The paper outlines a mathematical model describing the vibrations of buildings and engineering structures with general-type passive shock-absorbers, rigid bodies, and ideal constraints. Two modifications of systems with passive shock absorbers are considered assuming constancy of their structure. These systems are studied numerically; the dynamic processes excited in them are compared Introduction. Considerable damage and numerous victims of earthquakes challenge researchers to look for ways of minimizing the effect of such phenomena. The design of buildings is improved to enhance their capability of resisting loads due to vibrations of the foundation (ground). Dynamic loads on various mechanical systems can significantly be reduced by using shock-absorbing devices with flexible, frictional, and other elements [7,[13][14][15]. Currently, various shock-absorbers are intensively used to reduce seismic loads on buildings and above-ground structures [2,9,11,16,17]. Relevant research efforts are important because of the destructive earthquake in Japan (Kobe, 1995) and, for example, the recent (2005)(2006) earthquakes in Indonesia, Thailand, China, Turkey, Iran, Russia (Koryakiya), Pakistan, and other regions of the globe. This problem is also of importance for Ukraine, especially for the Crimea, the Carpathians, and adjacent regions. There has been a recent resurgence of interest in new designs and structures of seismic dampers with high damping capabilities owing to rubber and plastic elements and coatings [11]. Despite the different designs of the passive shock-absorbers to be discussed below, their mathematical models in a general dynamic system have a stereotypic description for many modifications.This paper outlines a deterministic model of a system with general-type passive seismic dampers and compares two modifications of this kind of shock-absorbers to assess how they reduce the inertial effect of an earthquake on a shock-mounted body (building or engineering structure). All components of the system are considered rigid. The translational motion exciting the system is considered kinematic and is specified as time-dependent accelerations. It is adopted that the maximum accelerations range from 0.2 to 0.4 m/sec 2 , the duration of excitation from 10 to 40 sec, and the dominant periods in the excitation spectrum from 0.1 to 2 sec [4,6]. The constrains are assumed ideal, i.e., the work done by constraint forces against a possible displacement is zero. Moreover, the constraints among bodies are considered to be ideal, holonomic, and bilateral. As possible examples, we will use the systems shown in Fig. 1 [2 , 8, 9, 17], where component 1 is the body (foundation) undergoing oscillatory motions with seismic acceleration W x x = && 1 , and component 2 is the body (engineering structure) subject to the dynamic load from the foundation. The contacting surfaces of bodies 1 and 2 (Fig. 1a) or bodies 2 and 3 (Fig. 1b) are represented by circular arcs of radii R and r (in the plane of the figure); other curves can also be u...
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