Abstract

The report examines the effects that occur when acoustic waves (the Berlage pulse) are applied to linearly elastic solids formed by a periodic structure. For a series of numerical experiments based on the finite element method, various types of lattice structures were modeled in the Fidesys strength analysis package. In these lattice structures, the parameters of the undulation of the bars forming the lattice structure, as well as the frequency of the applied pulse and the distance at which the sound insulation level was measured, were varied. The number of points forming cells of the lattice structure was also varied. For the calculation using the finite element method, grid convergence is established and a formula is found that allows predicting the level of accuracy for a given grid refinement. In the course of direct calculations, the presence of frequency filtering was established for some of the specified variable parameters. The analysis of dependences of variable parameters and sound insulation level is made. Also, based on a series of virtual experiments, a model predicting the level of sound insulation is built based on combining the following machine learning methods: Gradient Boosting, Random Forest, Gaussian Process. This algorithm was configured using the Python programming language and the scikit-learn library. The use of this algorithm allowed to reduce the time for calculating the sound insulation level by several hundred times, as well as to solve the inverse problem: specifying the necessary parameters of the lattice structure at a fixed level of sound insulation. As a development of the idea, further research of three-dimensional lattices, layered lattices, lattices with viscoelastic filler, lattices with artificially introduced deformations in the path of acoustic wave propagation, and variation of a larger number of lattice parameters is proposed. It is also possible to use high-order beam spectral elements to improve the accuracy of calculations instead of additional refinement of the finite element method grid.