scholarly journals Damage Evaluation of Critical Components of Tilted Support Spring Nonlinear System under a Rectangular Pulse

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ningning Duan ◽  
Meng Hao ◽  
Anjun Chen
Keyword(s):  
Nonlinear System ◽  
Damping Ratio ◽  
Damage Zone ◽  
Boundary Surface ◽  
Rectangular Pulse ◽  
Frequency Parameter ◽  
Mass Ratio ◽  
Dynamical Equations ◽  
Parameter Ratio ◽  
Critical Components

Dimensionless nonlinear dynamical equations of a tilted support spring nonlinear packaging system with critical components were obtained under a rectangular pulse. To evaluate the damage characteristics of shocks to packaged products with critical components, a concept of the damage boundary surface was presented and applied to a titled support spring system, with the dimensionless critical acceleration of the system, the dimensionless critical velocity, and the frequency parameter ratio of the system taken as the three basic parameters. Based on the numerical results, the effects of the frequency parameter ratio, the mass ratio, the dimensionless peak pulse acceleration, the angle of the system, and the damping ratio on the damage boundary surface of critical components were discussed. It was demonstrated that with the increase of the frequency parameter ratio, the decrease of the angle, and/or the increase of the mass ratio, the safety zone of critical components can be broadened, and increasing the dimensionless peak pulse acceleration or the damping ratio may lead to a decrease of the damage zone for critical components. The results may lead to a thorough understanding of the design principles for the tilted support spring nonlinear system.

scholarly journals The Shock Characteristics of Tilted Support Spring Packaging System with Critical Components

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
An-Jun Chen
Keyword(s):  
Frequency Ratio ◽  
Response Spectrum ◽  
Three Dimensional ◽  
Frequency Parameter ◽  
Mass Ratio ◽  
Packaging System ◽  
Parameter Ratio ◽  
Shock Response ◽  
Shock Response Spectrum ◽  
Critical Components

The nonlinear dynamical equations of tilted support spring packaging system with critical components were obtained under the action of half-sine pulse. To evaluate the shock characteristics of the critical components, a new concept of three-dimensional shock response spectrum was proposed. The ratio of the maximum shock response acceleration of the critical components to the peak pulse acceleration, the dimensionless pulse duration, and the frequency parameter ratio of system or the angle of tilted support spring system were three basic parameters of the three-dimensional shock response spectrum. Based on the numerical results, the effects of the peak pulse acceleration, the angle of the tilted support spring, the frequency parameter ratio, and the mass ratio on the shock response spectrum were discussed. It is shown that the effects of the angle of the tilted support spring and the frequency ratio on the shock response spectrum are particularly noticeable, increasing frequency parameter ratio of the system can obviously decrease the maximum shock response acceleration of the critical components, and the peak of the shock response of the critical components can be decreased at low frequency ratio by increasing mass ratio.

scholarly journals The Dynamic Evaluation of Tilted Support Spring Nonlinear System with Critical Components under the Action of a Rectangular Pulse

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ningning Duan ◽  
Shuang Song ◽  
Anjun Chen
Keyword(s):  
Nonlinear System ◽  
Pulse Duration ◽  
Frequency Ratio ◽  
Three Dimensional ◽  
Response Spectra ◽  
Rectangular Pulse ◽  
Numerical Results ◽  
Dynamical Equations ◽  
Shock Response ◽  
Critical Components

Dimensionless nonlinear dynamical equations of a tilted support spring nonlinear system with critical components were obtained under the action of a rectangular pulse, and the numerical results of the shock response were studied using Runge-Kutta method. To evaluate the dynamic characteristics of critical components, a new concept of three-dimensional shock response spectra was proposed, where the ratio of the maximum shock response acceleration of critical components to the peak pulse acceleration, the pulse duration, and the frequency ratio were three basic parameters of three-dimensional shock response spectra. Based on the numerical results, the effects of the angle, the peak pulse acceleration, the mass ratio, the frequency ratio, and the pulse duration on the shock response spectra were discussed.

scholarly journals Three-Dimensional Shock Spectrum of Critical Component for Nonlinear Packaging System

2011 ◽  
Vol 18 (3) ◽  
pp. 437-445 ◽  
Author(s):  
Jun Wang ◽  
Zhi-Wei Wang ◽  
Li-Xin Lu ◽  
Yong Zhu ◽  
Yong-Guang Wang
Keyword(s):  
System Parameter ◽  
Damping Ratio ◽  
Three Dimensional ◽  
Low Frequency ◽  
Frequency Parameter ◽  
Critical Component ◽  
Packaging System ◽  
System A ◽  
Parameter Ratio ◽  
Shock Response

To evaluate the shock characteristics of critical component for a nonlinear packaging system, a new concept of three-dimensional shock spectrum was proposed. Three key coordinate parameters, such as the nondimensional pulse duration, the frequency parameter ratio and the ratio of the maximum response acceleration to the peak pulse acceleration, were governed in a novel dynamical mathematical model. It is shown that the shock response of critical component is weakened owning to the decrease in the defined system parameter. Furthermore, at low frequency parameter ratio, the enhancement of the damping ratio of the critical component leads to the decrease in the peak of the shock response, which can also be reduced by the increase in damping ratio of cushioning pad at both lower and higher frequency parameter ratios. The discussion and analysis provide some insights into the design of cushioning packaging as well.

scholarly journals Dropping Shock Characteristics of the Suspension Cushioning System with Critical Components

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Hui Li ◽  
Anjun Chen ◽  
Ningning Duan
Keyword(s):  
Frequency Ratio ◽  
Dynamic Properties ◽  
Damping Ratio ◽  
Boundary Surface ◽  
Boundary Curve ◽  
Suspension System ◽  
Numerical Results ◽  
Shock Response ◽  
Response Peak ◽  
Critical Components

Dimensionless dropping shock dynamic equations of suspension nonlinear packaging system with critical components were obtained. The numerical results of shock response were gained using Runge-Kutta method. To evaluate the dropping shock characteristics of critical components, the dropping damage boundary curve was established, where the system parameter and the dimensionless shock velocity were selected as two coordinate parameters. Then, the frequency ratio and the system damping ratio were taken as third basic parameters of the dropping damage boundary surface, respectively. To study dynamic properties of the suspension system with critical components, the shock response acceleration, shock response displacements, and dropping damage boundary were analyzed. Based on the numerical results, the effects of the relevant parameters on dropping shock response and damage boundary of critical component were investigated. It is demonstrated that both a higher frequency ratio and a system damping ratio in the specific range can exert a positive effect on the product protection and should be selected in design process of the suspension system. Furthermore, with the decrease of suspension angle, the acceleration response peak decreases, the displacement response peak increases, and the safety zone enlarges.

Dropping damage evaluation for a hyperbolic tangent cushioning system with a critical component

2011 ◽  
Vol 18 (10) ◽  
pp. 1417-1421 ◽  
Author(s):  
Jun Wang ◽  
Fang Duan ◽  
Jiu-hong Jiang ◽  
Li-xin Lu ◽  
Zhi-wei Wang
Keyword(s):  
Boundary Surface ◽  
Frequency Parameter ◽  
Damage Evaluation ◽  
Critical Component ◽  
Hyperbolic Tangent ◽  
Damage Potential ◽  
Packaging System ◽  
System A ◽  
Parameter Ratio ◽  
Good Agreement

A new concept of dropping damage boundary surface is proposed to evaluate the dropping damage of a critical component for a hyperbolic tangent nonlinear packaging system. A novel dynamic model is established to analyze the effect of three key coordinate parameters, i.e., the non-dimensional dropping shock velocity, the frequency parameter ratio and the defined system parameter, on dropping damage potential. An experiment, which showed good agreement, was conducted to verify the theory proposed.

The Damage Boundary Curve of the Suspension Packaging System under Rectangular Pulse

2011 ◽  
Vol 105-107 ◽  
pp. 70-73 ◽  
Author(s):  
Lei Wang ◽  
An Jun Chen
Keyword(s):  
Damping Ratio ◽  
Boundary Curve ◽  
Rectangular Pulse ◽  
Three Dimension ◽  
Dynamical Equations ◽  
Packaging System ◽  
Suspension Spring ◽  
Runge Kutta Method ◽  
Safe Region ◽  
Boundary Curves

The geometric nonlinear dimensionless dynamical equations of suspension spring cushioning packaging system were established and a new concept of damage boundary curves of the system was developed under the action of rectangular pulse. Considering the angle of the suspension spring ,a three-dimension damage boundary curve is obtained.The mathematic results of the equation are calculated by using the four steps Runge-Kutta method. Studies have shown that the dimensionless pulse peak, the angle of suspension spring and the damping ratio of the system can affect the safe region, and that increasing damping can enlarge the safe region of the system. The shock of the packed product can reduce by adjusting the parameters of the system properly. These results have important application value in design of the suspension cushioning system.

Humans Jumping on Flexible Structures: Effect of Structural Properties

Volume 2 ◽  
2004 ◽  
Author(s):  
ShiPing Yao ◽  
Robert E. Harrison ◽  
Jan R. Wright ◽  
Aleksandar Pavic ◽  
Paul Reynolds
Keyword(s):  
Structural Integrity ◽  
Damping Ratio ◽  
Flexible Structures ◽  
Vertical Motion ◽  
Drop Out ◽  
Mass Ratio ◽  
Test Rig ◽  
Near Resonance ◽  
The Subject ◽  
Force Drop

The behaviour of humans jumping on flexible structures has become a matter of some importance for both structural integrity and also human tolerance. The issue is of great interest for stadia, footbridge and floor structures. A test rig has been developed for exploring the forces, accelerations and displacements that occur when a human subject jumps on a flexible structure where motion can be perceived. In tests reported earlier, it was found that the human is able to generate near resonant response of the structure but it was extremely difficult, if not impossible, to jump at or very near to the natural frequency of the structure when the structural vertical motion is significant. Also, the force developed by the subject was found to drop significantly near resonance. In this paper, the effect of the subject-to-structure mass ratio and the damping ratio of the structure on the ability of the subject to jump near resonance, and on the force drop out, is presented. It is shown that as the structure becomes more massive and more highly damped it moves less for nominally the same jumping excitation. In this situation, it becomes easier to jump near resonance and the degree of force drop out reduces, though it is still significant.

Boundaries Effects on the Movements of a Sphere Immersed in a Free Surface Flow

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
D. Mirauda ◽  
A. Volpe Plantamura ◽  
S. Malavasi
Keyword(s):  
Experimental Data ◽  
Image Analysis ◽  
Free Surface ◽  
Damping Ratio ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Mass Ratio ◽  
Amplitude Response ◽  
Charge Coupled Device ◽  
A Charge

This work analyzes the influence of boundary conditions on the movements of a sphere immersed in a steady free surface flow. The sphere is free to move both in the transverse and streamwise directions and it is characterized by the values of the mass ratio m∗ equal to 1.34 and of the damping ratio ζ equal to 0.004. In all the experiments the blockage coefficient is kept constant, while the sphere is located at different distances from the free surface and from the bottom wall of the channel. The movements of the sphere have been measured by means of the image analysis of a charge coupled device camera which provides the 2D (streamwise and transverse) displacements of the sphere with a temporal resolution of 0.02 s. The experimental data show a significant influence of the boundaries on the sphere movement and highlight a different behavior of the amplitude response between the three different experimental setups considered.

Analysis on the Influence Factors of Multi-Functional Vibration-Absorption Enclosure Wall Structures

2011 ◽  
Vol 50-51 ◽  
pp. 319-322
Author(s):  
Ming Sheng He ◽  
Jun Wei Zheng ◽  
Gui Ju Shi
Keyword(s):  
Damping Ratio ◽  
Influence Factors ◽  
Control Mode ◽  
Mass Ratio ◽  
Vibration Absorption ◽  
Wall Structures ◽  
Optimal Value ◽  
Enclosure Wall ◽  
And Control ◽  
Main Influence

Enclosure wall multi-functional vibration-absorption structures (MVEW) is a new style of damping structure, it integrates the merits of infilled frame, tuned mass control (MTMD) and the energy dissipation structures. The main influence factors of MVEW is analyzed in the paper, The results indicate that there are optimal value of the mass ratio, the stiffness ratio and the damping ratio of substructure in MVEW, and the damping effect become obvious as the increase of the number of substructure, it also shows that the best location ought to synthetically consider the number of substructure, the tuned frequency ratio and control mode instead of being fixed. In the end, the paper proposed the determine principle of the damping device’s performance parameters as well as necessary optimization of MTMD parameters according to the specific case of actual structure1.

scholarly journals Optimal Design of a Damped Single Degree of Freedom Platform for Vibration Suppression in Harmonically Forced Undamped Systems

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Jimmy S. Issa
Keyword(s):  
Objective Function ◽  
Frequency Response Function ◽  
Damping Ratio ◽  
Optimal Solution ◽  
Vibration Absorber ◽  
Primary System ◽  
Mass Ratio ◽  
Optimal Damping ◽  
Mass Ratios ◽  
Invariant Points

Vibration reduction in harmonically forced undamped systems is considered using a new vibration absorber setup. The vibration absorber is a platform that is connected to the ground by a spring and damper. The primary system is attached to the platform, and the optimal parameters of the latter are obtained with the aim of minimizing the peaks of the primary system frequency response function. The minimax problem is solved using a method based on invariant points of the objective function. For a given mass ratio of the system, the optimal tuning and damping ratios are determined separately. First, it is shown that the objective function passes through three invariant points, which are independent of the damping ratio. Two optimal tuning ratios are determined analytically such that two of the three invariant points are equally leveled. Then, the optimal damping ratio is obtained such that the peaks of the frequency response function are equally leveled. The optimal damping ratio is determined in a closed form, except for a small range of the mass ratio, where it is calculated numerically from two nonlinear equations. For a range of mass ratios, the optimal solution obtained is exact, because the two peaks coincide with the two equally leveled invariant points. For the remaining range, the optimal solution is semiexact. Unlike the case of the classical absorber setup, where the absorber performance increases with increasing mass ratios, it is shown that an optimal mass ratio exists for this setup, for which the absorber reaches its utmost performance. The objective function is shown in its optimal shape for a range of mass ratios, including its utmost shape associated with the optimal mass ratio of the setup.

Sign in / Sign up

Export Citation Format

Share Document