High sensitivity non-contact method for dynamic quantification of elastic waves and strains in transparent media

Abstract

This paper presents time resolved quantitative evaluation of elastic stress waves in solid media by utilising an adaptation of the well-established laser Doppler vibrometry method. We show that the introduction of elastic stress waves in a transparent medium gives rise to detectable and quantifiable changes in the refractive index, which is proportional to stress. The method is tested for mechanical excitation at frequencies from 10 to 25kHz in an acrylic bar. This refractometric quantification can measure internal strains as low as 1x10 -11 . Additionally, finite element analysis is conducted to gauge the validity of the results. In the presented work an acrylic bar is used, this method however should be applicable to any transparent solid. Theoretical backgroundThe refractive index, n, of a medium is defined as;With c 0 : velocity of light in a vacuum and v: the velocity of light in the medium. The refractive index of a medium is influenced by stress, density and temperature of the host medium [7][8]. If we consider a simple adiabatic (no change in system temperature), isochoric (no change in system volume) event in a solid domain where there is a change in stress, this will result in a corresponding change in n. Solids will exhibit either a positive or negative linear relationship between n and stress. Monitoring the change in n (refractometry) can therefore be used to monitor stresses within solids. Probing dynamic events with traditional refractometry where n changes at frequencies in the kHz range is, as yet, not possible. What can be probed however, using Laser Doppler interferometry, is the variation in velocity, v, of light in the medium and therefore allowing stress to be estimated. The principle of the measurement technique is elegantly described by Nakamura et al.[11] and is reported here in Figure 1. Monochromatic laser light is directed through a region of the medium, of length a, in which the stress fluctuates. The laser exits the region and if reflected from a rigid wall, back through the region and into the interferometer. This modulated path length, Δa, appears identical to a physical displacement of the reflective rigid wall.(2)The output signal from a laser Doppler vibrometer (LDV) is the velocity of the apparent displacement of the rigid wall, as shown in [12].Where f: frequency of stress fluctuation and, v LDV : velocity from LDV, which is integrated with respect to time to give the apparent displacement, Δa, as shown in Eq 2. Most refracto-vibrometry is primarily based on using the method for either air or water pressure measurement [13][14][15][16][17], with some preliminary work conducted into stresses in solids by Zipser et. al. [18]. The principle of measurement however holds for any medium, not just air. Therefore we developed an experimental procedure that enables the quantitative investigation of elastic waves propagating in a solid.An empirical relation between the longitudinal strain, ε, of a block of polymethyl methacrylate (PMMA), and n, from Nazarov et al [10], is show...

Research Progress of Stress Measurement Technologies for Optical Elements

“…In 2014, Malkin et al proposed a highly sensitive, noncontact, quantitative measurement method for elastic wave and dynamic strain based on laser Doppler vibrometer [33]. A mechanical excitation test was carried out in an acrylic rod at the frequency of 10-25 kHz.…”

Damage detection in structural element through propagating waves using radially weighted and factored RMS

“…In the recent years the experimental investigations are carried out by Scanning Laser Doppler Vibrometer (SLDV) [11][12][13][14]. Contrary to most wave propagation-based measurement strategies, based on the employment of PZT transducer networks attached to or integrated within hosting structures and thus introducing undesired changes in the local stiffness and mass distributions, the SLDV technique is free of these issues.…”

Underwater Acoustic Wavefront Visualization by Scanning Laser Doppler Vibrometer for the Characterization of Focused Ultrasonic Transducers

“…The applicability of LDV to the field of non-destructive testing (NDT) and experimental modal analysis (EMA) has been discussed in [ 8 , 9 , 10 , 11 ]. Many research activities count on LDV for wavefront visualization in air [ 12 , 13 , 14 , 15 ], solids [ 16 ] and water-based experimentation [ 17 , 18 , 19 , 20 ]. LDV measurements in water pose more problems compared to the ones in air.…”