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Design, test and modelling evaluation approach of a novelSi-oil shock absorber for protection of electronic equipment

in moving vehicles

Ping Yang *, Ninbo Liao, Jianbo Yang

Laboratory of Advanced Design and Manufacturing, School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China

Received 28 March 2006; received in revised form 18 May 2007; accepted 4 June 2007

Available online 31 July 2007

Abstract

Electronic equipment systems are precision system. There are some vibrations and impact in moving vehicles for roadenvironments. Therefore, shock absorber is significant in protection of electronic equipment in moving vehicles. The objec-tive of this paper is to provide a systematic investigation to design or evaluation of a shock absorber for protection of elec-tronic equipment system in harsh vibration-impact environment. A novel Si-oil coupling damping shock absorber isdesigned and manufactured through coupling Si-oil, rubber ball and spring by ingenious tactics. The physical mechanismof a prototype shock absorber is systematically investigated by dynamic test. A nonlinear dynamic model for the shock

absorber is presented by analyzing the internal fluid dynamic phenomenon with respect to the prototype. Comparisonsbetween experimental data and simulation result confirm the validity of the model. In the meantime, evaluation of theimportance of some key factors by using the mathematical model for designing is discussed. It shows amplitude and fre-quency of excitation, as well as fluid viscosity, ratio of damping area are the key factors to ensure the performances of theshock absorber. The change of these factors will change the working characteristics and performances of the shockabsorber.Ó 2007 Elsevier Ltd. All rights reserved.

Keywords: Electronic equipment; Si-oil coupling shock absorber; Dynamics; Model; Simulation and evaluation

1. Introduction

There are some vibrations and impact in moving vehicles for road environments, so electronic equipmentmust be designed for safety. For example, vibrations come from the road, motion interfere by other instru-ments, gravitation of the sun and the moon, etc. The frequency of vibrations from these vibration fountainsis maybe in 0–2000 Hz. For example, the computer in moving vehicles will be acted by vibrations and impact.So it must be reinforced in actual applying processing. Research on design of shock absorbers to improve the

0094-114X/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mechmachtheory.2007.06.001

* Corresponding author. Tel.: +86 511 8790779.E-mail addresses: [email protected], [email protected] (P. Yang).

Available online at www.sciencedirect.com

Mechanism and Machine Theory 43 (2008) 18–32

www.elsevier.com/locate/mechmt

MechanismandMachine Theory

mailto:[email protected]






dynamic characteristics of electronic equipment system in harsh environment is a very important technologyproblem. Most designs include a shock absorber to moderate violent impacts and to attenuate vibrations so asto improve vibration-impact safety. An accurate characterization of the shock absorber is of paramountimportance for sufficiently precise mathematical models of the shock absorber for design purposes [1–9].

More recently, some literatures have discussed the characteristics of vibration isolator or shock absorber intheoretical aspect or in test investigation. For example, Yang Ping [1–4] discussed the performance and

response of a shock absorber or vibration isolator with combined Coulomb damping, viscous damping qua-dratic damping and Duffing spring in humorous or random vibration excitations in theoretical and experimen-tal aspect. A mathematical model of the multi-medium vibration isolator is presented. An approximatesolution was implemented to analyze numerical characteristics of the multi-medium coupling vibration sys-tem. Some numerical characteristics of the system are shown by changing the parameters. Yang [5], discusseddevelopment of a design curve for particle impact dampers. A power measurement technique enabled time-effi-cient measurement of the damping properties of the PID. Using the power measurement technique, a largenumber of experiments were conducted to determine the effects of vibration amplitude, excitation frequency,gap size, nominal particle diameter, and particle mass on the dissipated power and effective mass of the PID. Aphysical interpretation of the design curves is given. The performance of a PID on a structure verified the pre-dictive capabilities.

Lee and Moon [6] discussed a new mathematical dynamic model of a displacement-sensitive shock absorberto predict the dynamic characteristics of an automotive shock absorber. The proposed model of the DSSA isconsidered as two modes of the damping force (i.e. soft and hard) according to the position of the piston. Theanalytical results of the damping force characteristics are compared with the experimental results to prove theeffectiveness. The results reported provided a better understanding of the shock absorber. Evel’son and Rafa-lovskaya [7] discussed a method of calculation of quasistatic deformation of metal-elastomer elements of shock absorbers. Information about methods, algorithm and software for FEM analysis of quasistatic defor-mation of elastomer in metal-elastomer elements of shock absorbers is presented in the study. The geometricalnonlinearity of the process and incompressibility of elastomer as well as complicated boundary conditions(including dry friction) are taken into account. Kostek et al. [8] discussed an eigenvector analysis of an activevibration control system. In this paper active vibration control is studied via the system eigenvectors. The spe-cific control system analyzed uses a single actuator-sensor pair in a one-dimensional system. The results illus-

trate the complexity that is overlooked by focusing exclusively on attenuation at a single point.

Nomenclature

Q the oil flowrate between the two oil chambersC d dynamic discharge coefficient (oil)d diameter of the oil orificem kinematic viscosity of oilC a estimating coefficient of the additional dampingn number of orificea1a experimental estimation value of linear stiffness coefficient of air ball elastic propertya3a experimental estimation value of cubic stiffness coefficient of air ball elastic propertya1o experimental estimation value of linear stiffness coefficient of oil elastic propertya3o experimental estimation value of cubic stiffness coefficient of oil elastic propertyc1 correspond coefficient of the area of the orifice when circumfluencec2 correspond coefficient of the diameter of the orifice when circumfluenceAg average area of piston by considering the rodq hydraulic oil density

An orifice area (oil)L length of the oil orificeF f estimation of the friction of the system

P. Yang et al. / Mechanism and Machine Theory 43 (2008) 18–32 19



The objective of this paper is to provide a systematic investigation to design or evaluation for protection of electronic equipments system in harsh vibration and impact environment (for example, the computer system inmoving vehicles). A micro-structure oil damping shock absorber is designed through coupling oil and air ball.In fact, damping forces of the shock absorber show complex nonlinear characteristics in dynamic test. On thebasis of the geometric construction and physical construction of a prototype, adopting different degrees of

simplification regarding fluid-dynamic phenomena, this paper will develop a mathematical model to describethe nonlinear phenomena occurring within the shock absorber. The results obtained by numerical simulationare then compared with experimental results to confirm the validity of the model. In the last, evaluation of theimportance of some key factors by using the mathematical model for designing is discussed. So the researchwork establishes theoretical and experimental foundation for design of the shock absorber.

2. Description of reinforcement for electronic equipment system

Fig. 1 shows a system scheme of protection design for electronic equipments in moving vehicle. The systemmust package many types of electronic equipment in moving vehicle. The shock absorber were fixed on thebase packaging board if there are some vibrations or impacts applied on straight direction because road envi-

ronment, and the other side will be fixed by some shock absorbers in order to resist the vibrations if vibrationsbeing in other side. In general, the straight direction is the leading vibration direction. It must be consideredchiefly in reinforcement design for system. In fact, reinforcement design is the most economic measure if applying the general electronic equipments to work in harsh environment. In Fig. 1, shock absorber is thekey factor for the dynamics of the reinforcement system. So the dynamics of the shock absorber must bedesigned well-connected.

3. Description of physical structure and mechanical model of the novel oil coupled shock absorber

Fig. 2 shows a cross-section of the novel oil coupled shock absorber and its mechanical model. A noveldamping structure is designed to achieve oil damping function. There are some orifices on low-ring of the

damping pot 4 (damping structure). The oil will flow in a pressing state and dissipate energy by extrusion

Fig. 1. Protection design for electronic equipments in moving vehicle.

20 P. Yang et al. / Mechanism and Machine Theory 43 (2008) 18–32



of the piston 5 reciprocating motion for external vibration excitation. In oil flow process, it will press air ball 3and shows adjustment for elastic property of the system.

4. Experimental results of the working characteristics of the shock absorber

4.1. Experimental set-up

Fig. 3 shows the experimental set-up. The performances of the novel shock absorber can be tested by thissystem. The shock absorber is mounted on an electrodynamic shaker; the lower end is fixed to the vibratingtable of the shaker and the opposite end to the mass block. The signal producer and the power amplifier inFig. 3a are used to control the shaker, while the time histories of input state variables and output state vari-ables are acquired by means of two accelerometer sensors and a acquisition system (a two-channel data col-lecting instrument). The electrograph is used to observe the natural state of the signal. The picture of the

dynamic testing system is showed in Fig. 3b.Large amounts of experimental data have been gathered regarding the shock absorber filled with hydraulicoil and air. The influence of amplitude and frequency of sine excitation, as well as the influence of fluid vis-cosity, ratio of damping area, additional damping force and friction were investigated.

4.2. Processing of damping force by measure data

One of the basic assumptions made in this test is that the shock absorber behaves as a Single-Degree-of-Freedom (SDOF) system. Under this assumption, because one end of the absorber is held fixed to the shakerand an external time-varying displacement xðt Þ or acceleration € xðt Þ is applied to the this end, the equation of motion of the free end is given by Newton’ second law,

m€ y ðt Þ þ f ð z ;

_ z Þ þ ða1a þ a1oÞ z ðt Þ þ ða3a þ a3oÞ z 3

ðt Þ ¼ 0 ð1Þ

Fig. 2. Physical structure and mechanical model of the prototype shock absorber.




Where m is the mass which fixed to the another end of the shock absorber (it represents the mass of equip-ment), a1; a3 is the nonlinear coefficient of the spring, and f ð z ; _ z Þ is the coupling damping force of the shock

absorber. Based on above equation we can get, f ð z ; _ z Þ ¼ Àm€ y ðt Þ À ða1a þ a1oÞ z ðt Þ À ða3a þ a3oÞ z 3ðt Þ ð2Þ

Because z ðt Þ ¼ y ðt Þ À xðt Þ So we can get,

f ð z ; _ z Þ ¼ Àm€ y ðt Þ À ða1a þ a1oÞ Á ½ y ðt Þ À xðt Þ À ða3a þ a3oÞ Á ½ y ðt Þ À xðt Þ3 ð3Þ

In the experimental set-up, we can test the data of € y ðt Þ;€ xðt Þ. They are the input data and output data in theexperimental set-up. So we can get the coupling damping force by applying Eq. (3).

4.3. Performance of the shock absorber

Fig. 4a illustrates the performance of the shock absorber in vibration test. It can be evaluated by absoluteacceleration transmissibility vs. frequency of the excitation. The absolute acceleration transmissibility isdefined as the ratio of maximum acceleration of the mass block to that of the base motion (the motion of the vibrating table of the shaker). In Fig. 4a, every one of the curves shows two-frequency bands, whichhas distinct characteristic of acceleration transmissibility. One is named resonance band. In resonance band,the shock absorber shows a high-level damping characteristic. It can make the acceleration transmissibilityapproach 1, which means the resonance hump can be silenced. All the absolute acceleration transmissibilityin vibration is less than 2.5. The other is named isolation band. It has a quick drop. In Fig. 4b, it is the descrip-tion of performance of the shock absorber in impact experimental test. It can be evaluated by input and outputabsolute acceleration on mass vs. impulse time when the base is acted by impact excitation. The curves showthe output absolute acceleration amplitude is less than input absolute acceleration amplitude in markedsituation and the ratio between output and input falls in 0.4–0.6. This shows the novel shock absorber can

resist violent impact.

Fig. 3. Experimental set-up for dynamic testing.




All of above show the novel oil coupling shock absorber has a good dynamic performance for resisting vio-lent impact and attenuating vibration and controllable design-capability, for example we can design the shockabsorber with non-resonance peak and a good performance of resisting impact.

Figs. 5 and 6 illustrate the working characteristics of the shock absorber. The curves are presented as damp-ing force versus relative velocity and relative displacement to clearly show the effect of the sine excitation.Comparing Figs. 5 and 6 shows that the nonlinear effect changed as the excitation frequency increased withthe higher frequency giving lower output force at the maximum velocity point. The test results show that theshock absorber provides a good repeatable performance. The experimental results were used as basis for the

engineering model.

0 5 10 15 20 25 30 35 40 45 50

0

0.5

1

1.5

2

2.5

3

Frequency of the excitation f-Hz

A b s o l u t e a c c e l e r a t i o n t r a n s

m i s s i b i l i t y

1--400cst

2--600cst

3--900cst

(a) The acceleration transmissibility under vibration

0 0.005 0.01 0.015 0.02 0.025 0.03-50

0

50

100

150

200

250

300

Time t -s

A c c e l e r a t i o n a - m / s 2

(b) The output and input curves under impact

Fig. 4. The performances of the novel oil shock absorber.




5. Mathematical model and simulation

5.1. Oil damping

During shock absorber motion, the oil flow through the orifices varies with time, not only in value but alsoin sign. The various damping effects of the hydraulic oil were included in the model. Assuming that the oil is

incompressible, the oil damping force is given by

-200 -150 -100 -50 0 50 100 150 200-80

-60

-40

-20

0

20

40

60

80

Relative velocity v -mm/s

D a m p i n g f o r c e F - N

(a) Coupling damping force–relative velocity

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-60

-40

-20

0

20

40

60

Relative displacement z -mm

D a m p i n g f o r c e

F - N

(b) Coupling damping force–relative displacement

Fig. 5. Damping force variations sine excitation, frequency of 12 Hz.




(1) Throttling damping force along the flow path

Q ¼ Ag Á _ z ðt Þ ð4Þ

Laminar flow theory yields Poiseuille’s equation, where the pressure drop for the throttling loss can be calcu-lated by

Q ¼ C d Á c1 An Á ffiffiffiffiffiffiffiffiffiffiffiffiffi2jD P 1j

qs signðD P 1Þ ð5Þ

-250 -200 -150 -100 -50 0 50 100 150 200 250

-80

-60

-40

-20

0

20

40

60


The first amplitude

The second amplitude

(a) Coupling damping force–relative velocity

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-80

-60

-40

-20

0

20

40

60


C o u p l i n g d a m p i n g f o r c e F - N


The first amplitude

The second amplitude

(b) Coupling damping force–relative displacement

Fig. 6. Damping force variations sine excitation, frequency of 15 Hz.




So the throttling damping force along the flow path can be calculated as

F 1 ¼ Ag Á D P 1 ¼q Á A3

g Á _ z 2ðt Þ

2C 2d Á c21 A

2n

signð_ z ðt ÞÞ ð6Þ

(2) Laminar flow damping force along the flow path

Using the same principle, the pressure drop for the laminar flow losses through the orifices can be cal-culated as

Q ¼ n Ápd

4 Á D P 2128 Lqm

ð7Þ

Therefore

D P 2 ¼ 128 Lqm Ag

npðc2d Þ4

Á _ z ðt Þ ð8Þ

So the oil damping force along the flow path due to the laminar flow losses can be calculated as

F 2 ¼ Ag Á D P 2 ¼ 128 Lqm A2

g

npðc2d Þ

4Á _ z ðt Þ ð9Þ

(3) Inertia flow damping force along the flow pathThe pressure drop due to the inertia flow loss can be calculated as

D P 3 ¼ Lq Ag

c1 An

Á € z ðt Þ ð10Þ

F 3 ¼ Ag Á D P 3 ¼ Lq A2

g

An

Á € z ðt Þ ð11Þ

5.2. Structural damping force

The system will produce additional damping forces as the relative displacement changes. Harris and Credeshowed that a system with micro-damping material will express a strong damping force as the amplitudeincreases which can be evaluated as

F 4 ¼ C a Á z ðt Þ ð12Þ

5.3. Friction damping force

The friction damping force is given by

F 5 ¼ F f Á signð_ z ðt ÞÞ ð13Þ

5.4. Mathematical model

Combining these five forces into a mathematical model of the shock absorber dynamics gives

m€ z ðt Þ þq Á A3

g Á _ z 2ðt Þ

2C 2d Á c21 A

2n

signð_ z ðt ÞÞ þ 128 Lqm A2

g

npðc2d Þ4

Á _ z ðt Þ þ Lq A2

g

c1 An

Á € z ðt Þ þ C a Á z ðt Þ þ F f Á signð_ z ðt ÞÞ

þ ða1a þ a1oÞ z ðt Þ þ ða3a þ a3oÞ z 3ðt Þ ¼ Àm€ xðt Þ ð14Þ

The model contains all the physical parameters of the shock absorbers, so it can be used for shock absorber

design.




5.5. Comparison between the experimental results and simulation

Fig. 7 is the comparison between one of the test results and simulation, the numerical simulation can beobtained by using Eq. (14) in MATLAB, € xðt Þ is the actual input signal.

The numerical simulation can simulate the actual characteristics of the shock absorber in approximate by

contrasting the experimental results and the numerical simulation. There is a light distortion in simulatingresults that may be caused without introducing the compressibility of oil or other errors (metrical and datamanaging error). The research on more accurate mathematical model of the shock absorber is a future work.

-150 -100 -50 0 50 100 150-80

-60

-40

-20

0

20

40

60


D a m p i n g f o r c e

F - N

simulation

test data

(a) Damping force–relative velocity

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-80

-60

-40

-20

0

20

40

60


D a m p i n g f o r c e F - N

simulation

test data

(b) Damping force–relative displacement

Fig. 7. Comparison between the test results and simulation with the third amplitude in Fig. 5.




6. Evaluation of the importance of some key factors by using the mathematical model for designing

In general, fluid viscosity, ratio of oil damping area, as well as amplitude and frequency of excitation are thekey factors to ensure the performances of the shock absorber. It is necessary to discuss the influence of thesefactors with the mathematical model to get some the theoretical reference for actual designing.

6.1. Change of oil viscosity

During shock absorber operations, the oil flow through the orifice is notably time varying, not only in valuebut also in sign. Fig. 8 shows the curves of characteristics under the change of oil viscosity. The model hasbeen used to investigate the influence of oil viscosity on damping force–relative velocity cycle shape. The other

-500 0 500-80

-60

-40

-20

0

20

40

60

80

100


C o u p l i n g d a m p i n

g f o r c e F - N

a =25 m/s2

f=20(Hz)viscidityis 400

-500 0 500-80

-60

-40

-20

0

20

40

60

80

100a =25 m/s2


-500 0 500-80

-60

-40

-20

0

20

40

60

80

100


a =25 m/s2


-5 0 5-80

-60

-40

-20

0

20

40

60

80

100

viscidityis 400

-5 0 5-80

-60

-40

-20

0

20

40

60

80

100

viscidityis 600

-5 0 5-80

-60

-40

-20

0

20

40

60

80

100


viscidityis 800

Fig. 8. The influence of oil viscosity on damping force–relative velocity.




parameters were fixed and oil viscosity was varied from 400 mm2/s to 800 mm2/s. The results obtained for sineexcitation are shown in Fig. 8. It is clear that by increasing oil viscosity, the area of the cycle remainsunchanged and become steeper. The maximum relative velocity decrease grows with oil viscosity.

6.2. Change of the number of oil orifices (the ratio of oil damping area)

Fig. 9 shows the curves of characteristics under change of the number of oil orifices. The model has beenused to investigate the influence of ratio of oil damping area on damping force–relative velocity cycle shape.The other parameters were fixed and the number of orifices was varied from 20 to 80.

The results obtained for sine excitation (at acceleration amplitude = 25 m/s2, frequency = 20 Hz) areshown in Fig. 9. It is clear that by increasing the number of oil orifices, the area of the cycle increase and

-500 0 500-100

-50

0

50

100

150

C o u p l i n g d a m p i n g f o r c e

F - N

-500 0 500-100

-50

0

50

100

150

-500 0 500-100

-50

0

50

100

150


a =25 m/s2

f=20Hzn=20

a =25 m/s2

f=20Hzn=40

a =25 m/s2

f=20Hzn=60

-5 0 5-100

-50

0

50

100

150

C o u p l i n g d a m p i

n g f o r c e F - N

-5 0 5-100

-50

0

50

100

150

-5 0 5-100

-50

0

50

100

150


a =25 m/s2

f=20Hzn=20

a =25 m/s2

f=20Hzn=40

a =25 m/s2

f=20Hzn=40

Fig. 9. The influence of the number of oil orifices on damping force–relative velocity.




become more gently, the damping force obtained at maximum relative velocity decreases. The maximum rel-ative velocity increases, grows with the number of oil orifice.

6.3. Change of amplitude of the excitation

The model has been used to investigate the influence of excitation amplitude on damping force–relative veloc-ity cycle shape. The other parameters were fixed and acceleration amplitude was varied from 15 m/s2 to 35 m/s2.The results obtained for sine excitation are shown in Fig. 10. It is clear that by increasing the acceleration

amplitude of excitation, the area of the cycle increase and the damping force obtained at maximum relativevelocity increase. The maximum relative velocity increases, grows with the acceleration amplitude.

-500 0 500-150

-100

-50

0

50

100

150

C o u p l i n g d a m p i n g f o r c e F

- N

a =15 m/s2

-500 0 500-150

-100

-50

0

50

100

150

a =25 m/s2

-500 0 500-150

-100

-50

0

50

100

150


a =35 m/s2

-2 0 2-60

-40

-20

0

20

40

60


g f o r c e F - N

a =15 m/s2

f=20(Hz)

-5 0 5-100

-50

0

50

100

150

a =25 m/s2

f=20(Hz)

-5 0 5-150

-100

-50

0

50

100

150


a =35 m/s2

f=20(Hz)

Fig. 10. The influence of excitation amplitude on damping force–relative velocity.




6.4. Change of frequency of the excitation

Fig. 11 shows the curves of characteristic under change of frequency of the excitation. The model hasbeen used to investigate the influence of excitation frequency on damping force–relative velocity cycle shape.The other parameters were fixed and frequency was varied from 8 Hz to 15 Hz (the acceleration amplitude

is 25 m/s

2

).The results obtained for sine excitation are shown in Fig. 11. It is clear that by increasing the frequency of excitation, the area of the cycle decrease and the damping force obtained at maximum relative velocitydecrease.

-200 0 200-80

-60

-40

-20

0

20

40

60

80


a =25 m/s2

f=8(Hz)

-200 0 200-60

-40

-20

0

20

40

60

80

a =25 m/s2

f=15(Hz)

-200 0 200-80

-60

-40

-20

0

20

40

60

80


a =25 m/s2

f=20(Hz)

-5 0 5-60

-40

-20

0

20

40

60


g f o r c e F - N

a =25 m/s2

f=8(Hz)

-2 0 2-60

-40

-20

0

20

40

60

80

a =25 m/s2

f=15(Hz)

-2 0 2-60

-40

-20

0

20

40

60


a =25 m/s2

f=20(Hz)

Fig. 11. The influence of excitation frequency on damping force–relative velocity.




7. Conclusions and future work

(1) A novel oil coupling shock absorber was investigated for reinforcement of electronic in system. It has agood dynamic performance and controllable design-capability.

(2) A mathematical model of the dynamic behavior of the shock absorber has been developed in order to

describe the characteristics occurring within the shock absorber, the numerical simulation show themodel can simulate the actual shock absorber in approximate. The model will be the academic basisfor a future work, for example, optimum design and application for engineering.

(3) By contrasting the experimental results and the numerical simulation, there is a light distortion that maybe caused modeling error, test error and experimental estimation value of some parameters, for examplethe air or oil elastic property in the model. The research on more accurate mathematical model of theshock absorber is a future work.

(4) Evaluation of the importance of some key factors by using the mathematical model for designing is dis-cussed. It shows amplitude and frequency of excitation, as well as oil viscosity, ratio of damping area arethe key factor to ensure the performance of the shock absorber. The change of these factors will changeworking characteristics and performance of the shock absorber. So it establishes theoretical foundationfor the design of the shock absorber.

Acknowledgements

The author acknowledge the support of National Natural Science Foundation of China, National DefenseNatural Science Foundation of China (No. 00J16.2.5.DZ0502), Special Science Foundation for Middle-Young academic leader of Jiangsu high education in China (Qinglan Gongcheng Project), the support of Nat-ural Science Foundation of Gangxi province of China (No. 0339037), the Natural Science Foundation forQualified Personnel of Jiangsu University (04JDG027) and the Science Foundation of Jiangsu Higher Educa-tion Institution (06KJD460044), Special Science Foundation for Middle-Young academic leader of Guangxihigh education in China during the course of this work.

References

[1] Ping Yang, Yonghong Tan, Jianming Yang, et al., Simulation on dynamic characteristics of a wire gauze-fluid damping shockabsorber, Mech. Syst. Sig. Process. 20 (3) (2006) 745–756.

[2] Yang Ping, Experimental and mathematical evaluation of dynamic behaviour of an oil-air coupling shock absorber, Mech. Syst. Sig.Process. 17 (6) (2003) 1367–1379.

[3] Ping Yang, Numerical characteristics analysis of multi-medium coupling vibration isolator, J. Mech. Eng. 56 (5) (2005) 289–305.[4] Ping Yang, Approximate solution of a multi-medium coupling nonlinear isolator under random vibration excitation, Eng. Mech. 23 (7)

(2006) 170–175, In Chinese.[5] M.Y. Yang, G.A. Lesieutre, S.A. Hambric, G.H. Koopmann, Development of a design curve for particle impact dampers, Noise

Control Eng. J. 53 (1) (2005) 5–13.[6] Choon-Tae Lee, Byung-young Moon, Study of the simulation model of a displacement-sensitive shock absorber of a vehicle by

considering the fluid force, Proc. Institut. Mech. Eng. Part D (Journal of Automobile Engineering) 219 (8) (2005) 965–975.[7] L.I. Evel’son, M.Ya. Rafalovskaya, Method of calculation of quasistatic deformation of metal-elastomer elements of shock absorbers,Kauchuk i Rezina 2 (2005) 50–58.

[8] Theodore M. Kostek, Charles Krousgrill, Matthew A. Franchek, Eigenvector analysis of an active vibration control system, NoiseControl Eng. J. 52 (4) (2004) 169–178.

[9] C.M. Harris, C.E. Crede, Shock and Vibration Handbook, MC-Graw-Hill, 1990.

Yang Ping: He is currently a professor in Jiangsu University in China, also is currently a director of China Precision Machine Society and asenior member of Chinese Institute of Electronics. He received his Ph.D in mechanical engineering from Huazhong University of Scienceand Technology (HUST) in 2001. He engaged in sciences research in Concordia University. His research interests focus on the theoreticalaspect and CAD of mechanical system for the purposes of design and control.


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