DESIGN OPTIMIZATION OF FOUNDATION FOR ROTATING MACHINERY AGAINST STANDING-WAVE VIBRATION IN A BUILDING

Abstract. This paper deals with the problem of optimum design of a foundation for rotating machinery on a storey of a building with a view to minimize the level of standing-wave vibration in the building. The foundation is usually designed as a base INTRODUCTION Rotating machinery in buildings is usually applied in central heating and ventilation systems, and larger machinery of this type including a pump is normally mounted on a foundation, which is usually designed as a base plate for the machinery with some resilient mounts fixed to the bottom of the base plate and supported by the floor of the storey. Due to variable service speeds and the existence of non-balanced masses, the rotating machinery may be considered a source that within a given range of excitation frequencies excites forced vibration of the foundation, and thereby the floors and walls, etc., of the building. The transmission of such vibrations through the building may result in undesirable sound emission and unsatisfactory comfort conditions for the people in dwellings and offices of the building. Aside from that, vibrations increase safety hazards in machinery, buildings and installations. The primary goals of vibration insulation are to restrict the detrimental effects of vibrations on people to within reasonable limits, and to protect sensitive apparatus and safety systems from excessive stresses from vibrations. Problems of design optimization of machinery foundations against vibration have been mainly studied from two aspects: 1. Free vibration design, also termed as frequency design. This aims at keeping the operating frequency as far away as possible from the eigenfrequencies of the machinery mounting system by adjusting the mounting system in order to avoid resonance. It is usually realized by maximization of the fundamental eigenfrequency or frequency gaps between two consecutive eigenfrequencies of the machinery mounting system. 2. Forced vibration design. The machinery mounting system is assumed to be subjected to a time-varying unbalanced mechanical loading, and this system will be designed by minimizing a chosen cost function describing the level of vibration response or transmission. The problem of forced vibration design optimization of the installation systems of machinery in buildings has been extensively researched under the assumption of a rigid supporting structure When rotating machinery is to be mounted on building floors rather than directly on a soil foundation, suitable resilient mounts should be provided as vibration isolation elements under the machine with a view to reduce the transmission of vibration. The design optimization of machinery mounting systems is studied in this paper. The system consists of a rotating, unbalanced machine as vibration source, a mounting system as isolator, and a flexible floor as receiver. By assuming a simple time harmonic excitatio

Szerkezetek topológiai optimalizálásának új elméletei és módszerei számítástechnikai nehézségek megoldására = Topology optimization of structures - new theories and methods for overcoming computational difficulties

A kutatás során újszerű elméleti megállapításokat, új, numerikus vizsgálatokra alkalmas számítási módszereket, hatékony, ipari alkalmazásra alkalmas algoritmusokat és számítógépes programokat, tesztfeladatokat dolgoztunk ki, amelyek a következő eredményekre vezettek: (A) Új eljárásokat hoztunk létrehozása a "sakktábla mintázat" néven ismert számítási hiba elkerülésére és a "nagyság szabályozás" vizsgálatára. Ezek: másodlagos végeselemes hálózás, új büntetőfüggvények bevezetése. (B) Továbbfejlesztettük a gradiens nélküli u.n. SERA (Sequential Element Rejections and Admissions = sorozatos véges elem eltávolítások és beillesztések) módszert egy szigorú "rigorózus" elmélet alapján különböző kombinált mellékfeltételek és többszörös terhelés esetére és a helyes Lagrange szorzókat alkalmaztuk intuitív súlyozási faktorok helyett. (C) Új módszert dolgoztunk ki a szinguláris topológiák által okozott számítástechnikai nehézségek elkerülésére a Prager és Rozványi által kifejlesztett "layout theory" alapján. (D) Az u.n. SIMP (Solid Isotropic Material with Penalization for intermediate density = tömör izotróp anyag a közbenső sűrűségek büntetésével) módszert új területeken alkalmaztuk. Az eredményeket nemzetközi szakfolyóiratokban (kb. évente 2-3), és hazai és nemzetközi konferenciákon (kb. évente 3-4) ismertettük. Az eredmények egy részét a doktorandusz képzésben is felhasználtuk. | During the research new theories, new numerical methods, efficient algorithms and computer programs with test problems were developed what are applicable for the industry. The detailed result are as follows: (A) Novel procedures were developed for the avoidance of the discretization error called 'checkerboard pattern' and for size control in optimal topologies. These are in details: introducing the secondary meshing of the ground elements, very efficient new type of penalty functions. (B) The gradientless method SERA (Sequential Element Rejections and Admissions) was improved for multiconstraints and multiloading cases by the use of rigorous formulation instead of heuristic one. (C) Based on the 'layout theory' of Prager and Rozvany a new method was elaborated for the avoidance of computational difficulties caused by singular topologies. (D) The so called SIMP (Solid Isotropic Material with Penalization for intermediate density) method was applied in new areas. The results were published in international journals (yearly 2-3) and conferences (yearly 3-4). The elaborated theories are used in PhD. education