The Influence of the Friction-Sliding Coefficient of Support Structures and Parameters of Seismic Actions on Reactions and Reliability of Structures with Seismic Protection

The study is focused on a structure represented by a multimass elastic cantilever rod with dry friction seismic isolation elements in the support part under a horizontal random impact of a seismic type. The paper aims at investigating the seismic reaction and selecting optimal parameters of the seismic isolation system involving random impact characteristics, limit parameters of the structure, and the seismic isolation system. The researches are based on dynamic computations; the impacts and fluctuations of the system are random processes. The dynamic model of the structure with the considered seismic isolation is presented in the form of a cantilever rod with concentrated masses; a system of differential equations describing the displacement of the structure with the seismic-isolating sliding elements at the level of the top of the foundations is compiled; and a seismic impact is modeled in the form of a nonstationary random process. An algorithm is developed to integrate the system of differential equations of motion and to determine the statistical characteristics of the seismic reaction and reliability indicators of the structures with the seismic isolation. A method aimed at evaluating effectiveness of the seismic isolation system and selecting its rational parameters is suggested. We developed the computational dynamic model of the structure with the seismic-isolating sliding elements installed at the top level of the foundations, and elastic and rigid limiters for the movement of the sliding supports. This model is made in the form of a multimass cantilever rod that takes into account the relative movements of the masses and the stops of the system on the movement limiters. The structure’s movement under a seismic impact is described by a system of differential equations that takes into account the conditions of transitions of the structure from the state of sticking to the state of sliding and vice versa. The statistical characteristics of the seismic reaction and the reliability indicators of the structure in the process of vibrations are determined for different values of the maximum acceleration of the ground vibration, the prevailing period of impact, the number of masses in the calculated model and the coefficient of friction-sliding of the support elements. The influence of the impact parameters and the system on the efficiency of the seismic isolation of the structures with sliding elements is estimated. The proposed approach to selecting the optimal parameters of the seismic isolation system can be used as a research method aimed at improving efficiency of systems with different design options for seismic isolation of structures.

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Settlement Researches of Seismically Isolated Buildings

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.752-753.599 ◽

2015 ◽

Vol 752-753 ◽

pp. 599-604 ◽

Cited By ~ 1

Author(s):

Vladimir I. Andreev ◽

O.V. Mkrtychev ◽

Guram A. Dzhinchvelashvili ◽

A.A. Bunov

Keyword(s):

Software Package ◽

Seismic Isolation ◽

Explicit Scheme ◽

Direct Integration ◽

Isolation System ◽

Motion Equations ◽

Seismic Insulation ◽

Rubber Bearings ◽

Seismic Impact ◽

Nonlinear Nature

The paper studies the efficiency of seismic isolation system in the form of rubber-metal bearings with different height buildings at multicomponent seismic impact. As an example, seismically insulated monolithic reinforced concrete 5-, 9-and 16-storey buildings are considered. The solution of the problem is obtained by a direct integration of the motion equations for an explicit scheme in the software package LS-DYNA. The calculation is performed considering nonlinear nature of rubber bearings. The analysis of the effectiveness of buildings with seismic insulation and without it is performed.

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The Seismic Response Investigation on the Multi-Storey Buildings with Seismically Insulating Rubber-Metal Supports

Materials Science Forum ◽

10.4028/www.scientific.net/msf.931.362 ◽

2018 ◽

Vol 931 ◽

pp. 362-367

Author(s):

Khadjimurad M. Omarov ◽

Abakar D. Abakarov

Keyword(s):

Differential Equations ◽

Random Process ◽

Seismic Response ◽

Seismic Isolation ◽

Seismic Action ◽

System Of Differential Equations ◽

Metal Supports ◽

Isolation Systems ◽

Seismic Isolation Systems ◽

Storey Building

The buildings of various constructive solutions with seismic isolation and without seismic isolation are considered. The system of differential equations of a multi-storey building motion with seismic isolating rubber-metal supports is presented. The graphs of the seismic response of 5, 9 and 12-storey buildings with seismic insulating rubber-metal bearings are obtained as well as with seismic action in the form of the unsteady random process. The effectiveness of seismic isolation systems with rubber-metal bearings with lead core and without it is estimated.

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A Dynamic Model of a Belt Driven Electromechanical XY Plotter Cutter

Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2012-71004 ◽

2012 ◽

Cited By ~ 1

Author(s):

Joseph V. Prisco ◽

Philip A. Voglewede

Keyword(s):

Differential Equations ◽

Dynamic Model ◽

Motion Control ◽

Development Time ◽

Arts And Crafts ◽

Performance Parameters ◽

System Of Differential Equations ◽

Electromechanical Model ◽

Governing System

Currently, models for XY plotter cutters specific to industrial and arts and crafts applications are not publicly available. This paper mathematically models the XY motion control for a commercial plotter cutter. In this particular application, the Y motion is controlled by media feed and the X motion is controlled by a gantry arm. A dynamic, electromechanical model consisting of a governing system of differential equations for the gantry arm is developed and simulated using Matlab. Once the model is developed, it will be used to decrease development time and optimize performance parameters.

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Dynamic Model of Growing File-Sharing P2P Network

Modeling and Analysis of Information Systems ◽

10.18255/1818-1015-2019-3-351-359 ◽

2019 ◽

Vol 26 (3) ◽

pp. 351-359

Author(s):

Alexandra I. Kononova ◽

Larisa G. Gagarina

Keyword(s):

Differential Equations ◽

Dynamic Model ◽

Information Exchange ◽

Equilibrium Points ◽

Phase Portraits ◽

System Of Differential Equations ◽

First Approximation ◽

The Stability ◽

General Provision ◽

Exchange Network

In this work, the model of development of the P2P file exchange network organized by a torrent tracker is considered. The model is constructed on the basis of ordinary differential equations. The phase variables describing a status of a torrent tracker and the network organized by it (in first approximation is the number of the users of the tracker who are actively participate in information exchange, and the number of active torrents) are defined, the factors influencing the change of users number and the number of torrents are analyzed. On the basis of the analysis the system of differential equations, in first approximation describing evolution of the file exchange network organized by the torrent tracker — a hard dynamic model of evolution of the torrent tracker is written. Equilibrium points of hard model of evolution of the tracker are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a hard model of evolution of the torrent tracker are described. The phase portrait of the hard model is represented. On the basis of the analysis of the hard model the system of differential equations describing evolution of a file exchange network with accounting of dependence of new users inflow intensity on a total quantity of potential audience of the torrent tracker, and also dependences of speed of torrents extinction on the number of users falling on one torrent — a soft dynamic model of evolution of a torrent tracker is written. Equilibrium points of a soft model of tracker evolution are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a soft model of evolution of the torrent tracker are described. Phase portraits of each configuration are represented. The ratio of parameters necessary for the stability of the tracker a stable status is received. The influence of different administrative measures on a stock of the tracker stability in whole is analyzed. The need of support of torrents by administration at highly specialized torrent trackers with small potential audience is shown.

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CONSTRUCTION OF DYNAMIC INSTABILITY ZONES FOR HIGH STUCTURES UNDER SEISMIC IMPACT

Mechanics And Mathematical Methods ◽

10.31650/2618-0650-2020-2-2-42-50 ◽

2020 ◽

Vol 2 (2) ◽

pp. 42-50

Author(s):

V Fomin ◽

◽

І Fomina ◽

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Coordinate System ◽

Mechanical System ◽

Dynamic Instability ◽

Vertical Component ◽

System Of Differential Equations ◽

High Rise ◽

Concentrated Masses ◽

Seismic Impact

Seismic impacts create the possibility of parametric resonances, i.e. the possibility of the appearance of intense transverse vibrations of structure elements (in particular, of high-rise structures) from the action of periodic longitudinal forces. As a design model of a high-rise structure, a model is used which adopted in the calculation of high-rise structures for seismic effects, - a weightless vertical rod (column) rigidly restrained at the base with a system of concentrated masses (loads) located on it (Fig. 1). By solving the differential equation of the curved axis influence function for a rod is constructed by means of which influence coefficients are determined for the rod points, in which the concentrated masses are situated. These coefficients are elements of the compliance matrix . Next, the elements of the stiffness matrix are determined by inverting the matrix . Using a diagonal matrix of the load masses and matrix a system of differential equations of free vibrations of a mechanical system, consisting of concentrated masses, is constructed, and the frequencies and forms of these vibrations are determined. From the vertical component of the seismic impact, its most significant part is picked out in the form of harmonic vibrations with the predominant frequency of the impact. Column vibrations are considered in a moving coordinate system, the origin of which is at the base of the column. The forces acting on the points of the mechanical system (concentrated masses) are added by the forces of inertia of their masses associated with the translational motion of the coordinate system. The forces of the load weights and forces of inertia create longitudinal forces in the column, periodically depending on time. Further, the integro-differential equation of the dynamic stability of the rod, proposed by V. V. Bolotin in [8], is written. The solution to this equation is sought in the form of a linear combination of free vibration forms with time-dependent factors. Substitution of this solution into the integro-differential equation of dynamic stability allows it to be reduced to a system of differential equations with respect to the mentioned above factors with coefficients that periodically depend on time. For some values of the vertical component parameters of the seismic action, namely the frequency and amplitude, the solutions of these equations are infinitely increasing functions, i.e. at these values of the indicated parameters, a parametric resonance arises. These values form regions in the parameter plane called regions of dynamic instability. Next, these regions are being constructed. A concrete example is considered.

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The problem of digitalization of the dynamic input-output model

Economic Analysis Theory and Practice ◽

10.24891/ea.19.5.946 ◽

2020 ◽

Vol 16 (5) ◽

pp. 946-972

Author(s):

E.L. Toroptsev ◽

A.S. Marakhovskii ◽

R.R. Duszynski

Keyword(s):

Economic Growth ◽

Differential Equations ◽

Dynamic Model ◽

System Of Differential Equations ◽

Input Output ◽

Statistical Research ◽

Output Analysis ◽

Structural Dynamic ◽

The Cauchy Problem ◽

First Time

Subject. The article addresses the digitalization of the dynamic model of inter industry balance. Objectives. We focus on developing our own statistical research base for input-output analysis, structural forecasting, sustainability, economic dynamics and economic growth. Mathematically, the study is formalized by the Cauchy problem for ordinary differential equations. Methods. The methodology components include theoretical and practical bases of the systems, statistical, input-output, and structural dynamic analysis. Results. Based on official statistics, we solved the problem of digitalization of the dynamic model of input-output balance, written in the form of a system of differential equations. For the first time, this model was transferred from a set of purely theoretical structures to a class of computable models. We developed a sequence of coordinated actions and calculations, which serve as a methodology for the said transfer. We also devised and presented the elements of our own statistical research base. Conclusions. The quantitative measurement of the dynamic inter-industry model in the form of a system of differential equations opens up broad perspectives on the sustainability of macroeconomics, its structural readiness for expanded reproduction, i.e. economic growth. The model can be used both independently and in combination with equilibrium and other agent-oriented models.

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Predicting the end-stage of the COVID-19 epidemic in Brazil

10.1101/2020.05.28.20116103 ◽

2020 ◽

Author(s):

W.E. Fitzgibbon ◽

J.J. Morgan ◽

G.F. Webb ◽

Y. Wu

Keyword(s):

Differential Equations ◽

Dynamic Model ◽

Model Output ◽

System Of Differential Equations ◽

Asymptomatic Infections ◽

Infectious Stage ◽

End Stage

AbstractWe develop a dynamic model of a COVID-19 epidemic as a system of differential equations. The model incorporates an asymptomatic infectious stage and a symptomatic infectious stage. We apply the model to the current COVID-19 epidemic in Brazil. We compare the model output to current epidemic data, and project forward in time possible end-stages of the epidemic in Brazil. The model emphasizes the importance of reducing asymptomatic infections in controlling the epidemic.

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A Dynamic Model of Insurgency: The Case of the War in Iraq

Peace Economics Peace Science and Public Policy ◽

10.2202/1554-8597.1120 ◽

2008 ◽

Vol 14 (2) ◽

Cited By ~ 11

Author(s):

Larry Blank ◽

Carl E. Enomoto ◽

Douglas Gegax ◽

Thomas McGuckin ◽

Cade Simmons

Keyword(s):

Differential Equations ◽

Dynamic Model ◽

Policy Implications ◽

System Of Differential Equations ◽

Combat Effectiveness ◽

War In Iraq ◽

The U.S

This paper uses a system of differential equations to describe the insurgency in Iraq. The system has four possible outcomes or cases: (1) The U.S.-led coalition increases in size and the number of attacks by the insurgents increases. (2) The size of the U.S.-led coalition decreases and the number of attacks by insurgents decreases. (3) The size of the U.S.-led coalition increases and the number of insurgent attacks decreases. (4) The size of the U.S.-led coalition decreases and the number of insurgent attacks increases. Which case is relevant depends on the recruitment rates of the U.S.-led coalition and insurgents as well as the combat effectiveness of both sides. Policy implications are provided.

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