Basics of ship vibration

Basics of Ship Vibration

Ship Vibration

• SOURCES of SHIP VIBRATION

Internal Sources [Unbalanced machinery forces]

(1) Main & Auxiliary Machines

• Main Propulsion Engine (esp. 4 or 5 cylinder engine)generating large unbalanced force at high frequencyclose to hull’s natural frequency.

• Rotary Machines (Electric motors, auxiliary machinesetc) generate high frequency but low amplitude

• Reciprocating Engines – Usually low frequency

(2) Unbalanced Shaft ( frequency = shaft RPM)

Ship Vibration


Internal Sources [Unbalanced machinery forces]

UNBALANCE: occurs when centre of mass is different fromcentre of rotation. Can be caused by improper assembly,material buildup, wear, broken or missing parts

Detection: High level radial vibration

MISALIGNMENT: is a condition when two coupled machineshave shafts whose center lines are not parallel andintersecting, or where one or more bearings are offset orcocked. Mis-alignment can be caused by improperassembly and adjustment, foundation failure, thermalgrowth, or locked coupling

Detection: High level axial vibration

Ship Vibration


External Sources [Hydrodynamic loading by direct actionor induced by the ship motions]

(1) Hydrodynamic loading on Propellers

Blades in non-uniform flow (freq. = RPM x No. ofblades). More pronounced for low propellersubmergence and in shallow water

(2) Unstable cavitation of blades

(3) Vortex induced forces (not on propeller)

Eg. Brackets that holds the propeller

(4) Slamming Load – short duration forces but give rise tohigh frequency forces.

Ship Vibration

• SHIP RESPONSE

• In response to excitation forces, the ship execute elasticvibrations, some of which are observed only locally and someare observed throughout the hull.

Local Vibration: Usually high frequency and loweramplitude

Difficult to predetermine

Amended easily post-construction (common practice tooverlook during design stage)

Hull Vibration: Lower frequency and higher amplitude(Compared to local)

Must be carefully considered and avoided in the designstage itself

Hull Girder VibrationDistribution of Weights

Source: MUN Notes

The weight will not equal thebuoyancy at each section alongthe ship

The weights are combinationof lightship and cargo weights

The buoyancy forces aredetermined by the shape of thehull and the position of thevessel in the water (draft & trim)

Local segments of the vesselmay have more or less weightthan the local buoyancy. Thedifference will be made up by atransfer of shear forces alongthe vessel.

Hull Girder Vibration

• SHIP as a UNIFORM BEAM

• Vibrations that exist throughout the hull are of the same typethat may exist in a beam free in space

• Surrounding water plays an important role but it does notdestroy their beamlike characteristic and it is helpful toconsider the vibrations of the ideal solid beam free in space(free-free beam)

l = 2L

l = L

l = 2L/3

L


• Types of Elastic Deformation

• A beam free in space can undergo FOUR principal types ofElastic Deformation:

1) Bending

2) Twisting

3) Shearing

4) Extensional

• Elastic deformations that play a significant role, in the case ofship are:

Bending and Shearing in both vertical and horizontalplanes through its longitudinal axis (Flexural)

Torsion about the longitudinal axis (Twist)


• Types of Elastic Deformation

Flexural: Bending like a beam

Horizontal bending mode

Vertical bending mode (usually more of a concern thanthe horizontal mode)

Torsional: Twist of a beam

More likely for container ships


• MODES and NODES

• Mode: the pattern or configuration (shape) which the bodyassumes periodically while in vibratory conditions

• Node: is a point in the body which has no displacement whenthe vibration is confined to one particular mode.

• Normal Modes: are patterns in which the body can vibratefreely after the removal of external forces

Connecting nodes, give corresponding mode


In both Flexural and Torsional vibrations, a naturalfrequency is associated with each pattern of vibration andthe natural frequencies increase as the number of nodes(points at which curves cross x-axis).

If a free-free beam is unsymmetric w.r.t either the verticalor horizontal planes through its longitudinal axis, it will befound that the natural modes of vibration involve Torsion,Bending and Shearing simultaneously.


A hull is much more complicated structure than a solid beamand therefore it behaves like the free-free beam ONLY in itslower modes of vibration.

These are called beam-like modes and may be excited byeither:

(a) Transient disturbances (due to wave or slammingimpact)

(b) Steady-state disturbances (rotating unbalanced engineor machine elements, unbalanced propellers,unbalanced shaftings)


How to avoid dangerous vibrations of the ship’s hull?

Avoid exciting forces at frequencies close to the naturalfrequencies of the ship’s hull.

How to determine the natural frequencies of the hullgirder?

Basic concepts are developed from the simple notions of auniform beam vibration.

It’s then extended to the vibration of a ship with somemore added complexities that would reflect the realities of aship in the way that a ship differs from a uniform beam

Natural Frequency of Hull Girder


Minimum number of nodes = 2

Fundamental Mode of Flexural Vibration

Frequency (in cpm) corresponding to this 2 noded verticalvibration (fundamental mode) is denoted by N2V or NV2

(number of cycles per minute in 2-noded vertical vibration)

Otto Schlick:

32L

IN V

I = Imidship of the cross-section of the ship (beam) = Weight displacement of the ship (beam)L = Length of the ship (beam)

Z

X

q (x, t)

q – the driving force / unit length

in the z-direction


Uniform Beam Vibration Equation

Just as a S-DOF system provides basis for understandingvibrating characteristics of many mechanical systems, similarly,a uniform FREE-FREE BEAM provides the basis forunderstanding the essential vibratory characteristics of ship.

Free-Free Beam is a continuous system

Beam is assume to have a mass/unit length, = A andBending stiffness – EI in x-z plane

BM due to normal internal stresses acting at any cross-sectionis related to the mean radius of curvature

;R

EIM R – radius of curvature



Mdx

zdEI

2

2

For small deflections in z-direction, the approximation thatcurvature (1/R) is equal to 2nd derivative of z w.r.t x can be used

2

2

dx

zdEIM

The Euler-Bernoulli equation describing the relationshipbetween beams deflection and the applied load

OR

qdx

zdEI

dx

d

2

2

2 )(4

4

xqdx

zdEI OR

Equation relating BM and deflection in simple beam theory.



Inertia effect of surrounding water

The relative high density of water makes the inertial effect a serious concern

Apparent increase in mass of a body vibrating in water

),(4

4

2

2

txqx

zEI

t

zA

Inertia effect

Restoring force as a result of elasticity

Loading on the beam

Technology

Basics of ship vibration