Shock Vibration Control of MDOF Structures using Fluid Viscous Dampers

Transcription

1 Shock Vibration Control of MDOF Structures using Fluid Viscous Dampers by Prof. Dilip I Narkhede PhD Faculty of Civil Engineering College of Military Engineering Pune--31 Pune

2 College of Military Engineering, F-Civil, Structures Dept., Pune Outline of Presentation Behavior of fluid viscous dampers under shock excitation Mathematical Model Sinusoidal excitation on FVD Shock excitation on FVD Behavior of 2-DOF system with fluid viscous dampers under shock excitation Behavior of example MDOF system with fluid viscous dampers under shock excitation Conclusions

3 College of Military Engineering, F-Civil, Structures Dept., Pune Behaviour of SDOF System under Shock Excitation Shock: Shock is a single principal impulse of arbitrary form, and generally is of very short duration. It is non-periodic in nature and often characterized by a sudden and severe application. p0 is often very high in shock loads. Various types of shock pulses Shock loads can produce very high response

4 College of Military Engineering, F-Civil, Structures Dept., Pune Response of SDOF System to Shock Excitation Response magnitude depends on the ratio of duration (td) of the shock to the fundamental natural period (Tn) of the system The maximum response of SDOF system may occur during or after the application of the shock. 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 to become quasi static. Vibration control of structures with td /Tn < 0.25 has been investigated for MDOF system

5 College of Military Engineering, F-Civil, Structures Dept., Pune Typical Situations of Short-Duration Impulse Loading Aircraft landing and braking Missile launching Projectile impact & Explosion Impact Explosion Booster staging

6 College of Military Engineering, F-Civil, Structures Dept., Pune Fluid Viscous Dampers L-section of fluid viscous damper Fluidic control orifice Components FVD consists of a stainless steel piston, with a bronze orifice head, and accumulator housed in a telescopic cylinder. The piston head consists of orifices that are designed with a series of specially shaped passages to alter flow characteristics with fluid speed. The mechanical construction and orifice properties can be varied to obtain the desirable damper properties. The damper is filled with a viscous fluid which is silicone oil.

7 College of Military Engineering, F-Civil, Structures Dept., Pune Mathematical Model Damping force, α : Controls shape of damper force hysteresis loop cα : Represents damper force in FVD at impressed unit velocity For sinusoidal excitation: Hysteresis loop for nonlinear FVD with 0<α<1 fall between elliptical and rectangular loops For shock excitation: As the velocity increases, the damping force in a nonlinear FVD increases at a lower rate. This limits maximum damper force transmitted to structure

8 College of Military Engineering, F-Civil, Structures Dept., Pune FVD for Sinusoidal and Shock Excitation (Courtesy M/s Taylor Devices, USA)

9 College of Military Engineering, F-Civil, Structures Dept., Pune Sinusoidal Excitation of Fluid Viscous Dampers Video Clip 1

10 Results of Sinusoidal Testing of Fluid Viscous Damper Damper Type A Damper Type B a) Measured forceforce-displacement behaviour b) Measured forceforce-velocity relationship c) Skeleton curve for forceforce-velocity relationship d) for forceforce-velocity relationship using signum function e) Analytical and measured velocity timetime-history.

11 Experimental Setup for Characterization of Fluid Viscous Dampers (Half-cycle sine shock) Experimental setup at STM lab of R&DE (Engrs (Engrs), ), Pune Video Clip 1 2

12 Experimental and Numerical Damper Force Output Response for Damper TypeType-A The power law of velocity for damper Type- A

13 Experimental and Numerical Damper Force Output Response for Damper TypeType-B The power law of velocity for damper Type- B

14 College of Military Engineering, F-Civil, Structures Dept., Pune Equation of motion of MDOF system with n dynamic degrees of freedom ) t ( p u k ) u 0 u ( n g c s u c u m m, c0, cα and k are, respectively, the (n n) mass, structural damping, supplemental damping and the stiffness matrices and u are, respectively, (n 1) vectors of nodal u, u displacements, velocities and accelerations p(t) is the (n 1) vector of nodal time-varying applied forces

15 Response of Two Storey Shear Flexible Structural System System Properties: Mass: m1 = 1000 kg Mass: m2 = 4000 kg Structural Damping: ξ = 2% Shock Specifications: Peak acceleration a0 = 40g Duration of shock td =10ms Applied at node 2 Damping constant required is calculated as: c 2 sd mtotal 1 a01 N Damping constant required for each storey is calculated as: c c i 2 cos

16 Linearization of Nonlinear Damping To incorporate nonlinear damper in SDOF system and to represent ξsd in terms of cα Using the concept of equal energy dissipation for nonlinear FVD subjected to halfhalf-cycle sine shock m a0 c 2 sd where, 3 / 2 and Г is Gamma function 2 ( 2) c 2 sd m a01 For linear fluid viscous damper α = 1, and κ = 1, above reduces to: c1 2 sd m n For a nonlinear fluid viscous damper α = ,, ,, 0.35 and 0.1 the value of κ = ,, ,,1.33 and 1.45 respectively respectively..

17 Displacement response spectra for a SDOF system with FVD subjected to initial-peak saw tooth shock (Narkhede and Sinha 2013, Journal of Sound and Vibration) a) Linear FVD (α=1.0) (c) Nonlinear FVD (α=0.35) (b) Nonlinear FVD (α=0.5) (d) Nonlinear FVD (α=0.1)

18 Comparison of Response of Two Storey Shear Flexible Structural System using TimeTime-History Analysis and Design Charts Structural System Supplemental damping ratio ξsd (%) Response analysis using time-history analysis (mm) Response analysis using design charts (mm) Without damper α= α= α= α= The results of response using the design charts and time-history analysis are in good agreement with each other. Thus, the design charts can be used for preliminary design of dampers for MDOF system subjected to initial-peak saw tooth excitation.

19 b) Response of Example MDOF structure (a) Plan and Elevation of example MDOF structure (b) Constrained base and distribution of masses (c) Node-A and Node-C considered for response of the MDOF structure (d) Rendered view of example MDOF structure

20 b) Modeling of Example MDOF structure A 3-D model of the example MDOF structure was created using ABAQUS v The members of the structure are modeled as 3-D cubic beam element. The cubic interpolation in these elements allows one to use a single element for each member and still obtain accurate results. The welded joint in the structure provide complete continuity of translation and rotations from one element to the next. We therefore need a single node at each welded joint in the model. The structure is attached firmly to the base; therefore nodes at the attachment point are constrained.

21 The target displacement for vibration control of given system with damper has been taken at approximately 20% of the maximum displacement of the system without damper. The Modal Dynamic procedure in Abaqus/Standard is used for transient modal dynamic analysis. Two steps are required for this analysis. The first step, the frequency analysis calculates the generalized mass, natural frequencies and mode shapes of the structure. The second step then uses this data to calculate the transient dynamic response of the structure.

22 1T Dynamic characteristics of example MDOF structure Generalized Generalized First mode First mode Maximum Displacement Mass (m*) Stiffness (k*) Frequency Time Period (umax) (mm) kg MN/m (ω1) (Tn) (rad/s) (s) Node-A Node-C First mode frequency, mass participation and mode shape in - and - direction Mode shape T 1 Direction First mode frequency (ω1) (rad/s) Mass Participation % x0.782x0.565x0.373x0.177x0.083x x0.782 x0.565 x0.373x0.177 x0.083x0.020 Distribution of fluid viscous dampers at the top 4 levels in MDOF structure Level Number Frame in - direction Middle Frame Total Frame in - direction Total Adjacent to FVDs Middle Adjacent to FVDs Middle Frame -direction Frame Middle -direction Frame 4,5,6, each each 06

23 College of Military Engineering, F-Civil, Structures Dept., Pune * s d Response of the 7th level of example MDOF structure using generalized coordinates * u max sd c* (MNs/m) cαi per damper (MNs/m) % Maximum displacement umax (mm) Maximum acceleration (g) u max Node-A Node-C Node-A Node-C Structure Without Time required for decay of maximum deformation to 5% of its value for system without FVDs (s) Maximum Damping force per damper (kn) Dampers With α = 1.00 With α = 0.50 With α = 0.35

24 College of Military Engineering, F-Civil, Structures Dept., Pune Maximum displacement response of 7th level of example MDOF structure using design chart td/tn Maximum displacement sd* Structure (umax) With α = With α = Without Dampers With α =

25 College of Military Engineering, F-Civil, Structures Dept., Pune CONCLUSIONS 1. The inclusion of fluid viscous damper in the structure subjected to shock excitation effectively reduces the maximum displacement and maximum acceleration of the structure. 2. It is noticed that the fluid viscous dampers considerably reduce the time required for attenuation of maximum response to 5% of its value for the structure without FVDs 3. The analysis results also shows that a smaller coefficient of damper is required for nonlinear dampers, indicating a smaller size of the damper. 4. The maximum damping force in the nonlinear fluid viscous dampers is comparatively lesser than that of the corresponding linear damper for the structure subjected to shock excitation.

26 College of Military Engineering, F-Civil, Structures Dept., Pune FUTURE SCOPE 1. Parametric study can be carried out that gives the optimum dampers capacities and distribution of dampers in multi-degree-of-freedom-system subjected to shock excitation. 2. The study can be extended with the use of semi-active damping systems. These devices are designed to alter the properties to suit the frequency of excitation, to obtain more efficient performance

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

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