The dynamics of the pendulum suspended on the forced Duffing oscillator

We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic solutions of the pendulum has been performed. We identify the areas with low number of coexisting attractors in the parameter space as the coexistence of different attractors has a significant impact on the practical usage of the proposed system as a tuned mass absorber.Comment: Accepte

The dynamics of co- and counter rotating coupled spherical pendulums

The dynamics of co- and counter-rotating coupled spherical pendulums (two lower pendulums are mounted at the end of the upper pendulum) is considered. Linear mode analysis shows the existence of three rotating modes. Starting from linear modes allow we calculate the nonlinear normal modes, which are and present them in frequency-energy plots. With the increase of energy in one mode we observe a symmetry breaking pitchfork bifurcation. In the second part of the paper we consider energy transfer between pendulums having different energies. The results for co-rotating (all pendulums rotate in the same direction) and counter-rotating motion (one of lower pendulums rotates in the opposite direction) are presented. In general, the energy fluctuations in counter-rotating pendulums are found to be higher than in the co-rotating case.Comment: The European Physical Journal Special Topics 201

Synchronization of two self-excited double pendula

We consider the synchronization of two self-excited double pendula. We show that such pendula hanging on the same beam can have four different synchronous configurations. Our approximate analytical analysis allows us to derive the synchronization conditions and explain the observed types of synchronization. We consider an energy balance in the system and describe how the energy is transferred between the pendula via the oscillating beam, allowing thus the pendula synchronization. Changes and stability ranges of the obtained solutions with increasing and decreasing masses of the pendula are shown using path-following

A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method

This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems

Influence of dash-pot with controllable damping coefficient on damping efficiency of TMDI

In this paper we study the dynamics of two degree freedom system, which is consist of main body and tuned mass damper with inerter (TMDI). We add the dash-pot with variable damping coefficient to TMDI to study the overall efficiency of the device. The shape of non-linear characteristic of the dash-pot is dependent on one control parameter which governs the steepness of the function and the value of damping coefficient changes according to the relative displacement or velocity between main mass and tuned mass damper. We show the two parameters diagrams showing the maximum amplitude of the main body versus frequency of excitation of main body and controlling parameter

Influence of dash-pot with controllable damping coefficient on damping efficiency of TMDI

In this paper we study the dynamics of two degree freedom system, which is consist of main body and tuned mass damper with inerter (TMDI). We add the dash-pot with variable damping coefficient to TMDI to study the overall efficiency of the device. The shape of non-linear characteristic of the dash-pot is dependent on one control parameter which governs the steepness of the function and the value of damping coefficient changes according to the relative displacement or velocity between main mass and tuned mass damper. We show the two parameters diagrams showing the maximum amplitude of the main body versus frequency of excitation of main body and controlling parameter

Influence of Variable Damping Coefficient on Efficiency of TMD with Inerter

In this paper, we study the dynamics of a two-degree freedom system consisting of the main body and tuned mass damper with inerter (TMDI). We add the dash-pot with variable damping coefficient to TMDI to study the overall efficiency of the device. We investigate different types of the non-linear characteristic of the dash-pot. We investigate devices in which damping coefficient change according to the relative displacement or the relative velocity between the damped mass and tuned mass damper. We also include in the investigation of different types of control functions. We show the two-parameter diagrams presenting the main body’s maximum amplitude versus the frequency of excitation of the damped body and different control parameter. We show how the application of a non-linear damper lets us control the main system’s oscillation amplitude