A Nonclassical Vibration Absorber for Pendulation Reduction

Abstract

A passive vibration absorber for reducing the motion of a planar pendulum is developed. The system is excited by the horizontal motion of the support. The design transforms the original one-degree-of- freedom pendulum into a double pendulum by adding a small secondary pendulating sacrificial mass between the main system and the base excitation point and two pretensioned springs that generate negative restoring moments (i.e., of opposite sign to that of the gravity-induced restoring moments). Optimal conditions for enhancing the transfer of energy from the main (lower) to the secondary (upper) pendulum are sought. The damping is assumed to be of a linear viscous-type. Due to the action of the springs, the transfer function between the pendulation angle of the main system and the disturbance, in the undamped linearized case, can be reduced to zero for any excitation frequency This is accomplished by requiring that the two spring stiffnesses satisfy an algebraic tuning relation. Due to the inherent inertial coupling, the two normal coordi nates are coupled through off-diagonal terms in the damping matrix. Hence, the vibration absorber acts to block the transfer of disturbance energy to the main system while enhancing the transfer of energy due to initial conditions from the main pendulum to the secondary pendulum. The absorber design is based on a frequency-domain approach borrowed from linear theory. Therefore, to corroborate the effectiveness of the absorber in the nonlinear operating regime (for higher excitation levels), representative responses to initial conditions and frequency-response curves are computed by applying a path-following algorithm to the full nonlinear governing equations. The overall effect of the design is somehow a "linearization" of the system behavior with increased damping properties. In fact, the proposed absorber reduces the response of the sys tem by more than 30 decibels near resonance, exhibits good attenuation characteristics in a broad range of frequencies away from resonance, and remarkably improves the initial-condition response.

Nonlinear generalization of Den Hartog׳s equal-peak method

“…Because pendulum absorbers have a natural frequency that scales with the rate of rotation, they can be tuned over a continuous range of rotor speeds, e.g., to follow an engine order line. In the same way, Lacarbonara et al [22] proposed a carefully-tuned secondary pendulating mass in order to reduce the vibrations of a planar pendulum in a relatively large interval of disturbance amplitudes. Other studies looked at the influence of absorber nonlinearity on vibration suppression performance.…”

Payload Pendulation Reduction Using a Variable-Geometry-Truss Architecture with LQR and Fuzzy Controls

“…Iwasaki et al (1997) and Imazeki et al (1998) designed an active mass-damper system and installed it on the sling of a barge-mounted boom crane. Lacarbonara et al (2000) designed a fully passive spring-mass double-pendulum system to reduce payload pendulations and showed that it possessed broad-band vibration absorption characteristics. Balachandran and Li (1997), Balachandran et al (1999), and Li and Balachandran (1999) designed a two-and three-dimensional pivot, which is in turn suspended from either a fixed-shape or a shape-controlled track under the boom.…”

Analysis of Free Pendulum Vibration Absorber Using Flexible Multi-Body Dynamics

“…Autoparametric resonance is a special case of parametric vibration and is said to exist if the conditions at the internal resonance and external resonance are met simultaneously due to external force [5][6][7]. Autoparametric vibration absorber has received considerable attention since mid-1980s and researchers published many interesting papers [8][9][10][11][12][13][14][15][16][17][18][19]. There are many practical examples of designing vibration absorber published using the concept of autoparametric resonance [20][21][22][23][24][25][26].…”