The paper is aimed at the parametric dynamic analysis of the two degrees of freedom (DoF) phenomenological model of aero-elastic interaction between a friction-damped flexible mounted body and a ...flowing fluid. A coupled system of a linear structure oscillator and the van der Pol based wake oscillator is introduced. Firstly, the complex eigenvalue problem is used for the comprehensive analysis of frequency lock-in, veering and crossing areas from the structural mode stability point of view. Further, an in-depth analysis of the fully nonlinear model based on the numerical continuation method is presented. The analysis focuses on non-synchronous vibration in the resonance areas. Attention is paid to the investigation of transition mechanisms to frequency lock-in and frequency veering in the structural response. In experimental studies, the amplitude and frequency jumps are observed. Here, we show that the origin of these jump phenomena results from the mutual coexistence of two stable solutions, which form a hysteresis region, which can be found in experimentally gained data. Moreover, the influence of structure friction-damping on nonlinear response is evaluated. The proposed phenomenological model is validated concerning two different experimental-based investigations.
•Phenomenological model for fluid–structure interaction with dry-friction damper.•In-depth linear and nonlinear analysis of frequency lock-in phenomenon with respect to cross-coupling parameters.•Dry-friction damper qualitatively changes subharmonic response.•Numerical continuation of periodic solutions reveals the mechanism of frequency lock-in.
This article presents an energy-based method for examining the dynamics of an autoparametric double pendulum with quadratic coupling. The method is based on decomposing the total energy (Hamiltonian) ...into partial terms and studying these terms in the time domain. The article then demonstrates using this method to analyse internal resonances in various regimes, including regular periodic, quasiperiodic, and chaotic motion. This study also explores higher-order resonances linked to the geometric tuning parameter and initial energy, which enrich the complexity of the system. The work focuses on identifying conditions that lead to the development of internal resonances and analysing energy exchange mechanisms at various initial energy levels. This analysis uses Fast Lyapunov Indicators and Poincaré maps for these higher energy levels to identify chaotic regimes. Within these regimes, the assessment of coupling energy contributes to a deeper understanding of the studied system. Moreover, the research demonstrates how energy-based methods can be used to investigate auto-parametric systems.
•Energy-based approach for autoparametric pendulum with quadratic coupling.•In-depth exploration of internal resonances across motion types.•Chaos detection using Fast Lyapunov Indicators.•Higher-order resonances linked to system parameters revealed.•Method applicable for various autoparametric systems.
This paper deals with the modelling and dynamic analysis of thin or slender flexible bodies characterized by axial motion, contacts and friction interaction. Such mechanical systems can be found in ...cable applications, in petroleum drilling industry, in biomedical applications and in nuclear equipments. An original combination of the absolute nodal coordinate formulation and the classical finite element method is used for the modelling of flexible slender structures moving inside flexible tubes and channels considering the overall system vibration. In a nuclear power plant, it allows to analyse mainly the influence of guide thimbles vibration on the control rod drop. The novelty of the introduced methodology is also in the original usage of the absolute nodal coordinate formulation in the problems of nuclear engineering. All the interaction phenomena such as effect of fluid flow, contact forces, gravitation and buoyancy forces are considered in the mathematical model. The particular application of the presented methodology on the problem of the nuclear control rod drop through vibrating bowed guide thimble helps to formulate interesting conclusions on the rod drop time affected by vibrating guide thimbles.
This paper introduces a method for identifying internal resonance regimes in free-vibrating systems with multiple nonlinear couplings, illustrated using a chain of two Rott’s pendula. The method ...based on decomposing Hamiltonian and subsequent treatment of the coupling energies allows for a comprehensive understanding of autoparametric system behaviour. A novel signal-processing-based coupling energy evaluation significantly enhances the effectiveness of the method, revealing internal resonances with slow energy exchange. In the theoretical part, a general step-by-step procedure applicable to any conservative coupled oscillators is introduced. We demonstrate that concerning such free-vibrating systems, the proposed method effectively uncovers internal resonances influenced by system parameters, initial conditions, and the initial energy of the system. Through an illustrative example of the system with multiple quadratic couplings, we also show that slow energy exchange occurs for sum and difference internal resonances.
•Identifying internal resonances using decomposition of Hamiltonian.•General procedure applicable to any conservative oscillator.•Novel signal-processing boosts efficiency, revealing slow energy exchange modes.•Illustrative demonstration via chain of two Rott’s pendula.
The paper presents linearized coefficients for finite-length journal bearings based on the HD forces with multiplicative correction polynomials applied to the infinitely short and the infinitely long ...solutions under the assumption of π-film boundary condition. Based on the linear theory, stability thresholds and their dependence on the length-to-diameter ratio are investigated. Moreover, using the numerical continuation method the change of the generalized Hopf bifurcation which separates regions with subcritical and supercritical Hopf is documented. All results are compared with those of the solution obtained using the finite differences method.
•Stiffness and damping coefficients for the finite-length journal bearings.•Analysis of the influence of length-to-diameter ratio on the dynamic coefficients.•Stability analysis of a single finite-length bearing using Routh-Hurwitz criterion.•Determination of stability curve properties using numerical continuation.•Comparison with FDM-based solution.
The scope of this paper is to provide a general model of a turbocharger using approximate analytical solutions of the hydrodynamic forces in oil films improved by correction polynomials. This ...approach brings two main advantages: the considered analytical solutions hold for wide range of bearing's length-to-diameter ratios and it is not restricted to infinitely short or infinitely long journal bearing approximations whose assumptions are often not satisfied. The usage of the closed-form approximate analytical solution of the Reynolds equation is more time efficient compared to the usage of common numerical methods and enables to effectively solve complex problems like parametric studies. The influence of various models of hydrodynamic forces on the turbochargers behaviour is studied on two different model systems.
•Turbochargers with oating ring bearings show interesting sub-synchronous vibrations•Approximate analytical solutions are used to study oating ring bearing dynamics•Approximate analytical solutions of Reynolds equation are fast computational tools•Pattern of subharmonics in a signal is a_ected by an employed type of solution
•Various approaches to the linearization of floating ring bearings.•Estimation of instability regions using enhanced Campbell diagrams.•Comparison of the linear analysis results with fully nonlinear ...run-up simulations.
A floating-ring bearing (FRB) is composed of a journal, a floating ring and a housing which are separated by two thin oil films. This system is inherently nonlinear and if it is lightly loaded or operated at high speeds, it is prone to the fluid-induced instability. The threshold speed for the instability of a journal bearing with one oil film can be estimated using linearized forces acting in the film. However, the linear analysis of FRB might be problematic because results of such an analysis are usually difficult to interpret. Nevertheless, the linear analysis can provide some fundamental insights into system behaviour. This work aims to evaluate in detail the use of linear theory in the stability analysis of rotating systems supported on FRBs. Several approaches for the linearization of the forces acting in FRB are proposed and analysed. The results are visualized in the form of a holistic Campbell diagram which together depicts natural frequencies, whirl frequencies, modal damping and precession of mode shapes. Moreover, it is demonstrated that the holistic Campbell diagram can be used to interpret – and to some extent, also to predict – results of nonlinear analysis.
Due to the lateral and axial forces or irradiation growth, nuclear fuel assemblies (FAs) are prone to bowing during reactor operation. In some cases, FAs can even mutually contact. The paper focuses ...on the modelling of the bowed hexagonal FAs in mutual interaction considering complex operation conditions given by coolant pressure pulsations. The multi-stage modelling is used to describe the behaviour of the chosen FA in the reactor core. A possible contact between FA and reactor core–shell is also taken into account. All the analyses are performed with respect to the fuel burn-up that significantly influences FAs dynamic behaviour.
Lignocellulose is a complex substrate which requires a variety of enzymes, acting in synergy, for its complete hydrolysis. These synergistic interactions between different enzymes have been ...investigated in order to design optimal combinations and ratios of enzymes for different lignocellulosic substrates that have been subjected to different pretreatments. This review examines the enzymes required to degrade various components of lignocellulose and the impact of pretreatments on the lignocellulose components and the enzymes required for degradation. Many factors affect the enzymes and the optimisation of the hydrolysis process, such as enzyme ratios, substrate loadings, enzyme loadings, inhibitors, adsorption and surfactants. Consideration is also given to the calculation of degrees of synergy and yield. A model is further proposed for the optimisation of enzyme combinations based on a selection of individual or commercial enzyme mixtures. The main area for further study is the effect of and interaction between different hemicellulases on complex substrates.
Nuclear fuel rod consists of the cladding and fuel pellets stack. Fuel rods are mounted in fuel assemblies and they are linked by spacer grids. Due to vibration of a fuel assembly during the reactor ...operation, grid-to-rod fretting (GTRF) occurs in contact points between the cladding of the fuel rod and spacer grid cells. The GTRF phenomenon causes the loss of mass of the cladding in contact points and it can possibly lead to leakage of fission products into a coolant. The paper presents a complex modelling concept for the GTRF analysis of fuel rods due to vibration caused by pressure pulsations of the coolant. The method deals with several essential subproblems. The key part of the method is a dynamic model that simulates vibration of the fuel rod. To estimate wear properties of the cladding, an experimental procedure is used and to determine the state of burnup, a physical model is used. Based on the simulated vibration of the fuel rod and the subsequent GTRF analysis, the evolution of the GTRF during burnup can be determined.
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