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عدد المساهمات : 19001 التقييم : 35505 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: بحث بعنوان Two Notes About Random Vibration Equations الإثنين 09 أغسطس 2021, 1:55 am | |
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أخواني في الله أحضرت لكم بحث بعنوان Two Notes About Random Vibration Equations Reza Habibi Department of Statistics Central Bank of Iran, Tehran, Iran Hamed Habibi Department of Mechanics KNT University, Tehran, Iran Hamid Habibi Department of Airworthiness Civil Aviation Organization, Tehran, Iran
و المحتوى كما يلي :
Abstract Two notes concerning the linear random vibration equations are given. The first note studies the solution of equations under general random excitation processes. The second one considers the measurement error problem. Keywords: Excitation processes; Langevin equation; Measurement error; Random vibration; Stochastic differential equation Introduction. Random vibration equations appear in many examples of applications. A spring mass system effected by a stochastic excitation process, car vibrations on the road, body vibration of airplane in flight and pendulum with stochastic damping, all, are examples of random vibrated systems. This topic has a history in engineering. Ozaki (1980) presented the non linear time series models for non linear random vibrations. Ricciardi (1994) surveyed random vibration of a beam under moving load. Grue and Oksendal (1997) considered stochastic forced oscillations of a spring mass system with time dependent and stochastic damping. Iwankiewicz (2002) studied dynamic response of non linear systems to random trains of non overlapping pulses. Iwankiewicz and Sotera (2004) considered non linear oscillator under random renewal driven trains of impulses. Henderson and Plaschko (2006) studied a stochastic pendulum with stochastic excitation and damping forces. Linear random vibrations constitute a rich family for analyzing the mechanical phenomena, for example, Allen (2007) surveyed a single degree of freedom spring mass system with a random excitation process. Stochastic differential equations (SDE) are valuable tools for analyzing the random vibration observations. There are a lot of good literatures for analyzing SDE’s, see Kloeden and Platen (1999), Oksendal (2000) and Kutoyants (2004) among the others. The SDE has been applied to model phenomena in other fields of engineering, for example, it is used to model the fatigue damage of materials or fluid mechanical turbulence (see Henderson and Plaschko, 2006). These are not the purpose of the current paper. Linear random vibrations are supposed to follow the stochastic linear differential equation x¨t + αx˙ t + βxt = ft, where xt denotes displacement, α is damping term, β a real constant. The ft is stochastic excitation process. For example, in one degree of freedom spring mass system, we have mx¨t + bx˙ t + kxt = vft, where m, b and k are the mass, damping coefficient and spring constant, respectively. Parameter v2 is the expectation of squared momentum (v > 0). In this case, ftdt = dWt where Wt stands for Wiener process. This equation is a form of stochastic Lienard equation see Allen (2007) pages 156-158. The general form of vector SDE’s in this paper is given by dz∗ t = A∗z∗ tdt + B∗dUt∗, where z∗ t is a random vector, A∗ and B∗ are two matrices, and Ut∗ is a suitable (vector) stochastic process. In all cases, assuming z0 = 0, following Henderson and Plaschko (2006), the solution is given by z∗ t = 0t eA∗(t−s)B∗dUs∗. In this paper, we consider two notes about linear random vibration equations. The first notes relates to generalizations of ft which is contained in section 2. In section 3, we study the measurement error problem in random vibration observations.
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