Search

Introduction. The widespread use of piezoelectric materials in various industries stimulates the study of their physical characteristics and determines the urgency of such research. In this case, modal analysis makes it possible to determine the operating frequency and the coefficient of electromechanical coupling of piezoelectric elements of various devices. These indicators are of serious theoretical and applied interest. The study was aimed at the development of numerical methods for solving the problem of determining resonance frequencies in a system of elastic bodies. To achieve this goal, we needed new approaches to the discretization of the problem based on the finite element method and the execution of the software implementation of the selected method in C# on the .net platform. Current solutions were created in the context of the ACELAN-COMPOS class library. The known methods of solving the generalized eigenvalue problem based on matrix inversion are not applicable to large-dimensional matrices. To overcome this limitation, the presented scientific work implemented the logic of constructing mass matrices and created software interfaces for exchanging data on eigenvalue problems with pre- and postprocessing modules.Materials and Methods. A platform was used to implement numerical methods .net and the C# programming language. Validation of the research results was carried out through comparing the values found with solutions obtained in well-known SAE packages (computer-aided engineering). The created routines were evaluated in terms of performance and applicability for large-scale tasks. Numerical experiments were carried out to validate new algorithms in small-dimensional problems that were solved by known methods in MATLAB. Next, the approach was tested on tasks with a large number of unknowns and taking into account the parallelization of individual operations. To avoid finding the inverse matrix, a modified Lanczos method was programmatically implemented. We examined the formats for storing matrices in RAM: triplets, CSR, СSC, Skyline. To solve a system of linear algebraic equations (SLAE), an iterative symmetric LQ method adapted to these storage formats was used.Results. New calculation modules integrated into the class library of the ACELAN-COMPOS complex were developed. Calculations were carried out to determine the applicability of various formats for storing sparse matrices in RAM and various methods for implementing operations with sparse matrices. The structure of stiffness matrices constructed for the same task, but with different renumbering of nodes of a finite element grid, was graphically visualized. In relation to the problem of the theory of electroelasticity, data on the time required to perform basic operations with stiffness matrices in various storage formats were summarized and presented in the form of a table. It has been established that the renumbering of grid nodes gives a significant increase in performance even without changing the internal structure of the matrix in memory. Taking into account the objectives of the study, the advantages and weaknesses of known matrix storage formats were named. Thus, CSR was optimal when multiplying a matrix by a vector, SKS was optimal when inverting a matrix. In problems with the number of unknowns of the order of 103, iterative methods for solving a generalized eigenvalue problem won in speed. The performance of the software implementation of the Lanczos method was evaluated. The contribution of all operations to the total solution time was measured. It has been found that the operation of solving SLAE takes up to 95% of the total time of the algorithm. When solving the SLAE by symmetric LQ method, the greatest computational costs were needed to multiply the matrix by a vector. To increase the performance of the algorithm, parallelization with shared memory was resorted to. When using eight threads, the performance gain increased by 40–50%.Discussion and Conclusion. The software modules obtained as part of the scientific work were implemented in the ACELAN-COMPOS package. Their performance for model problems with quasi-regular finite element grids was estimated. Taking into account the features of the structures of the stiffness and mass matrices obtained through solving the generalized eigenvalue problem for an electroelastic body, the preferred methods for their processing were determined.

A study of the changes in psychophysical function of the human body before and after relaxation sessions and acupuncture application has been conducted. The impact of relaxation sessions on psychophysical performance was studied on a group of university students and postgraduates aged between 18 and 30 years old; the impact of an acupuncture session course - on a group of subjects of a broad age range between 14 and 72, as they underwent rehabilitation therapy for their supportive locomotive apparatus disorders. The recording techniques used included electroencephalography (EEG), psychomotor reaction recording, minute-long time span accuracy reproduction; TST technique (Tactile Solar Test) of meridian and microsystem examination The results of this study suggest that relaxation sessions contribute to the enhancement of neurodynamical performance and mental activity efficiency. After the acupuncture therapy, relaxation effect, and restored tactile sensation on the meridians and microsystems was noted. A conclusion has been made that relaxation sessions and acupuncture may be used to improve psychophysical function.

Within-pair similarity of topographic maps of the cortical electrical activity was studied in 11 monozygotic pairs of twins (MZ) and 20 genetically unrelated persons (UP) during rest and solving four mental tasks. During rest similarity of topographic maps higher in MZ in comparison with UP. We showed that no specific frequency band influenced formation of high similarity between MZ maps. The maximal similarity between MZ maps was seen in the anterior zones of the left hemisphere and in parieto-temporal areas of the right hemisphere. Differences between MZ and UP maps were revealed both in the anterior areas of the left hemisphere and parieto-temporal areas of the right hemisphere, but they were most pronounced in the right hemisphere. The data obtained lead to the conclusion that genetic factor influences not only the separate EEG components, but the system organization of the cortical processes. This was confirmed by the results of topographic similarity analysis carried out for various tasks, i.e. similarity coefficients attained the level of significance only for the right-hemispheric tasks (simultaneous analysis of non-verbal material).