A Ball-Type Passive Tuned Mass Vibration Absorber for Response Control of Structures under Harmonic Loading

Ball-type tuned mass absorbers are growing in popularity. They combine a multi-directional effect with compact dimensions, properties that make them attractive for use at slender structures prone to wind excitation. Their main drawback lies in limited adjustability of damping level to a prescribed value. Insufficient damping makes ball-type absorbers more prone than pendula to objectionable effects stemming from the non-linear character of the system. Thus, the structure and design of the damping device have to be made so that the autoparametric resonance states, occurrence of which depends on system parameters and properties of possible excitation, are avoided for safety reasons. This chapter summarises available 3D mathematical models of a ball-pendulum and introduces the non-linear approach based on the Appell–Gibbs function. Efficiency of the models is then illustrated for the case of kinematic and random excitation. Interaction of the absorber and the harmonically forced simple linear structure is numerically analysed. Finally, the chapter provides examples of typical patterns of the autoparametric response and outlines possibilities of applications in practical engineering.

EFFECT OF ADDED TIP MASS ON THE NONLINEAR FLAPWISE AND CHORDWISE VIBRATION OF CANTILEVER COMPOSITE BEAM UNDER BASE EXCITATION

In this paper, a comparative study is performed for a symmetrically laminated composite cantilever beam with and without a tip mass under harmonic base excitation. The base is subjected to both flapwise and chordwise excitations tuned to the primary resonances of the two directions and conditions of 2:1 autoparametric resonance. In the literature, the governing nonlinear equations of the same problem without tip mass have been derived using the extended Hamilton's principle. Extension is made in this study to include the effect of a tip mass on the response of the beam. The natural frequencies are obtained numerically using the diversity guided evolutionary algorithm (DGEA). Next, the multiple scales method is applied to determine the nonlinear response and stability of the system. A set of four first-order differential equations describing the modulation of the amplitudes and phases of interacting modes are derived for the perturbation analysis. For verification, the above equations are reduced to the special case of the cantilever beam without tip mass for comparison with existing results. Finally, the effect of the tip mass on the stability of the fixed points and on the amplitude of oscillation about the equilibrium points in both the frequency and force modulation responses is examined.