Predicting vibration-induced displacement for a resonant friction slider

Dynamics and Optimization of Multibody Systems in the Presence of Dry Friction

“…The mass m 0 , the length l of the end links, the duration T of the slow motion, and the friction coefficients k 0 and k 1 are to be chosen in order to maximize the speed v 1 = Δx(2T ) −1 ; see (7). The imposed constraints comprise the inequality (17) and the bounds on the friction coefficients:…”

Some General Effects of Strong High-Frequency Excitation: Stiffening, Biasing and Smoothening

“…High-frequency excited systems, representative of the effects of stiffening (b,e,f,g), biasing (a,b,c,d,e,h), and smoothening (a,h,i). (a) Vibration-induced movement using friction layers and a HF-resonator [13,14]. (b) Change of equilibriums, stability, natural frequencies, and non-linear response for a HF-excited twobar link [15].…”

“…By this, a set of generally non-linear differential equations is transformed into two exact subsets, that may each be approximately solved: one describing the fast components of motion, and the other describing slow components, the latter typically being those of primary interest. Originating from Kapitza's heuristic approach for a specific problem [5], this method was generalized and applied to a wide variety of physical systems and phenomena by Blekhman (e.g., references [1,51], see references [14,20,22,26,39] for recent applications).…”

“…Some early works in this field by Stephenson [2,3], Hirsch [4], and Kapitza [5] deal with the now well-known effect of the upright stabilization of a pendulum with a rapidly oscillating support, and Chelomei [6] proposed to use similar effects for stabilizing elastic systems. More recent investigations include using resonant HF excitation to transport fluid or strings through pipes [7,8], damp resonant vibrations of strings and beams [9][10][11][12], induce linear motion in systems with asymmetrical friction [13,14], change the equilibriums, stability, natural frequencies, and non-linear frequency response for a two-bar link [15], increase the buckling load and natural frequencies for columns [16][17][18], quench friction-induced periodic or chaotic oscillations for non-linear oscillators [19][20][21], stabilize or change the non-linear behavior of follower-loaded double pendulums and articulated fluid-carrying pipes [22][23][24], explain the ''floating'' of the disk on the inverted so-called ''Chelomei's pendulum'' [16,25,26], and form other properties of non-linear mechanical systems [27]. Effects of HF excitation have been investigated for continuous flexible structures such as strings, beams and rotating disks [28][29][30][31], and with consideration to change in basic material properties such as creep, relaxation, plasticity [1,32] (plus a number of works published only in Russian).…”

Vibrational self-alignment of a rigid object exploiting friction

“…[7]. In [8], the method of averaging is used to analyze high-frequency vibration-induced movements of a mass between two layers of different friction, while in [23] the method of direct separation of motion (see [3]) is used to calculate equilibrium speeds (including zero speed) of a mass on a table vibrating at high frequency. In [24], analytical approximations for stick-slip vibration amplitudes are derived for the classical mass-on-movingbelt system.…”