The thesis is a competition of a scientific degree of candidate of technical Sciences on the specialty 05.01.01 – Applied geometry, engineering graphics. – Kyiv National University of Construction and Architecture. – Kyiv, 2021.
Theory of architectural acoustics of the XX century and modern one considers the spectacular halls from the point of view of reflections from the inner surfaces. Good acoustics is achieved due to enforcing of the direct reflected sound for listeners and diffusing sound on the surface of the audience. Existing methods of applied geometry in the study of reflections in halls, use simple reflective surfaces, such as plane and sphere, because characteristics of these surfaces are known and it is relatively easy to build graphically reflection from them.
Modern architecture requires the use of new forms of surfaces, not limited to the above mentioned. New sculptural forms have replaced the old simplicity. Thanks to the development of scientific and technological progress, computer technology, software which simplified methods of design in three-dimensional space, the architects can give free rein to their imagination and to build a complex curved shapes of surfaces. Modern geometry may offer a wide range of analytic surfaces with the investigated properties. These surfaces are described analytically and geometrically. Surfaces are used in various fields of science and technology, but due to the known properties can be used in architecture.
Architecture and acoustics adds the following to traditional tasks for engineer acoustics:
1. The use of complex forms of reflecting surfaces in the form of analytical surfaces of the 2nd degree, surfaces of revolution, translation surfaces, developable surfaces, cyclides, canal surfaces and others;
2. Construction of reflections from the surfaces;
3. The constructing of the reflecting surfaces of the 2nd and more complex, under the condition of interchangeability, when parameters of reflections are known;
4. The use of the transformed reflective surfaces that change their position and shape;
5. Reflective surfaces conjugation.
It is proposed to divide the reflecting surfaces into five groups with surfaces of normals along the lines forming in the form of a flat beam of parallel normals, a circular cone, a hyperbolic paraboloid, a flat beam of normals and a linear surface of the fourth order. Accordingly, the first group includes a plane and developable surface with normals along strait line generatrises, and as is the particular case, a cone and a cylinder. The second group combines oblique linear surfaces. The third includes canal surfaces, surfaces of revolution. In the surfaces of the fourth group, the normals in the form of a flat beam are created in some cases for second-order surfaces, or exist for curvilinear generatrises straight cylindrical surfaces, translation surfaces, and ruled surfaces. The fifth group consists of reflective surfaces of the general form of the second order. As known their analytical description, the properties of their cross sections and surface normals in these sections, appeared the opportunity to create equations of the surfaces of the reflected rays, to study their properties and classify them.
Еhere was the possibility of solving the inverse problem modeling reflective screens according to the specified parameters in the acoustic environment of the hall. There was created the model of inverse problem whith help of classification of the five groups of reflecting surfaces depending on the normal surface to the generating line was created, were created analytical descriptions and geometric analysis of normals surface for forming the reflecting surfaces in the context of five groups of systematization was created, analytical and geometrical description and analysis of the surface of reflected rays that was reflected from generatrises of surfaces of the 2nd and more complex was made, a method for solving the inverse problem of the allocation from congruence of reflected rays of a number of reflecting surfaces of a given group with known surface of reflected rays was developed, methods for acoustics calculation of religious halls was improved.
