shock vibration control of mdof structures using … · shock vibration control of mdof structures...

Shock Vibration Control of MDOF Structures usingFluid Viscous Dampers

bbyyProf. DilipProf. Dilip II NarkhedeNarkhede

PhDPhD

FacultyFaculty of Civil Engineeringof Civil EngineeringCollege ofCollege of Military EngineeringMilitary Engineering

PunePune--3131

Outline of PresentationOutline of Presentation

• Behavior of fluid viscous dampers undershock excitation

• Mathematical Model• Sinusoidal excitation on FVD• Shock excitation on FVD

• Behavior of 2-DOF system with fluid viscousdampers under shock excitation

• Behavior of example MDOF system with fluidviscous dampers under shock excitation

• Conclusions

College of Military Engineering, F-Civil, Structures Dept., Pune - 411031

• Behavior of fluid viscous dampers undershock excitation

• Mathematical Model• Sinusoidal excitation on FVD• Shock excitation on FVD

• Behavior of 2-DOF system with fluid viscousdampers under shock excitation

• Behavior of example MDOF system with fluidviscous dampers under shock excitation

• Conclusions

Shock Vibration Control of MDOF Structures using Fluid Viscous Dampers


Behaviour of SDOF System under ShockExcitation

• Shock is a single principal impulse of arbitrary form, andgenerally is of very short duration.

• It is non-periodic in nature and often characterized by asudden and severe application.

• p0 is often very high in shock loads.

Shock:


Various types of shock pulsesShock loads can produce very high response


Analysis of Response Behaviour:• If td /Tn < 0.25, the maximum response is

smaller than the amplitude of the shock.• If td /Tn > 0.5 but < 2, the maximum response

is greater than the input amplitude.• If td /Tn > 2, the shape of shock may be of

greater significance. The response tends tobecome quasi static.

Response magnitude depends on the ratio ofduration (td) of the shock to the fundamentalnatural period (Tn) of the systemThe maximum response of SDOF systemmay occur during or after the application ofthe shock.

Response of SDOF System to Shock Excitation


Analysis of Response Behaviour:• If td /Tn < 0.25, the maximum response is

smaller than the amplitude of the shock.• If td /Tn > 0.5 but < 2, the maximum response

is greater than the input amplitude.• If td /Tn > 2, the shape of shock may be of

greater significance. The response tends tobecome quasi static.

Vibration control of structures with td /Tn < 0.25has been investigated for MDOF system


Typical Situations of Short-Duration ImpulseLoading

Aircraft landing and braking


Projectile impact & Explosion Missile launchingAircraft landing and braking

Explosion

Impact

Booster staging

Fluid Viscous Dampers

L-section of fluid viscous damper Fluidic control orifice

FVD consists of a stainless steel piston, with a bronze orificehead, and accumulator housed in a telescopic cylinder.

The piston head consists of orifices that are designed with aseries of specially shaped passages to alter flowcharacteristics with fluid speed.

The mechanical construction and orifice properties can bevaried to obtain the desirable damper properties.

The damper is filled with a viscous fluid which is silicone oil.

ComponentsComponents


FVD consists of a stainless steel piston, with a bronze orificehead, and accumulator housed in a telescopic cylinder.

The piston head consists of orifices that are designed with aseries of specially shaped passages to alter flowcharacteristics with fluid speed.

The mechanical construction and orifice properties can bevaried to obtain the desirable damper properties.

The damper is filled with a viscous fluid which is silicone oil.Shock Vibration Control of MDOF Structures using Fluid Viscous Dampers


Damping force,Damping force,α : Controls shape of damper force hysteresis loopcα : Represents damper force in FVD at impressed

unit velocity

MathematicalMathematical ModelModel


For shock excitation:As the velocity increases, thedamping force in a nonlinearFVD increases at a lower rate.This limits maximum damperforce transmitted to structure

For sinusoidal excitation:Hysteresis loop fornonlinear FVD with 0<α<1fall between elliptical andrectangular loops


FVD for Sinusoidal and Shock Excitation


((Courtesy M/s Taylor Devices, USA)Courtesy M/s Taylor Devices, USA)


Sinusoidal Excitation of Fluid Viscous Dampers


Video ClipVideo Clip 1

Results of Sinusoidal Testing of Fluid Viscous DamperResults of Sinusoidal Testing of Fluid Viscous DamperDamper Type ADamper Type A Damper Type BDamper Type B


a) Measured forcea) Measured force--displacementdisplacement behaviourbehaviour b) Measured forceb) Measured force--velocity relationshipvelocity relationshipc) Skeleton curve for forcec) Skeleton curve for force--velocity relationship d)velocity relationship d) for forcefor force--velocity relationship usingvelocity relationship usingsignumsignum function e) Analytical and measured velocity timefunction e) Analytical and measured velocity time--history.history.

Experimental Setup for Characterization of Fluid ViscousDampers (Half-cycle sine shock)

Video ClipVideo Clip 1 2Experimental setup at STM lab of R&DE (Experimental setup at STM lab of R&DE (EngrsEngrs),), PunePune

Experimental and Numerical Damper Force OutputExperimental and Numerical Damper Force OutputResponse for Damper TypeResponse for Damper Type--AA

The power law of velocity for damper Type- A

Experimental and Numerical Damper Force OutputExperimental and Numerical Damper Force OutputResponse for Damper TypeResponse for Damper Type--BB

The power law of velocity for damper Type- B

0

sgn ( ) ( )m u c u c u u k u p t

Equation of motion of MDOF system with ndynamic degrees of freedom

m, c0, cα and k are, respectively, the (n×n) mass,structural damping, supplemental damping and thestiffness matrices

u, are, respectively, (n×1) vectors of nodaldisplacements, velocities and accelerations

p(t) is the (n×1) vector of nodal time-varying applied forces


m, c0, cα and k are, respectively, the (n×n) mass,structural damping, supplemental damping and thestiffness matrices

u, are, respectively, (n×1) vectors of nodaldisplacements, velocities and accelerations

p(t) is the (n×1) vector of nodal time-varying applied forces

u and u


ResponseResponse ofof TwoTwo SStoreytorey SShearhear FlexibleFlexible SStructuraltructural SSystemystem

System Properties:Mass: m1 = 1000 kgMass: m2 = 4000 kgStructural Damping: ξ = 2%

Shock Specifications:Peak acceleration a0 = 40gDuration of shock td =10msApplied at node 2


Shock Specifications:Peak acceleration a0 = 40gDuration of shock td =10msApplied at node 2

Damping constant required is calculated as:Damping constant required is calculated as:

11 02 sd totalc m a N

Damping constant required for each storey is calculated as:Damping constant required for each storey is calculated as:

2cosi

cc

Linearization of Nonlinear DampingLinearization of Nonlinear Damping

Using the concept of equal energy dissipation for nonlinear FVDUsing the concept of equal energy dissipation for nonlinear FVDsubjected to halfsubjected to half--cycle sine shockcycle sine shock

3 / 22 ( 2)

andand ГГ is Gammais Gammafunctionfunctionwherewhere,,

To incorporate nonlinear damper in SDOF system and toTo incorporate nonlinear damper in SDOF system and torepresentrepresent ξsd in terms ofin terms of cα

110

2 0.592 sdc m a

12 0.59


3 / 22 ( 2)

andand ГГ is Gammais Gammafunctionfunction

ForFor aa nonlinearnonlinear fluidfluid viscousviscous damperdamper αα == 00..7070,, 00..5050,, 00..3535 andand 00..11 thethevaluevalue ofof κκ == 11..1515,,11..2525,,11..3333 andand 11..4545 respectivelyrespectively..

wherewhere,,

For linear fluid viscous damperFor linear fluid viscous damper α =α = 1, and1, and κκ = 1, above reduces to:= 1, above reduces to: 1 2 nsdc m

12 0.59

1

02 sdc m a

Displacement response spectra for a SDOF system with FVDsubjected to initial-peak saw tooth shock(Narkhede and Sinha 2013, Journal of Sound and Vibration)

a) Linear FVD (α=1.0) (b) Nonlinear FVD (α=0.5)

(c) Nonlinear FVD (α=0.35) (d) Nonlinear FVD (α=0.1)

StructuralSystem

Supplementaldamping ratio

ξsd (%)

Response analysis usingtime-history analysis

(mm)

Response analysis usingdesign charts

(mm)

Without damper - 32.17 29.66

α=1 200 8.97 6.47

α=0.5 50 10.38 7.36

Comparison of ResponseComparison of Response of Twoof Two SStoreytorey ShearShear FFlexiblelexibleSStructuraltructural System using TimeSystem using Time--HistoryHistory AAnalysisnalysis andand

DesignDesign CChartsharts

α=0.35 30 11.96 8.85

α=0.1 20 9.52 6.70

The results of response using the design charts and time-historyanalysis are in good agreement with each other.

Thus, the design charts can be used for preliminary design ofdampers for MDOF system subjected to initial-peak saw toothexcitation.

b) Response of Example MDOF structureb) Response of Example MDOF structure(a) Plan and Elevation

of example MDOFstructure

(b) Constrained baseand distributionof masses

(c) Node-A and Node-Cconsidered forresponse of theMDOF structure

(d) Rendered viewof exampleMDOF structure

b) Modeling of Example MDOF structureb) Modeling of Example MDOF structure

• A 3-D model of the example MDOF structure was created using“ABAQUS v6.8-13”.

•The members of the structure are modeled as 3-D cubic beamelement.

•The cubic interpolation in these elements allows one to use asingle element for each member and still obtain accurate results.

•The welded joint in the structure provide complete continuity oftranslation and rotations from one element to the next. Wetherefore need a single node at each welded joint in the model.

•The structure is attached firmly to the base; therefore nodes at theattachment point are constrained.

• A 3-D model of the example MDOF structure was created using“ABAQUS v6.8-13”.

•The members of the structure are modeled as 3-D cubic beamelement.

•The cubic interpolation in these elements allows one to use asingle element for each member and still obtain accurate results.

•The welded joint in the structure provide complete continuity oftranslation and rotations from one element to the next. Wetherefore need a single node at each welded joint in the model.

•The structure is attached firmly to the base; therefore nodes at theattachment point are constrained.

• The target displacement for vibration control of given system withdamper has been taken at approximately 20% of the maximumdisplacement of the system without damper.

• The Modal Dynamic procedure in Abaqus/Standard is used fortransient modal dynamic analysis.

• Two steps are required for this analysis.

The first step, the frequency analysis calculates thegeneralized mass, natural frequencies and mode shapes ofthe structure.

The second step then uses this data to calculate the transientdynamic response of the structure.

• The target displacement for vibration control of given system withdamper has been taken at approximately 20% of the maximumdisplacement of the system without damper.

• The Modal Dynamic procedure in Abaqus/Standard is used fortransient modal dynamic analysis.

• Two steps are required for this analysis.

The first step, the frequency analysis calculates thegeneralized mass, natural frequencies and mode shapes ofthe structure.

The second step then uses this data to calculate the transientdynamic response of the structure.

Generalized

Mass (m*)

kg

Generalized

Stiffness (k*)

MN/m

First mode

Frequency

(ω1)

(rad/s)

First mode

Time Period

(Tn)

(s)

Maximum Displacement

(umax) (mm)

Node-A Node-C

X Z X Z X Z X Z X Z

26914 89.79 45.51 57.75 41.12 0.109 0.153 20.25 39.64 28.13 42.26

1

T

Direction First modefrequency

(ω1) (rad/s)

MassParticipation

%

Mode shape1

T

Dynamic characteristics of example MDOF structure

First mode frequency, mass participation and mode shape in X- and Z- directionFirst modefrequency

(ω1) (rad/s)

MassParticipation

%

X 57.75 93.11Z 41.12 95.23

1 0.782 0.565 0.373 0.177 0.083 0.020x x x x x x

1 0.782 0.565 0.373 0.177 0.083 0.020x x x x x x

Level

Number

Frame in X- direction Total

FVDs

X-direction

Frame in Z- direction Total

FVDs

Z-direction

Middle Frame Adjacent to

Middle Frame

Middle

Frame

Adjacent to

Middle

Frame

4,5,6,7 04 02 each 08 02 02 each 06

Distribution of fluid viscous dampers at the top 4 levels in MDOF structure

*s d

maxu

Structure

%

c*(MNs/m)

cαiper damper

(MNs/m)

Maximum displacementumax(mm)

Maximum acceleration(g)

Time required fordecay ofmaximum

deformation to 5%of its value forsystem without

FVDs(s)

Maximum Dampingforce

per damper(kN)

Node-A Node-C Node-A Node-C

*sd

maxu

Response of the 7th level of example MDOF structure using generalized coordinates


X Z X Z X Z X Z X Z X Z X Z X Z

Without

Dampers

- - - - - 29.93 39.6 28.1 42.26 26.30 26.52 27.16 26.83 3.75 4.19 - -

With

α = 1.00

200 30.74 21.96 3.66 3.85 9.66 9.54 8.81 9.57 26.21 22.35 26.76 20.83 0.068 1.093 671.15 600.58

With

α = 0.50

90 13.46 11.38 1.70 1.90 8.51 9.23 8.10 9.32 25.87 22.12 26.09 20.46 0.551 1.142 507.78 411.12

With

α = 0.35

30 4.13 3.67 0.50 0.60 11.11 9.16 8.92 9.14 24.61 21.95 24.96 20.53 0.831 1.284 397.21 362.68


Structure

td/Tn Maximum displacement

(umax)

X Z X Z X Z

Without Dampers - - 32.16 46.39

*sd

Maximum displacement response of 7th level of example MDOF structureusing design chart


Without Dampers

0.137 0.098

- - 32.16 46.39

With α = 1.00 200 200 9.74 12.19

With α = 0.50 90 90 6.27 7.48

With α = 0.35 30 30 8.94 11.35


1. The inclusion of fluid viscous damper in the structure subjectedto shock excitation effectively reduces the maximum displacementand maximum acceleration of the structure.

2. It is noticed that the fluid viscous dampers considerably reducethe time required for attenuation of maximum response to 5% ofits value for the structure without FVDs

3. The analysis results also shows that a smaller coefficient ofdamper is required for nonlinear dampers, indicating a smallersize of the damper.

4. The maximum damping force in the nonlinear fluid viscousdampers is comparatively lesser than that of the correspondinglinear damper for the structure subjected to shock excitation.

CONCLUSIONSCollege of Military Engineering, F-Civil, Structures Dept., Pune - 411031

1. The inclusion of fluid viscous damper in the structure subjectedto shock excitation effectively reduces the maximum displacementand maximum acceleration of the structure.

2. It is noticed that the fluid viscous dampers considerably reducethe time required for attenuation of maximum response to 5% ofits value for the structure without FVDs

3. The analysis results also shows that a smaller coefficient ofdamper is required for nonlinear dampers, indicating a smallersize of the damper.

4. The maximum damping force in the nonlinear fluid viscousdampers is comparatively lesser than that of the correspondinglinear damper for the structure subjected to shock excitation.


FUTURE SCOPECollege of Military Engineering, F-Civil, Structures Dept., Pune - 411031

1. Parametric study can be carried out that gives theoptimum dampers capacities and distribution ofdampers in multi-degree-of-freedom-system subjectedto shock excitation.

2. The study can be extended with the use of semi-activedamping systems. These devices are designed to alterthe properties to suit the frequency of excitation, toobtain more efficient performance


1. Parametric study can be carried out that gives theoptimum dampers capacities and distribution ofdampers in multi-degree-of-freedom-system subjectedto shock excitation.

2. The study can be extended with the use of semi-activedamping systems. These devices are designed to alterthe properties to suit the frequency of excitation, toobtain more efficient performance

THANK YOU

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