uncertainty in shock and vibration design for navy...

Uncertainty in Shock and Vibration Design for Navy Ships

Jay WarrenHull Engineering

Newport News ShipbuildingNewport News, VA

Predictability and Uncertainty Quantification Workshop

November 14, 2003

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Presentation Overview

• Description of the Navy shock and vibration problem

• Identification of major sources of uncertainty

• Current state of predictability for the Navy shock and vibration problem


Description of Shock and Vibration for Navy Ships

• The Navy shock problem involves protection of equipment (machinery, electronics, weapons, …) from the effects of a near miss underwater explosion

• The Navy vibration problem involves protecting equipment from environmental vibration caused by main propulsion or seaway loads



R

• For a large standoff underwater explosion the resulting pressure-time history is approximated by:P(t) = Pmaxe(-t/θ)

where,

Pmax = K1(W1/3/R)A1

θ = K2W1/3(W1/3/R)A2

K1, K2, A1, A2 = Constants that depend on the type of explosive material

W = Charge weight

R = Standoff distanceExplosive Charge



• Underwater explosion produces a pressure loading on the wet surface of the ship

• The pressure loading is transferred from the outer shell to major transverse bulkheads and stanchions

• The resulting motion of the transverse bulkheads and stanchions excites the structure throughout the rest of the ship



• The motion of the ship structure acts as a base excitation to the equipment

• The two basic approaches for shock design are:– Mitigate the base

excitation by using shock isolation

– Harden the equipment to resist the worst case shock event

u(t)

m1

m2

mn

x(t)


Identification of Major Sources of Uncertainty

u(t)

m1

m2

mn

x(t)• Uncertainty for the Navy

shock and vibration problem can be broken into two major parts:– Uncertainty in the base

motion input u(t)– Uncertainty in the

fragility and behavior of the equipment



• Simplifying the problem, the base motion input can be thought of as the uncertain variable Q (load) and the fragility of the equipment as the uncertain variable R (resistance)

• Any overlap of Q and R is defined as failure



)}({)}(]{[)}(]{[)}(]{[ tFtuKtuCtuM =++

• Uncertainty in the base motion input u(t)– Damping / Energy Loss

• Structural complexity causes energy conversion from bending to membrane and vice versa as the energy moves through the ship

• Frequency/strain-rate dependent• Local yielding

– Mass• Detailed mass distribution• Values for mass moments of inertia• Location of center of gravity



)}({)}(]{[)}(]{[)}(]{[ tFtuKtuCtuM =++

• Uncertainty in the base motion input u(t) (continued)– External pressure loading

• Charge location/configuration/geometry• Bulk cavitation caused by free surface reflections• Local cavitation from reflections near the hull

– Stiffness• Typical physical properties like thickness, variation in modulus

of elasticity, geometric imperfections, …



• Uncertainty in the behavior and fragility of the equipment– There are two distinct types of equipment on Navy ships

• Hardened Navy/combat specific equipment• Rugged off-the-shelf equipment often referred to as modified

off-the-shelf (MOTS) equipment– Testing of Navy equipment is performed in accordance with

MIL-S-901D for shock and MIL-STD-167 for vibration• Standard shock and vibration tests attempt to provide a worst

case environment for the equipment• No attempt is made to modally characterize the equipment• No attempt is made to determine the fragility of the equipment• If the equipment passes the test no other work is done

– Excessive costs prevent further testing


Predictability for Navy Shock and Vibration

u(t)

m1

m2

mn

x(t)

• Predictability for the Navy shock and vibration problem can also be broken into two major parts:– Predictability of the base

motion input u(t)– Predictability of the

behavior and fragility of the equipment

• Prediction of higher frequency response causes many problems



• Predictability for shock and vibration problems implies the use of numerical methods (Usually FEA!!!)

• Useful to think of predictability in terms of how well damping, mass, external loading, and stiffness can be modeled



• Predictability issues associated with damping/energy loss– No consistent method for predicting/modeling damping for a

generic structure• Recent analyses are using damping values from tests on similar

ships– Damping is very frequency dependent and current analysis

methods do not allow the user to control damping over the entire frequency range of interest

• Users are forced to fit values of α and β over an entire frequency range which usually results in too much damping at higher frequencies and/or too little damping at lower frequencies



• Predictability issues associated with mass– Mass distribution affects the modal characteristics of the structure

and becomes a major issue at higher frequencies– Incorrect mass distribution can cause filtering of the response

throughout the ship– Detailed mass distribution is usually not well understood

• Predictability issues associated with UNDEX loading– Bulk cavitation due to free surface reflections of the shock wave

require the analyst to model some of the external fluid– Propagating a high frequency shock event through an acoustic

finite element mesh requires a dense mesh– Coupled Lagrangian/Eulerian methods are promising but tend to

require more solution time



• Predictability issues associated with stiffness– Most stiffness issues are related to problem size/mesh

density• Even at moderate frequencies the required mesh density

causes the modeling effort and problem solution to grow out of control

• Local changes in geometry and materials properties are difficultto model without significant mesh refinement

• Resort to other analysis methods like SEA and Energy Finite Elements

– Higher strain-rate materials properties and failure models are not available for many ductile materials and their welds



• Predictability of equipment fragility– Finite element analyses can provide some insight into fragility

if the equipment is made from components having moderate frequency content

• Higher frequency components require dense meshes and the size of the problem can become very large

• Damping can have a significant impact on the results and is almost impossible for the user to predict

– Most heavy machinery can be successfully analyzed using FEA

• Higher frequency attachments may cause problems– Assemblies of electronic components are extremely difficult

to analyze


Summary

• Navy shock is caused by large standoff underwater explosions• Uncertainty for the Navy shock problem falls into two categories:

– Uncertainty in the shock environment below the equipment– Uncertainty in the fragility of the equipment

• Predictability for the Navy shock problem also falls into two categories– Predictability of the shock environment

• Nearly impossible to correctly model damping for a complex problem

• Mass distribution and stiffness may require very dense meshes for higher frequencies

– Predictability of equipment fragility• Make reasonable approximations for fragility of machinery but

electronics can cause problems


Summary

• State of UQ •Poor to very poor

• What questions are answered by predictive capability• Allow surrogate testing• How close to failure we really are• Helps to locate uncertainty

• What stands in the way of predictability• Physics •Ability to test at lethal level


Summary

• What can be done to mitigate obstacles• Enhanced awareness

• Benefits of improved predictability•Method for managing risk•Lower cost

• Contents of predictability-aware model• Ability to predict results with a certain level of confidence

uncertainty in shock and vibration design for navy...

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