Lecture No. 9: Harmonically Excited Vibration: Structural Damping

cyclically

internally

When materials are ____ stressed, energy is dissipated ____ within

the material itself.

solid damping or structural damping

Experiments by several investigators indicate that for most

structural metals, such as steel or aluminum, the energy dissipated per cycle is

independent of the frequency over a wide frequency range and proportional to

the square of the amplitude of vibration. Internal damping fitting this

classification is called

W_d = ax^2

Energy dissipated by structural damping (formula)

Fuselage

is the central body of an airplane and is designed to

accommodate the crew, passengers, and cargo. It also provides the

structural connection for the wings and tail assembly.

torsion

bending

tension

shear

compression

[Enumerate] Five types of stress the fuselage is subjected to

faulty design

faulty maintenance

manufacturing flaws

pilot error

weather conditions

sabotage

[Enumerate] Causes of Loss of Structural Integrity during flight

Damping in a material of a structure

Losses due to friction between contact areas

Dissipation in medium due to relative

motion within the system

[Enumerate] Structural damping includes:

Damping

is a phenomenon that makes any vibrating body/structure to decay

in amplitude of motion gradually by means of energy dissipation through

various mechanisms.

Damping

gradual transformation of energy

within the vibrating system is referred as

Dampers

are strategically placed in the building structure to control floor

vibrations and building displacement, cater for occupancy comfort and

mitigate against major seismic events.

Dampers

Dissipated through heat energy

The energy generated by floor

vibration and building displacement is absorbed by

Aerodynamic damping

prevents oscillations from occurring indefinitely.

material damping

The energy dissipation is caused by

amplitude of stress

number of cycles

geometry

[Enumerate] Factors affecting material damping

Viscous damping

Coulomb or Dry Friction Damping

Solid or Structural Damping or Material or Hysteretic Damping

Slip or Interfacial damping

Magnetic Damping

[enumerate] Types of Damping

Static structural analysis of the wing

is done to find deformation, stress, and

strain induced in the wing structure.

Modal analysis

is done to find the natural

frequency of the wing to reduce the noise and avoid vibration.

internal wing structure

external wing

Two essential parts of a wing

spars

ribs

stringers

Parts of a internal wing structure

the Skin

External Wing

Ribs

give the shape to the wing section, support the skin (prevent

buckling), and act to prevent the fuel flowing around as the aircraft

maneuvers.

lowers amplitude

Damping _______ during vibration of structure.

Viscous Damping

the damping force is proportional to the speed.

Coulomb

The damping force

of _______ damping is constant.

Solid damping or hysteretic damping

is caused by internal friction when a solid is deformed.

steady-state resonance

stationary random excitation

Damping is of primary importance in controlling vibration response

amplitudes under conditions of _____ and ______.

Damping

also plays a crucial role in fixing the borderline

between stability and instability in many dynamical systems.

resistance to motion

Damping decreases vibrations by removing energy through

Rotating Equipment

For ______, damping is necessary to control vibrations

and prevent them from damaging the rotor, bearings or other components in

the machine.

Stiffness

is defined as the deflection resulting from a force load.

more

The longer the wing, the ____ the wingtip deflects as a result of a

certain load.

Shear stiffness

torsional stiffness

Two type of stiffness

shear stiffness

the ratio of applied shear force to shear deformation.

Torsional stiffness

the ratio of applied torsion moment to the angle of twist.

Axial Stiffness

Rotational Stiffness

Lateral Stiffness

Torsional Stiffness

Bending Stiffness

Shear Stiffness

[Enumerate] Types of Stiffness based on type of Deformation

Axial Stiffness

Resistance towards axial deformation due to the applied tension (or compression) is called

Rotational Stiffness

The ability of a material to resist rotation caused by applied Moment is called

Lateral Stiffness

The ability of a body to resist lateral deflection when a lateral force is applied.

Storey Stiffness

Lateral Stiffness is also called ____

Torsional Stiffness

The ratio of applied torsional moment to the angle of twist is called

Bending Stiffness

The resistance of a member against bending. For beams, flexural rigidity is considered as ____

Shear Stiffness

The ration of shear force to shear deformation

broken

deformed

Strength : Hard to be ___

Stiffness : Hard to be ___

Strength : Low

Stiffness : High

[Glass] It is difficult to bend it, but easy to break it

Strength : High

Stiffness : Low

[Spring] It is easy to compress it, but difficult to break it.

Complex Airplanes

means an airplane that has a retractable landing gear,

flaps, and a controllable pitch propeller, including airplanes equipped with

an engine control system consisting of a digital computer and associated

accessories for controlling the engine and propeller, such as a Full Authority

Digital Engine Computer (FADEC).

In plane stiffness

If the member is bending in its own plane it is called

out of plane bending

if it is bending out of its plane it is called