Local defect modelling and nonlinear dynamic analysis for the inter-shaft bearing in a dual-rotor system

This paper presents a force model for the inter-shaft bearing with a local defect on the surface of the outer race or the inner race, and the nonlinear dynamic characteristics of a dual-rotor system affected by the local defect are investigated. A simplified dual-rotor system is presented with the consideration of the inter-shaft bearing's nonlinearities such as the Hertzian contact force and the radial clearance. The local defect is considered as a regular dent with a constant depth, thus the radial clearance will increase when rolling elements go through the range of the local defect. The motion equations of the system with eight degrees of freedom are formulated by using the Lagrange's equation. The nonlinear vibration responses of the dual-rotor system affected by the local defect are obtained using numerical method. The results show that there exist four abnormal resonances on the amplitude frequency curves of the system due to the effect of the local defect, apart from the couple of primary resonances excited by the unbalance excitations of the two rotors. With the aid of the characteristic defect frequency analysis, it is revealed that one pair of the abnormal resonances are excited by the characteristic defect frequency, and the other pair of the abnormal resonances are excited by the combination frequency. Furthermore, a comprehensive parametric analysis is carried out to give an insight into the nonlinear resonant response characteristics affected by parameters such as the depth and the span of the defect, the rotation speed ratio, the unbalances of two rotors, the stiffness and the damping of the linear elastic spring, and the radial clearance, the stiffness and the roller number of the inter-shaft bearing. The results show that the vibration amplitudes for the abnormal resonances are mainly determined by the depth and the span of the defect, while the resonant frequencies for the abnormal resonances are mainly influenced by the rotation speed ratio and the roller number of the inter-shaft bearing. However, the rotors’ unbalances mainly affect the corresponding primary resonance rather than the abnormal resonances. The obtained results will contribute to a better understanding of the nonlinear resonant response characteristics of dual-rotor systems with a local defect on the inter-shaft bearing, which are helpful for the fault diagnostics of the inter-shaft bearing in a dual-rotor system.     

Acoustic band gaps in arrays of neutral inclusions

We analyse numerically the acoustic stop band properties of an array of orthotropic coated cylinders whose elastic parameters are deduced from a geometric transform [H. Chen, C.T. Chan, Acoustic cloaking in three dimensions using acoustic metamaterials, Appl. Phys. Lett. 91 (2007) 183518]. We find that whereas a single coated inclusion is acoustically neutral at any frequency, an array of them might display some stop bands. More precisely, an array of freely vibrating coated voids is always neutral, whereas an array of clamped coated inclusions might display a zero frequency stop band. Interestingly, an array of radially symmetric coated inclusions behaves as local Helmholtz resonators, for which the eigenfield within each cloak is obtained in closed form, leading to a frequency estimate associated with the lower edge of the low frequency stop band. A finite phononic crystal of such coated cylinders behaves either as an invisible material or a reflector depending on the frequency of an acoustic source.     

The fitness evaluation strategy in particle swarm optimization

The particle swarm optimization (PSO) computational method has recently become popular. However, it has limitations. It may trap into local optima and cause the premature convergence phenomenon, especially for multimodal and high-dimensional problems. In this paper, we focus on investigating the fitness evaluation in terms of a particle’s position. Particularly, we find that the fitness evaluation strategy in the standard PSO has two drawbacks, i.e., “two steps forward and one step back” and “two steps back and one step forward”. In addition, we propose a general fitness evaluation strategy (GFES), by which a particle is evaluated in multiple subspaces and different contexts in order to take diverse paces towards the destination position. As demonstrations of GFES, a series of PSOs with GFES are presented. Experiments are conducted on several benchmark optimization problems. The results show that GFES is effective at handling multimodal and high-dimensional problems.     

On the instability of resonances in parallel-plane waveguides

It has been observed¹³ that the propagation of acoustic waves in the region Ω₀= ?² × (0, 1), which are generated by a time-harmonic force density with compact support, leads to logarithmic resonances at the frequencies ω = 1, 2,… As we have shown⁹ in the case of Dirichlet's boundary condition U = 0 on ?Ω, the resonance at the smallest frequency ω = 1 is unstable and can be removed by a suitable small perturbation of the region. This paper contains similar instability results for all resonance frequencies ω = 1, 2,… under more restrictive assumptions on the perturbations Ω of Ω₀. By using integral equation methods, we prove that absence of admissible standing waves in the sense of Reference 7 implies the validity of the principle of limit amplitude for every frequency ω ≥ 0 in the region Ω =Ω₀ ?B, where B is a smooth bounded domain with B??Ω₀. In particular, it follows from Reference 7 in the case of Dirichlet's boundary condition that the principle of limit amplitude holds for every frequency ω ≥ 0 if n · x ′ ? 0 on ? B, where x ′ = (x₁, x₂, 0) and n is the normal unit vector pointing into the interior B of ? B. In the case of Neumann's boundary condition, the logarithmic resonance at ω = 0 is stable under the perturbations considered in this paper. The asymptotic behaviour of the solution for arbitary local perturbations of Ω₀ will be discussed in a subsequent paper.     

Multi-displacement continuum modelling of the metamaterial plate with periodical arranged resonators

Multi-displacement continuum modelling of a two-dimensional (2D) elastic metamaterials plate with periodically arranged local resonator over the surface of the plate is studied in this paper. The additional displacement fields are introduced to model the response of the local resonators. The continuous conditions between the adjacent unit-cells are used to reflect the periodicity of the microstructured continuum and resultantly turned into the constraint conditions between the additional displacement field and the other continuous field. The dispersion features of the multiple-displacement coupled wave propagating along the high symmetrical direction and any oblique direction are both studied numerically. It is found that the multi-displacement coupled waves can be divided into the coupled longitudinal wave and the coupled transversal wave when propagating along the highly symmetric direction but cannot be divided into the coupled longitudinal wave and the coupled transversal wave when propagating along any oblique direction. The effects of boundary conditions on the dispersion of acoustic and optical branches of coupled waves are discussed in detail. At last, the influences of the parameters of resonator on the dispersion feature of the multi-displacement coupled waves are investigated numerically.     

Seismic wave imaging in visco-acoustic media

Realistic representation of the earth may be achieved by combining the mechanical properties of elastic solids and viscous liquids. That is to say, the amplitude will be attenuated with different frequency and the phase will be changed in the seismic data acquisition. In the seismic data processing, this effect must be compensated. In this paper, we put forward a visco-acoustic wave propagator which is of better calculating stability and     

Seismic wave imaging in visco-acoustic media

Realistic representation of the earth may be achieved by combining the mechanical properties of elastic solids and viscous liquids. That is to say, the amplitude will be attenuated with different frequency and the phase will be changed in the seismic data acquisition. In the seismic data processing, this effect must be compensated. In this paper, we put forward a visco-acoustic wave propagator which is of better calculating stability and tolerable calculating cost (little more than an acoustic wave propagator). The quite good compensation effect is demonstrated by the numerical test results with synthetic seismic data and real data.     

Nonlinear resonances of a semi-infinite cable on a nonlinear elastic foundation

The Multiple Time Scale (MTS) method is applied to the study of nonlinear resonances of a semi-infinite cable resting on a nonlinear elastic foundation, subject to a constant uniformly distributed load and to a linear viscous damping force. The zero order solution provides the static displacement, which is governed by a nonlinear equation which has been solved in closed form. The first order solution provides the linear resonances, which are seen to be functions of the nonlinearity parameter and of the static displacement at the finite boundary only. Although the first-order governing equation is linear, it has non constant coefficients and cannot be solved in closed form, so that a numerical solution is considered; the eigenfrequencies obtained in this way are also compared with the approximate eigenvalues obtained by the WKB method. At the second order of the MTS expansion, we see that the solution is independent of the intermediate time scale; some additional terms are present, including a time-independent shift of the average position of the oscillations. Finally, the nonlinear frequency–amplitude response curves, which are investigated in detail and which represent the main result of this work, are obtained from the solvability condition at the third order.     

Hybrid computational aeroacoustics based on compressible flow data at low Mach numbers

In some practical applications (e.g. cavity with a lip), even at low Mach numbers, acoustic feedback mechanisms excite flow structures. The compressible flow simulation cannot distinguish between a pure fluid dynamic part and acoustic phenomena. With this in mind, we propose a workflow based on Helmholtz-Hodge decomposition, to extract pure source terms of the compressible flow simulation, to model the sound radiation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topology Optimization of Trusses—Random Cost Method Versus Evolutionary Algorithms

The recently proposed random cost method is applied to the topology optimization of trusses. Its performance is compared to previous genetic algorithm and evolution strategy simulations. Random cost turns out to be an optimization method with attractive features. In comparison to the genetic algorithm approach of Hajela, Lee and Lin, random cost turns out to be simpler and more efficient. Furthermore it is found that in contrast to evolution strategy, the random cost strategy's ability to find optima, is independent of the initial structure. This characteristic is related to the important capacity of escaping from local optima.     

Noncoaxial vibration of fluid-filled multi-walled carbon nanotubes

This paper is concerned with the free vibration of the fluid-filled multi-walled carbon nanotubes (MWCNTs) with simply supported ends. Based on simplified Donnell’s cylindrical shell model and potential flow theory, the effect of internal fluid on the coupling vibration of the MWCNTs-fluid system is discussed in detail. The results show that the resonant frequencies are decreased due to the effect of the fluid, and the fluid has only a little influence on the associated amplitude ratio in MWCNTs corresponding to the natural resonant frequency (frequency of the innermost tube), while plays a significant role in the associated amplitude ratios corresponding to the intertube resonant frequency. For the natural resonant frequency, the vibration mode is coaxial. However, for the intertube resonant frequency, the system shows complex noncoaxial vibration, which plays a critical role in electronic and transport properties of carbon nanotubes (CNTs).     

A differential evolution algorithm with cooperative coevolutionary selection operation for high-dimensional optimization

Although different kinds of evolutionary algorithms (EAs) have been designed and achieved great success on many optimization problems, they are usually limited to some small-scale problems, e.g. with less than 100 decision variables, which may be quite small comparing to the requirements of real-world applications. Therefore, scaling EAs to large size problems have attracted more and more interest. Conventional EAs mimic the seemingly random natural processes by which species evolve. These evolution processes are slow or inefficient. Now, genetic engineering has enabled man to increase both the yields and quality of some crops fast by modifying some part of their genome precisely. In this paper, inspired by the ideas of the genetic engineering, we designed a local selection operator by decomposing the high-dimensional problem into some subcomponents and assigning a local fitness function to evaluate each subcomponent. Then a new differential evolution (DE) is proposed by inserting the local selection operator into the framework of DE. Numerical experiments were carried out to evaluate the performance of the new algorithm on a large number of benchmark functions. The results show that the new algorithm is effective and efficient for high-dimensional optimization.     

The calculation of resonance separatrices for the near-integrable case of the standard mapping

The standard mapping arises in many physical applications, including the analysis of nonlinear resonant acoustic oscillations in a closed tube. A perturbation expansion, in powers of the amplitude parameter, is given for the calculation of the fixed points of various orders and the associated separatrices. It is shown how exact homoclinic orbits can be calculated numerically. Explicit analytic expressions are given for the separatrices associated with the first four resonances when the perturbation parameter is small.     

A two-phase tabu search based evolutionary algorithm for the maximum diversity problem

In this paper, we study the maximum diversity problem (MDP) which is equivalent to the quadratic unconstrained binary optimization (QUBO) problem with cardinality constraint. The MDP aims to select a subset of elements with given cardinality such that the sum of pairwise distances between any two elements in the selected subset is maximized. For solving this computationally challenging problem, we propose a two-phase tabu search based evolutionary algorithm (TPTS/EA), which integrates several distinguishing features to ensure the diversity and the quality of the evolution, such as a two-phase tabu search algorithm which consists of a dynamic candidate list (DCL) strategy-based traditional tabu search in the first phase and a solution-based tabu search procedure to refine the search in the second phase, and two path-relinking based recombination operators to generate new offspring solutions. Tested on three sets of totally 140 public instances in the literature, the study demonstrates the efficacy of the proposed TPTS/EA algorithm in terms of both solution quality and computational efficiency. Specifically, our proposed TPTS/EA algorithm is able to improve the previous best known results for 2 instances, while matching the previous best-known solutions for 130 instances. We also provide experimental evidences to highlight the beneficial effect of several important components in our TPTS/EA algorithm.     

Tubuloglomerular feedback in a dynamic nephron

A dynamic model for a short-looped mammalian nephron is developed to study tubuloglomerular feedback (TGF). Evolution equations for salt and urea concentrations and for fluid flux in the nephron are derived and coupled to a resistance network that serves as a schematic model of the glomerulus and associated structures. The evolution equations, which are semi-linear hyperbolic partial differential equations, are solved by the method of flux-corrected transport. The implementation and testing of this method is described and numerical results are presented. This investigation suggests that: (i) the concentrating nephron exhibits high gain, i.e., a small increase in single nephron glomerular filtration rate produces a large increase in the salt concentration of tubular fluid in the cortical thick ascending limb at the macula densa; (ii) the nephron, as a concentrating system, acts as a low-pass filter, i.e., high frequency pressure oscillations (1 Hz) of a prescribed amplitude at the proximal tubule produce relatively low amplitude oscillations in tubular concentrations, while low frequency oscillations (1/30 Hz) produce relatively high amplitude oscillations in tubular concentrations; and (iii) as a consequence of long time delay in TGF, some perturbations in afferent arteriolar blood pressure induce sustained periodic oscillations similar to those observed in recent experiments.     

Resonance phenomena for water waves in channels of arbitrary cross‐section

This article studies the evolutionary problem for linear gravity waves on the surface of water in a uniform, symmetric channel which is excited by an antisymmetric pressure force of frequency ω at the free surface. It is shown that there is a countably infinite set of frequencies {ω₀, ω₁, …} which give rise to resonance phenomena: the amplitude of the wave motion grows like t^1/2 as t→∞ in a sense which is precisely specified. Under pressure forcing at any other frequency the solution obeys the principle of limiting amplitude. These results are obtained by combining methods developed for problems in acoustic waveguides with regularity theory for elliptic boundary‐value problems in non‐smooth domains. Copyright © 1999 John Wiley & Sons, Ltd.     

Controlling a chaotic resonator by means of dynamic track control

Josephson junction oscillators can generate chaotic signals with a wide frequency spectrum. An improved scheme of Lyapunov functions is proposed to control chaotic resonators of this type and forces them to converge to an arbitrary selected target signal. A changeable gain coefficient is introduced into the Lyapunov function, and the controllers are designed analytically. The controllers operate automatically when the output series are deviated from the target orbit synchronously. A resistive‐capacitive‐inductive‐shunted Josephson junction in chaotic parameter region is investigated in our studies, and power consumption is estimated from the dimensionless model. It is found that the power consumption of controller is dependent on the amplitude and/or angular frequency of the external target signal to be tracked. For example, larger power costs are observed when the target signal is in larger amplitude and/or angular frequency. The numerical results are consistent with the analytical discussion. © 2014 Wiley Periodicals, Inc. Complexity 21: 370–378, 2015     

A general cost-benefit-based adaptation framework for multimeme algorithms

As memetic algorithms (MA) are a crossbreed between local searchers and evolutionary algorithms (EA) spreading of computational resources between evolutionary and local search is a key issue for a good performance, if not for success at all. This paper summarises and continues previous work on a general cost-benefit-based adaptation scheme for the choice of local searchers (memes), the frequency of their usage, and their search depth. This scheme eliminates the MA strategy parameters controlling meme usage, but raises new ones for steering the adaptation itself. Their impact is analysed and it will be shown that in the end the number of strategy parameters is decreased significantly as well as their range of meaningful values. In addition to this the number of fitness evaluations is reduced drastically. Both are necessary prerequisites for many practical applications as well as for the acceptance of the method by practitioners. Although the introduced framework is tailored to EAs producing more than one offspring per mating, it is also suited for those with only one child per pairing. So there are no preconditions to the EA for the described adaptation scheme to be applied.     

Convergence analysis and performance of the extended artificial physics optimization algorithm

This paper presents extended artificial physics optimization (EAPO), a population-based, stochastic, evolutionary algorithm (EA) for multidimensional search and optimization. EAPO extends the physicomimetics-based Artificial Physics Optimization (APO) algorithm by including each individual’s best fitness history. Including the history improves EAPO’s search capability compared to APO. EAPO and APO invoke a gravitational metaphor in which the force of gravity may be attractive or repulsive, the aggregate effect of which is to move individuals toward local and global optima. A proof of convergence is presented that reveals the conditions under which EAPO is guaranteed to converge. Discrete-time linear system theory is used to develop a second-order difference equation for an individual’s stochastic position vector as a function of time step. Stable solutions require eigenvalues inside the unit circle, leading to explicit convergence criteria relating the run parameters {m_i, w, G}. EAPO is tested against several benchmark functions with excellent results. The algorithm converges more quickly than APO and with better diversity.