ON THE DYNAMIC BEHAVIOR OF A NONLINEAR OSCILLATOR WITH SOFTENING CHARACTERISTICS ATTACHED TO AN ELECTRO-DYNAMIC ACTUATOR

Abstract eng:
This paper presents an investigation on the dynamics involved in a two degrees of freedom system consisting of a nonlinear oscillator attached to the moving head of a linear electro-dynamic shaker. The effective stiffness of the nonlinear attachment is realized to achieve a softening force-deflection curve characteristics, and magnets are exploited to this purpose. The shaker is modelled as a linear spring-mass-damper system excited by a harmonic force with a varying excitation frequency. The attached oscillator consists of a cantilever beam with a specified mass on its tip, and it behaves linearly in the given domain of investigation. The nonlinearity is then introduced by adopting magnets in an attractive configuration acting on the tip of the beam. This has the twofold effect of reducing the linear effective stiffness and adding a negative stiffness of cubic type. The equations of motion of the system are presented, and an analytical solution in terms of amplitude-frequency equation is reported. This allows to explore the role of the key parameters involved in the system dynamics, and their effects is investigated in terms of the frequency response curve. The relationship among the non-dimensional, dimensional and physical parameters of an equivalent mechanical prototype is presented.

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