AE02.pdf

# Normal mode theory has also been applied to the

• No School
• AA 1
• 82

This preview shows page 72 - 74 out of 82 pages.

experiment. Normal mode theory has also been applied to the simulation of acoustic emission hits in plates when the receiver is in the far field. 136 Several aspects of classical wave theory have been applied to acoustic emission testing in the field. 140 Diffuse Wave Fields In most acoustic emission tests, the motion at the detector results from a large number of waves that have been reflected several times before arriving at the detector. The mean length of all the paths that a wave can travel without encountering a surface is given by the expression: 141 (115) where L is the mean travel length (meter); S is the surface area (square meter) of the medium; and V is the volume (cubic meter) of the medium. Consider as an example a compact tension test sample with dimensions 50 × 50 × 25 mm (2 × 2 × 1 in.) and a mean travel length L of 25 mm (1 in.). If the medium is steel or aluminum, the maximum time between reflections is about 4 μs for longitudinal waves and 8 μs for shear waves. In a medium this size, the detected acoustic emission signal reaches its peak value in about 100 μs and has a duration on the order of 1 ms. The motion at the detector at the peak (100 μs) consists of waves reflected at least twelve times and as many as twenty-five times on the average. Because of the large number of reflections that the typical wave undergoes before arriving at the detector and the large number of possible paths from the source to the detector, the typical motion at the detector consists of many waves arriving from many directions. This is one of the factors complicating the analysis of wave motion associated with acoustic emission hits. The complexity of this situation can be reduced considerably if it is assumed that the waves propagating in the medium L V S = 4 c c v p 2 = 2 1 97 Fundamentals of Acoustic Emission Testing

Subscribe to view the full document.

(1) are large in number, (2) are distributed uniformly in orientation and (3) are uncorrelated with respect to phase. Such a wave field is called a diffuse wave field . For sound waves in fluids, this concept gives rise to a branch of acoustics called geometric acoustics. 141 Diffuse Wave Field Equations Using the assumptions given above and neglecting contributions from surface waves, it can be shown 142 that the time average of the acoustic energy per unit volume (energy density) is: (116) where ξ 1 and ξ 2 are energy densities (joule per cubic meter) of the longitudinal and transverse waves respectively. It can further be shown that each of these energy densities is independent of position in the medium. The equations of motion of the medium (assumed to be homogeneous and isotropic) then reduce: (117) and: (118) The terms P 1 and P 2 are the acoustic powers generated by the source in the form of longitudinal and transverse waves respectively. The terms γ 12 and γ 21 are the diffuse field power reflection coefficients (defined as the fraction of incident diffuse field longitudinal or transverse wave power converted to transverse or longitudinal waves caused by mode conversion at the boundary of the medium). The terms ξ 1 and ξ 2 are the
• Fall '19
• Nondestructive testing, Acoustic Emission, Acoustic Emission Testing

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern