Discussion: “The Wave Method for Solving Flexural Vibration Problems” (Jones, R. P. N., 1954, ASME J. Appl. Mech., 21, pp. 75–80)

Abstract In this paper the use of normal mode and wave methods in problems of dynamic loading on beams is discussed, and the methods are applied to simple problems of uniform beams under a suddenly applied load. For these problems, mathematically exact results have been obtained, enabling a comparison to be made between the two types of solution. Experimental results for these problems also have been obtained, using an apparatus which releases the beam from a deflected position, and displays a record of the resultant response on an oscillograph screen, using a time base synchronized with the release of the beam. Good agreement is obtained between the experimental and theoretical results, and it is shown that the wave solution is useful for determining the initial response of the beam, while the subsequent response can be better obtained from the normal-mode solution.

Download Full-text

Evaluation of the accuracy of reconstruction of the electrophysical and geometric parameters of multilayer dielectric coatings by the multi-frequency radio wave method of a slow surface electromagnetic waves

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2020-8-51-58 ◽

2020 ◽

pp. 51-58

Author(s):

Aleksandr I. Kazmin ◽

Pavel A. Fedjunin

Keyword(s):

Radio Wave ◽

Noise Level ◽

Electromagnetic Waves ◽

Dielectric Materials ◽

Geometric Parameters ◽

Experimental Investigations ◽

Wave Method ◽

Dielectric Coatings ◽

Surface Electromagnetic Waves ◽

Multilayer Dielectric

One of the most important diagnostic problems multilayer dielectric materials and coatings is the development of methods for quantitative interpretation of the checkout results their electrophysical and geometric parameters. The results of a study of the potential informativeness of the multi-frequency radio wave method of surface electromagnetic waves during reconstruction of the electrophysical and geometric parameters of multilayer dielectric coatings are presented. The simulation model is presented that makes it possible to evaluate of the accuracy of reconstruction of the electrophysical and geometric parameters of multilayer dielectric coatings. The model takes into account the values of the electrophysical and geometric parameters of the coating, the noise level in the measurement data and the measurement bandwidth. The results of simulation and experimental investigations of reconstruction of the structure of relative permittivitties and thicknesses of single-layer and double-layer dielectric coatings with different thicknesses, with different values of the standard deviation (RMS) of the noise level in the measured attenuation coefficients of the surface slow electromagnetic wave are presented. Coatings based on the following materials were investigated: polymethyl methacrylate, F-4D PTFE, RO3010. The accuracy of reconstruction of the electrophysical parameters of the layers decreases with an increase in the number of evaluated parameters and an increase in the noise level. The accuracy of the estimates of the electrophysical parameters of the layers also decreases with a decrease in their relative permittivity and thickness. The results of experimental studies confirm the adequacy of the developed simulation model. The presented model allows for a specific measuring complex that implements the multi-frequency radio wave method of surface electromagnetic waves, to quantify the potential possibilities for the accuracy of reconstruction of the electrophysical and geometric parameters of multilayer dielectric materials and coatings. Experimental investigations and simulation results of a multilayer dielectric coating demonstrated the theoretical capabilities gained relative error permittivity and thickness of the individual layers with relative error not greater than 10 %, with a measurement bandwidth of 1 GHz and RMS of noise level 0,003–0,004.

Download Full-text