Mathematical Algorithm for Estimating the Acoustic Conductivity of the Wavefront for Verification of a Diagnostic Model in an Analysis of Defects in a Polymer Composite Material

Abstract

The modal analysis is considered as one of the lines of technical diagnostics for evaluating the quality of polymer composite materials (PCMs). It allows one to link the structure of modal characteristics of PCM element base in the amplitude-frequency domain. In the course of modal analysis, the complex construction of PCM as a heterogeneous material is transformed into a set of easy-to-understand independent systems with one degree of freedom. This structural approach is used to analyze the structure of PCM components. A laser is used to form an external action, with the help of which PCM components can form a wave field when vibrations pass through its thickness. Vibrations and deformations of PCM structural elements under a mechanical excitation are considered as the intrinsic vibration forms (vibration modes) of PCM elements -the filler and matrices. High-frequency laser actions extracts a constant wavefront, which is used for constructing an algorithm for recognition of the structure of PCM, including the detection of possible defects, such as changes in its density and various stratifications. To assess the technical condition of structural elements of PCM, a mathematical model was developed to assess the effect of defects on passage of a wave and the excitation of modal vibrations by the element base of PCM. The mathematical algorithm for estimating the acoustic conductivity of the wavefront, together with experimental data, was used for constructing a wave diagnostics algorithm. It made it possible to create an algorithm for a technical diagnostics of PCM elements. An experiment was conducted on the laser action on a carbon fiber panel with specially created defects. The frequency values found in various zones of carbon fiber showed a qualitative and quantitative change in the structure of PCM. It is shown that, to construct an effective model for diagnosing the technical condition of PCM elements, more experimental studies are required.

Modeling the stress-strain state of variable-thickness composite shells and plates

“…We integrate equation (1) over 𝑋 3 , setting 𝛼 = 3, 𝛽 = 1, 𝛾 = 2, and using formulas (4), with boundary conditions (11)…”

“…Variable thickness can be used to increase strength in specific areas of the wall or bottom [1], without unnecessary mass cost to the rest of the structure. In addition, variable thickness can occur in the presence of object defects [2,3], for example, when a structure is made during curing [4,5]. Accounting for variable thickness can improve the quality of the product and reduce the cost of manufacturing structures.…”

“…We obtain the fourth equilibrium equation with moments by multiplying (1) by 𝑋3 for 𝛼 = 1, 𝛽 = 2, 𝛾 = 3 and then integrating it over 𝑋 3 :…”

Numerical analysis of wave processes under high-speed impact on an object from CFRP

“…At the same time, the speed of propagation of waves varies in different directions, as well as the speed of propagation of longitudinal and transverse waves. The study of elastic wave propagation in CFRP contributes to the development of methods of non-destructive testing of finished products [7,8]. However, in addition to these features, it is important to know that the impact velocity in most cases exceeds the speed of sound in the material, which leads to a qualitative difference in the results.…”