By DING WEN JING
Based on a scientific knowing of its theoretical foundations, “Self-Excited Vibration: thought, Paradigms, and study tools” bargains a style for studying any kind of self-excited vibration (SEV). After summarizing the learn result of numerous SEV phenomenon, together with chatter, shimmy, rotor whirl, flutter, gallop, and SEV of synthetic regulate platforms, the writer constructs a basic constitutive mechanism of SEV, in addition to a typical examine application and unique research process. All of those can help the reader independently examine any new SEV phenomena.
Prof. Wenjing Ding used to be the Director of the Dynamics and Vibration department of the Engineering Mechanics division of Tsinghua college, China.
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Sample text
A great number of complicated phenomena occur in non-smooth dynamic systems. Here, we choose two simple examples. 1. 50) where P is a parameter in the proportion of friction magnitude. The Sgn function is denoted as sgn x 1, x ! 0 . 51) 49 Chapter 2 Geometrical Method The phase diagram of Eq. 50) may be exactly obtained by Liénard construction[5]. Draw two lines x r P , which intersect the x axis at points B and C respectively, as shown in Fig. 24. The phase paths consist of a series of circular arcs with the centers C or B, depending on whether the phase point is in the upper or the lower half-plane.
The same results are true if paths are all outward across Ƚ1 and inward across Ƚ2. The Poincare-Bendixon theorem can be applied to obtaining two theorems covering broad types of differential equations. The proof for these may be found in mathematical textbooks[3]. 44) or the equivalent system x y, y h ( x, y ) g ( x ) , 41 Chapter 2 Geometrical Method where h and g are continuous, has at least one periodic solution under the following conditions: 1 (1) There exists a > 0 such that h(x, y) > 0 when ( x 2 y 2 ) 2 !
The relevant conclusions are obtained by phase plane method and point mapping method. In addition, two excitation mechanisms of friction leading to self-excited vibration are discussed in detail. Chapter 7 treats the shimmy of front wheel with pneumatic tire, whose mathematical model is composed of the equation of motion of the front wheel and the nonholonomic constraint equations of the tire. It is finally analyzed by stability criteria for steady linear systems. Chapter 8 is devoted to rotor whirls caused by fluid-film force and internal damping respectively in a deformed rotation shaft.