DYNAMICS OF VIBRATION: ATTENUATION

GROUP 4

VIBRATION

Refers to the oscillatory motion of a solid, fluid, or medium that occurs when its equilibrium condition is disturbed.

VIBRATION

It can also describe the periodic motion electromagnetic waves.

FREE VIBRATION

Occurs when a system oscillates naturally after an initial disturbance, with no external force continuously applied.

Longitudinal

Are vibrations in which the particles of the body move parallel to the direction of the wave or length of the body.

Transverse

Are vibrations in which the particles of the body move perpendicular to the direction of the wave or length of the body.

Torsional

Are vibrations in which the particles of the body undergo angular motion about the longitudinal axis of the body.

FORCED VIBRATION

Occurs when an external periodic force keeps acting on the system.

DAMPED VIBRATION

Occurs when vibration gradually decreases with time due to resistance like friction or air drag.

ATTENUATION

The waves are largest where they are formed and gradually get smaller as they move away. This decrease in size, or amplitude, of the waves with distance.

Seismic attenuation

Describes the energy loss experienced by seismic waves as they propagate.

Geometrical spreading

Wavefront radiating from a point source is distributed over a spherical surface of increasing size.

Absorption (anelastic attenuation)

This is the energy loss due to anelastic processes or internal friction during wave propagation.

Intrinsic/anelastic attenuation

Occurs mostly during shear wave motion associated with lateral movements of lattice and grain boundaries.

Scattering (elastic attenuation)

Attenuation is frequency-dependent and is strongly affected by scattering.

AMPLITUDE

Refers to the maximum amount of displacement of a particle on the medium from its rest position.

AMPLITUDE

Distance from rest to crest.

SCATTERING

Is the redirection of wave energy by heterogeneities in a medium, leading to reduced amplitude and distorted waveforms.

SCATTERING

K = 𝟐𝝅/𝒘𝒂𝒗𝒆𝒍𝒆𝒏𝒈𝒕h

K

Wave number

a

Size of the obstacle.

ka << 0.01 (quasi-homogeneous medium)

No significant scattering.

ka < 0.1 (Rayleigh scattering)

Produces apparent Q and anisotropy.

0.1 < ka 10 (Mie scattering)

Introduces strong attenuation and discernible scattering noise in the signal.

QUALITY FACTOR

Attenuation is measured by a dimensionless quality.

Higher Q

Indicates low energy loss.

Lower Q

Indicates high absorption and rapid signal weakening.

Temperature

Elevated temperatures reduce Q by increasing internal friction within minerals.

Porosity and Fluid Content

Rocks with higher porosity or fluid saturation generally exhibit lower Q values due to enhanced energy dissipation.

Frequency Dependence

Q is not constant; it varies with the frequency of the seismic wave.

Site Response Analysis

Q values are incorporated into models that predict how local geology will amplify or dampen earthquake shaking.

Structural Design

Understanding attenuation through Q helps in designing foundations and structures that can withstand prolonged vibrations.

Attenuation Factor

1/Q

E

Energy of seismic waves.

ΔE

Energy change per cycle.

Quality Factor

E/𝜟𝑬

Quality Factor

𝟐𝝅𝑬/𝜟E