Stability and Chaotic Vibrations of a Pipe Conveying Fluid under Harmonic Excitation

The stability and chaotic vibrations of a pipe conveying fluid with both ends fixed, excited by the harmonic motion of its supporting base in a direction normal to the pipe span, were investigated with the aid of modern numerical techniques,involving the phase portrait,Lyapunov exponent and Poincare map tc. The nonlinear differential equations of motion of the system were derived by considering the additional axial force due to the lateral motion of the pipe. Attention was concentrated on the effect of forcing frequency and flow velocity on the dynamics of the system. It is shown that chaotic motions can occur in this system in a certain region of parameter space,and it is also found that three types of routes to chaos exist in the system:(i)period doubling bifurcations;(ii)quasi periodic motions;and (iii)intermittent chaos.

Operational Modal Analysis of a Ship Model in the Presence of Harmonic Excitation

A ship is operated under an extremely complex environment, and waves and winds are assumed to be the stochastic excitations. Moreover, the propeller, host and mechanical equipment can also induce the harmonic responses. In order to reduce structural vibration, it is important to obtain the modal parameters information of a ship. However, the traditional modal parameter identification methods are not suitable since the excitation information is difficult to obtain. Natural excitation technique-eigensystem realization algorithm （NExT-ERA） is an operational modal identification method which abstracts modal parameters only from the response signals, and it is based on the assumption that the input to the structure is pure white noise. Hence, it is necessary to study the influence of harmonic excitations while applying the NExT-ERA method to a ship structure. The results of this research paper indicate the practical experiences under ambient excitation, ship model experiments were successfully done in the modal parameters identification only when the harmonic frequencies were not too close to the modal frequencies.

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

Continuumtopology optimization considering the vibration response is of great value in the engineering structure design.The aimof this studyis toaddress the topological designoptimizationof harmonic excitationstructureswith minimumlength scale control to facilitate structuralmanufacturing.Astructural topology design based on discrete variables is proposed to avoid localized vibration modes,gray regions and fuzzy boundaries in harmonic excitation topology optimization.The topological design model and sensitivity formulation are derived.The requirement of minimum size control is transformed into a geometric constraint using the discrete variables.Consequently,thin bars,small holes,and sharp corners,which are not conducive to the manufacturing process,can be eliminated from the design results.The present optimization design can efficiently achieve a 0–1 topology configuration with a significantly improved resonance frequency in a wide range of excitation frequencies.Additionally,the optimal solution for harmonic excitation topology optimization is not necessarily symmetric when the load and support are symmetric,which is a distinct difference fromthe static optimization design.Hence,one-half of the design domain cannot be selected according to the load and support symmetry.Numerical examples are presented to demonstrate the effectiveness of the discrete variable design for excitation frequency topology optimization,and to improve the design manufacturability.

Vibration Analysis of a Pipe Conveying Fluid Under Harmonic Excitation

In this paper, using Hamilton principle, the control equation of fluid-structure interaction vibration of a pipe conveying fluid under simple harmonic excitation was established and a novel method, Galerkin-Modality＇ s method was proposed to solve this equation. The influence of the damp, the flow velocity, the pressure and the length of the pipe supported by simple supports on the piping＇ s first two natural frequencies was discussed. The criti- cal pressure and the critical length of the pipe were obtained. The influence of the flow velocity and pressure on the piping＇s maximal relative displacements were analyzed.

Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink

Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass,a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra,and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed.The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity.

Sparse identification method of extracting hybrid energy harvesting system from observed data

Hybrid energy harvesters under external excitation have complex dynamical behavior and the superiority of promoting energy harvesting efficiency.Sometimes,it is difficult to model the governing equations of the hybrid energy harvesting system precisely,especially under external excitation.Accompanied with machine learning,data-driven methods play an important role in discovering the governing equations from massive datasets.Recently,there are many studies of datadriven models done in aspect of ordinary differential equations and stochastic differential equations(SDEs).However,few studies discover the governing equations for the hybrid energy harvesting system under harmonic excitation and Gaussian white noise(GWN).Thus,in this paper,a data-driven approach,with least square and sparse constraint,is devised to discover the governing equations of the systems from observed data.Firstly,the algorithm processing and pseudo code are given.Then,the effectiveness and accuracy of the method are verified by taking two examples with harmonic excitation and GWN,respectively.For harmonic excitation,all coefficients of the system can be simultaneously learned.For GWN,we approximate the drift term and diffusion term by using the Kramers-Moyal formulas,and separately learn the coefficients of the drift term and diffusion term.Cross-validation(CV)and mean-square error(MSE)are utilized to obtain the optimal number of iterations.Finally,the comparisons between true values and learned values are depicted to demonstrate that the approach is well utilized to obtain the governing equations for the hybrid energy harvester under harmonic excitation and GWN.

Shaking table test on a tunnel-group metro station in rock site under harmonic excitation

A tunnel-group metro station built in rock site is composed of a group of tunnels.Different tunnels and their interconnections can show inconsistent responses during an earthquake.This study investigates the dynamic responses of such a metro station in a rock site,by shaking table tests.The lining structures of each tunnel and surrounding rock are modeled based on the similitude law;foam concrete and gypsum are used to model the ground-structure system,keeping relative stiffness consistent with that of the prototype.A series of harmonic waves are employed as excitations,input along the transverse and longitudinal direction of the shaking table.The discrepant responses caused by the structural irregularities are revealed by measurement of acceleration and strain of the model.Site characteristics are identified by the transfer function method in white noise cases.The test results show that the acceleration response and strain response of the structure are controlled by the ground.In particular,the acceleration amplification effect at the opening section of the station hall is more significant than that at the standard section under transverse excitation;the amplification effect of the structural opening is insignificant under longitudinal excitation.

Feedback maximization of reliability of MDOF quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations

We studied the feedback maximization of reliability of multi-degree-of-freedom （MDOF） quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. First, the partially averaged Ito equations are derived by using the stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. Then, the dynamical programming equation and its boundary and final time conditions for the control problems of maximizing the reliability is established from the partially averaged equations by using the dynamical programming principle. The nonlinear stochastic optimal control for maximizing the reliability is determined from the dynamical programming equation and control constrains. The reliability function of optimally controlled systems is obtained by solving the final dynamical programming equation. Finally, the application of the proposed procedure and effectiveness of the control strategy are illustrated by using an example.

Pitch perception of harmonic complex tones based on excitation patterns

Fundamental frequency difference limens were measured to study whether pitch perception of medium-rank harmonic complex tones depends on the resolvability of the compo- nents and to study the effect of masker tone on discrimination performance. Target tone was presented alone, or mixed with the masker, which were filtered into the same bandpass frequency region （low, medium, or high） to obtain different resolvability. There were five kinds of funda- mental frequency difference and four kinds of phase combination between target and masker. Five young subjects participated in experiments, all of whom had normal hearing （thresholds ≤ 15 dB HL）. Results found fundamental frequency difference limens were increased with up-shift frequency region of the harmonics. The fundamental frequency difference between target and masker had a significant impact on the performance, while phase effects were small. Analysis suggested that resolvability of harmonics had a significant impact on the fundamental frequency difference limens, but pitch perception of medium-rank harmonics was not based on the resolv- ability. Analysis also suggested that most results of pitch perception of target-masker mixture were closely correlated with peaks on the excitation patterns.

Simultaneous optimization of structure together with attached tuned mass dampers considering dynamic performance

Tuned Mass Dampers(TMDs)are often attached to a main structure to reduce vibration,and the TMDs’positions are important to affect the structural dynamic performance.However,the TMDs’positions and the material layout of the structure act on each other.This paper suggests a design optimization method by combining the topology optimization of the main structure and the layout of the attached TMDs under harmonic excitations.The main structure with the attached TMDs are modeled by the continuum FEA method to consider the change of TMDs’locations.Then they are optimized simultaneously by introducing a multi-level optimization frame,which includes the structural topology optimization and the optimal tuning of TMDs.The locations and damping parameters of TMDs are optimized in every step of the SIMP-based topology optimization of the main structure,so as to fully consider the interactions between each other to improve the dynamic performance.Numerical examples of cantilever structures are studied,and the results show that when the main structure and TMDs are optimized simultaneously,the modal strain energy is more concentrated compared with that obtained by the non-simultaneous optimization approach.Therefore,the dynamic compliance of the target mode is dramatically reduced.

Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control

We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.

First-passage failure of harmonically and stochastically excited Duffing oscillator with delayed feedback control

The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged It? stochastic differential equations for the system are derived by using the stochastic averaging method. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of the first-passage time are established. Finally, the conditional reliability function, the conditional probability density and moments of the first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. The effects of time delay in feedback control force on the conditional reliability function, conditional probability density and moments of the first-passage time are analyzed. The validity of the proposed method is confirmed by digital simulation.

Investigation of a ship resonance through numerical simulation

Understanding dynamic stability of a ship on a resonance frequency is important because comparatively smaller external forces and moments generate larger motions.The roll motion is most susceptible because of smaller restoring moments.Most studies related to the failure modes such as parametric roll and dead ship condition,identified by second generation of intact stability criteria(SGISC)are performed at a resonance frequency.However,the nature of resonance,where the model experiences an incremental roll motion,has not been well understood.In this study,nonlinear unsteady computational fluid dynamics(CFD)simulations were conducted to investigate the resonance phenomenon using a containership under a sinusoidal roll exciting moment.To capture the complexity of the phenomenon,simulations were conducted over a range of frequencies to cover the resonance frequency including lower and higher amplitudes.In addition to the resonance frequency,the phase shift between roll exciting moment and roll angle,as well as the phase difference between acceleration and roll angle,were found to have significant effects on the occurrence of resonance.

Strong optical nonlinearities of self-assembled polymorphic microstructures of phenylethynyl functionalized fluorenones

Highly efficient nonlinear optical（NLO） materials with well-defined architectures in the wavelength and subwavelength length scales are of particular importance for next generation of integrated photonic circuits. Fluorenone analogues have been demonstrated to be promising candidates as building blocks for assembly of organic NLO materials thanks to their synergistic supramolecular interactions and brilliant optical properties. Here we have studied the polymorphs of a phenylethynyl functionalized fluorenone derivative, and their controlled self-assembly for microstructures with different morphologies. These polymorphic microcrystals exhibit very distinctive NLO properties, highly related to their supramolecular and electronic structures.

Advances on numerical and experimental investigation of ship roll damping

This paper presents recent developments towards efficient and reliable methods for roll damping estimation based on numerical simulations as well as model tests using the harmonic excited roll motion(HERM)technique.A newly designed automatic roll damping estimation procedure shows the advantage of a just-in-time post processing of experimental measurement results.Real-time analysis of the measured roll damping values permits a considerable shortening of the test times.Thus,a large number of investigations can be carried out with relatively manageable effort in order to determine the roll damping behavior of different keel configurations or at operating conditions,e.g.,different sized keels or Froude numbers.In addition,HERM measurement method is applied to investigate the memory effect.For this purpose,different excitation schemes are introduced and the results are analyzed.Moreover,a study of the scale effect on the roll damping properties is conducted,in which experimental and numerical investigations are performed for two scales of a ship model.Furthermore,a method is developed that significantly reduces the effort of Reynolds average Navier-Stokes(RANS)-based simulations of roll motion.The reduction of simulation time is achieved by introducing an artificial damping.The obtained results show that the developed method is very well applicable for numerical as well as in experimental investigations.During the model tests using HERM technique,the model is free and the rudder is used to keep the straight-ahead course.The analysis of the numerical and experimental results shows that the influence of the rudder induced force and moment during HERM tests is not negligible and the contribution of the rudder must be taken into account by estimating the roll damping.Finally,a new concept is developed to investigate the parametric roll behavior of ships,which allows neglecting the consideration of the complex modelling of free surface waves in the simulations.During the RANS computations,a potential-based method is applied to compute the variation of restoring terms due the roll motion.