Domain

Explanation

Vibrations

• The spatial & temporal variations of deformable bodies about the equilibrium states
• Reason for existence: due to material strength, stiffness & cohesion [free, unforced, impulsive vibration]; due to energy input from external (blast or excitations) or internal (fuel) sources [forced, excited vibration]
• Conservative vibrations: no energy loss/dissipation from the vibrating system, simpler problem solution, unrealistic but appropriate approximation for cases with other dominant factors
• Non-conservative vibrations: involves various models for energy loss/dissipation, realistic but solution more complex

Waves

• The spatial & temporal variations of a medium oscillating about the equilibrium state as a means of energy transfer
• Reason for existence: due to coexistence of the opposing forces of attraction and repulsion within a medium of transport subjected to a resultant unbalanced energy disturbance
• Types of waves:

1. Transverse waves: plane/direction of propagation (wave travel) perpendicular to plane/direction of vibration
2. Longitudinal waves: … parallel …

• Forms of waves:

1. Moving waves: all wave components vary periodically, spatially & temporally, seen to be travelling
2. Stationary/standing waves: all wave components static

• Temporal aspects of waves:

1. Periodic waves: wave oscillations are cyclic and predictable, composed of single or a few simple, stable sources
2. Nonperiodic/arbitrary waves: opposite, unpredictable, composed of multiple complex sources

• Periodic wave components:

1. Nodes: intersections of waves with the equilibrium states
2. Antinodes/loops: wave portions of maximum amplitude/displacement from the equilibrium states
3. Oscillation: to & fro motion/vibration
4. Phase: the angular displacement from the equilibrium position, measured either (0, 360) or (-180, 180)
5. Period, T: time for one complete oscillation or for the phase to change 360 degrees
6. Wavelength: distance along wave propagation plane/direction for one complete oscillation
7. Frequency, f: =1/T
8. Angular frequency/velocity, w: =2*pi/T =2*pi*f
9. Velocity, c: =f*wavelength

• Nonperiodic waves: modeling requires more variables as parameters of amplitude, wavelength, period, angular frequency and velocity changes continuously

Wave properties

• Medium-dependent: like water, waves' properties are altered according to the medium (container)
• Penetration: waves enter, travel through & leaves any medium including vacuum (for electromagnetic waves) due to the common ingredient of energy
• Reflection: angle of incidence = angle of reflection
• Refraction: change of wave propagation plane/direction due to the change from one medium to another (density changes), Snell's Law: sin i/sin r=c/v, both wavelength & velocity are changed
• Frequency invariant: waves are defined by their frequencies which do not change unless under interference
• Diffraction: spatial spreading of waves through openings/gaps or around objects (like radio waves), the longer the wavelength, the easier he diffraction; occurs due to slight curvature inherent to waves
• Interference: combined effects of waves that meet one another resulting in amplification, cancellation, phase changes, combined waves are new ones with own characteristic frequencies; realistic phenomenon

"The Dance of the Excited"

• Waves are inherently vibrations and vibrations are waves
• When two sinusoidal waves travelling in opposite directions in the same vibrating medium meet, the combined wave of vibration no longer travels but oscillate harmonically
• Thus, vibration in a given mode can be regarded as a standing wave
• Excitation: the vibration excitation forces can be modeled as waves transferring energy to the disturbed bodies
• Penetration: the excitation waves are refracted from the sources' medium into the disturbed bodies' medium
• Vibrating bodies: the penetrated, refracted excitation waves interfere with both the resident body waves as well as the later excitation waves to produce a vibrating cocktail or the dance of the excited as energy enters, passes through, alters and leaves the bodies