Dynamics of vibration isolation system with a quasi-isochronous roller shock absorber

Abstract

The low-frequency vibrations of a vibration isolation system of rigid bodies (roller shock absorber and carrying body) under external harmonic loading are considered. The working surface of the absorber has the form of a brachistochrone. The equations describing the slip-free motion of the absorber over the hinged roller and the motion of the carrying body are derived. A graphical method for optimizing the parameters of the roller absorber as a component of the vibration isolation system is proposed Keywords: vibration isolation system, kinematic constraints, roller shock absorber, carrying body, brachistochrone, rolling without slipping, amplitude-frequency characteristicsIntroduction. The vibration protection of flexible high-rise structures (such as TV towers, radio masts, metal vent stacks, wind turbine towers, etc.) has recently become important. This is because over time, these structures wear out and may require urgent restoration for (i) reduction of the dynamic loads on these structures and (ii) strengthening of their load-carrying components. Here we address only case (i) and propose a new engineering solution based on a roller shock absorber with working surface in the form of a brachistochrone [10,16,32].The dynamic analysis of high-rise structures for wind forces deals with forced vibrations excited by pulsating wind pressure and self-excited vibrations such as wind resonance [1,3,4]. The principal natural frequencies of such structures are low, and the displacements of the upper parts of high-rise structures are great (1 to 3 m).So far, suspended pendulum-type dynamic shock absorbers have been used [1,[3][4][5]14]. However, they have a number of disadvantages, including failure to normally operate in the low-frequency range (w = 0.2-2.0 rad/sec).The most promising new method of vibration protection of high-rise structures employs rolling-type shock absorbers that include heavy balls, cylinders, or rollers rolling without slipping over the curvilinear working surfaces of the carrying bodies [5-9, 17, 30]. They were successfully tested [5] on TV towers, vent stacks, and radio masts in the range of low natural frequencies (lower than 2.0 rad/sec). Compared with the conventional pendulum-type shock absorbers, they are compact, do not require a separate room for maintenance, and can reliably and safely operate in various climates.A cantilever rod of variable cross-section is a model standardized on to design flexible structures [3,4]. The spectrum of natural frequencies is sparse, which makes it possible, in most cases, to expand the solutions of dynamic problems into trigonometric series of natural modes that converge relatively rapidly. However, the full-scale test and measurement data [1,[3][4][5]14] demonstrate that the first vibration mode makes the major contribution to the dynamic load on such flexible structures. Therefore, use is made of one-mass absorbers tuned to a frequency close to the principal natural frequency of the structure. As a rule, the effectiveness of dynamic shock absorbers is as...

Determining the Amplitude–Frequency Response and Settings of a Nonlinear Vibration Isolation System with a Quasi-Isochronous Damper

“…The present paper continues the scientific research into the dynamic behavior of vibration isolation systems with roller dampers begun in [2,3,[12][13][14], where a theory of roller dampers for the vibration isolation of tall and flexible objects in a low-frequency range (below 3 rad/sec) was developed and theoretically and experimentally validated.…”

“…The lower face of the working body of the roller damper has identical convex depressions (surfaces) that interact with the respective rollers hinged to the carrying body. Each depression is formed by revolving a brachistochrone around the vertical axis of the roller [3,12,13]. Figure 1 shows a vertical section of one depression that moves over the respective roller.…”

“…The vibrational energy is absorbed by two pairs of air dampers hinged to the carrying body and the working body and functioning in two perpendicular directions [3,12,13]. The working body undergoes translational vibrations in a vertical plane perpendicular to the rotation axis of the roller.…”

“…In [12], the radius of curvature of the brachistochrone that forms each depression is given by r h h ( ) cos( ) = + 4R r , where r is the radius of the roller, R is a brachistochrone parameter, h is the angle between the vertical and the normal r n at the contact 234…”

“…Thus, this requirement is met at different values of h, except for the extreme angles h p = ± / 2at which the radius of curvature of the brachistochrone r p ( / ) ± = 2 r. The following nonlinear equations of motion of the vibration isolation system under the action of a harmonic force were derived in [12]: …”