On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation

Abstract

The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode response with respect to the excitation amplitude. The saturation phenomenon is observed in the decoupled modes of the system; however, the structural mode and the first anti-symmetric mode of liquid are a combination of the saturated mode and another mode whose scale factor is crucial for the structural response. The results of perturbation analysis are in good agreement with results obtained from numerical methods.

Vibration control through the robust nonlinear absorber with negative stiffness and internal resonance creation

“…Accordingly, autoparametric vibration absorbers were developed. The main idea in these absorbers was that the absorber was added to the host structure and adjusted to half the troublesome frequency while undergoing basic excitation (Attari and Rofooei, 2008; Attari and Rofooei, 2010; Attari et al, 2019; Jahangiri et al, 2020).…”

Stabilization of coupled inverted pendula: From discrete to continuous case

“…Models of the inverted pendulum and similar systems have a great applied interest in various fields of modern science, from medicine and biology to robotics and space technologies (see, e.g. Ivanenko et al (2004), Biswas et al (2018), Pham and Lee (2019), Antoniak et al (2019), Attari et al (2019), Bessa et al (2019) and related references). For example the work Ivanenko et al (2004) is devoted to investigations of the features of human motion depending on the age.…”