Numerical antiresonance continuation of structural systems

Abstract

a b s t r a c tTuned dynamic absorbers are usually used to counteract vibrations at a given frequency. Presence of non-linearities causes energy-dependent relationship of their resonance and antiresonance frequencies at large amplitude of motion, which consequently leads to a detuning of the absorber from the targeted frequency. This paper presents a procedure to track an extremum point (minimum or maximum) of nonlinear frequency responses, based on a numerical continuation technique coupled to the harmonic balance method to follow periodic solutions in forced steady-state. It thus enable to track a particular antiresonance. The procedure is tested and applied on some application cases to highlight the resonance and antiresonance behavior in presence of geometrically non-linear and/or inertial interactions.

Dynamic stability of centrifugal pendulum vibration absorbers allowing a rotational mobility

“…Looking at the response of 𝜃 (1) , one can see that the non-linearity shifted the antiresonance so that it does not correspond to the linear tuning order 𝑛 𝑝 . This problem is considered in [39]. The distortion of 𝜃 ′′ coming from the presence of 𝜃 (2) (and in a smaller amount, higher harmonics), can be seen in Fig.…”

Active nonlinear inerter damper for vibration mitigation of Duffing oscillators

“…The loci of resonant peaks are computed using the method proposed in Ref. [10]. As can be seen, the linear inerter-damper gets rapidly detuned and a clear nonlinear dependence with respect to the nonlinear forcing coefficient dis observed i.e.…”

Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

“…However, this strategy is heavily dependent on the numerical value precision and not applied well to bifurcation analysis of periodic response. A different tack is discretizing the continuous model to lowdimensional system and then deals with approximate analytical methods [40][41][42][43][44][45]. Practically, the features of nonlinear vibrations and dynamics of a continuous system are described by too many degrees of freedom.…”