping

2013 ◽  
Vol 20 (5) ◽  
pp. 921-931 ◽  
Author(s):  
Xiaojuan Sun ◽  
Jianrun Zhang
Keyword(s):  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Viscous Damping ◽  
Damping Force ◽  
Response Characteristics ◽  
Damping Characteristics ◽  
Linear Damping ◽  
Frequency Ratios ◽  
Good Agreement

The viscous damping force in the mixed form asfd(x˙)=c1x˙+c2|x˙|x˙can well describe damping characteristics of isolators and dampers in many cases. In this paper, performance characteristics of single-degree-of-freedom (SDOF) linear-stiffness isolators with mixed and piecewise mixed viscous damping are analytically examined under harmonic base excitation. Based on the first-order harmonic balance method (HBM), both relative and absolute displacement transmissibility expressions with the equivalent linear damping coefficient (ELDC) are given. And the analytical calculations show good agreement with the numerical results. Also, the influence of nonlinear damping on the response characteristics is investigated by comparing the transmissibility of linear and nonlinear systems. The resonant frequency always shifts to a lower value as the nonlinear damping component of the forcefd(x˙)=c1x˙+c2|x˙|x˙becomes stronger, and when the damping ratio in the corresponding linear model is relatively high, the relative transmissibility decreases at frequencies higher than the resonance frequency of the corresponding linear damping system and the absolute one increases for the frequency ratios above2. Finally, the displacement transmissibility of a nonlinear isolator with piecewise mixed viscous damping is discussed and the process shows research similarity with the non-piecewise case.

Impacting Analysis on the Coupler and Buffer of a Subway Vehicle for the Shunting Operations

2010 ◽  
Vol 44-47 ◽  
pp. 1687-1692
Author(s):  
Suo Huai Zhang ◽  
Ping Man Zhang ◽  
Kun Jia
Keyword(s):  
Kinetic Theory ◽  
General Model ◽  
Spline Function ◽  
Theory Method ◽  
Damping Force ◽  
Moving Vehicles ◽  
Non Linear ◽  
Linear Damping ◽  
The Relationship

After the general model of shunting operation was established, non-linear damping force was imported into ADAMS by means of spline function. Under the same coupling speed, the relationship between different shunting groups, the maximum impacting force and the buffer stroke was researched; the different impacting characteristics of the system were also analyzed under different shunting operations by means of the impulse transmission and kinetic theory method. In the condition of the same coupling speed and vehicles, the results are that the number difference of moving vehicles and static vehicles between the coupling interface was more, the maximum impacting force was smaller, and the buffer stroke was shorter.

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