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Harmonic balance simulation of the influence of component uniformity and reliability on the performance of a Josephson traveling wave parametric amplifier
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作者 郑煜臻 熊康林 +1 位作者 冯加贵 杨辉 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期339-343,共5页
A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A ... A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes. 展开更多
关键词 Josephson traveling wave parametric amplifier(JTWPA) harmonic balance method YIELDS UNIFORMITY
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A novel adaptive harmonic balance method with an asymptotic harmonic selection
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作者 Rongzhou LIN Lei HOU +3 位作者 Yi CHEN Yuhong JIN N.A.SAEED Yushu CHEN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第11期1887-1910,共24页
The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The a... The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems. 展开更多
关键词 harmonic balance method(HBM) adaptive harmonic balance(AHB)method harmonic selection nonlinear vibration multi-frequency excitation
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Harmonic Balance Methods:A Review and Recent Developments
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作者 Zipu Yan Honghua Dai +1 位作者 Qisi Wang Satya N.Atluri 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第11期1419-1459,共41页
The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to ... The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to complex symbolic operations.Many variants have been developed to improve the HB method,among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation.So far,there are two problems remaining to be addressed.i)A dozen of different versions of HB-like methods,in frequency domain or time domain or in hybrid,have been developed;unfortunately,misclassification pervades among them due to the unclear borderlines of different methods.ii)The time domain HB-like methods suffer from non-physical solutions,which have been shown to be caused by aliasing(mixture of the high-order into the low-order harmonics).Although a series of dealiasing techniques have been developed over the past two decades,the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic community.This paper aims to provide a comprehensive review of the development of HB-like methods and enunciate their principal differences.In particular,the time domain methods are emphasized with the famous aliasing phenomenon clearly addressed. 展开更多
关键词 harmonic balance frequency domain HB-like method time domain HB-like method dealiasing technique HB algebraic equation
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Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential 被引量:10
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作者 张智勇 陈予恕 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第4期423-436,共14页
Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time (HB-AFT) do- main technique has some advantages in dealing with nonlinear ... Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time (HB-AFT) do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis. 展开更多
关键词 fractional exponential nonlinearity harmonic balance method with alter-nating frequency/time (HB-AFT) domain technique global response stability
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Period-doubling bifurcation in two-stage power factor correction converters using the method of incremental harmonic balance and Floquet theory 被引量:4
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作者 Wang Fa-Qiang Zhang Hao Ma Xi-Kui 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第2期153-162,共10页
In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance (IHB) and Floquet theory. A two-stage power factor correcti... In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance (IHB) and Floquet theory. A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC-DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated postregulator DC-DC Buck converter is represented as a constant power sink and some other assumptions, the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB. And then, the stability of the system is investigated by using Floquet theory and the stable boundaries are presented on the selected parameter spaces. Finally, some experimental results are given to confirm the effectiveness of the theoretical analysis. 展开更多
关键词 two-stage power factor correction converter incremental harmonic balance Floquet theory period-doubling bifurcation
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Improving convergence of incremental harmonic balance method using homotopy analysis method 被引量:3
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作者 Yanmao Chen Jike Liu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第5期707-712,共6页
We have deduced incremental harmonic balance an iteration scheme in the (IHB) method using the harmonic balance plus the Newton-Raphson method. Since the convergence of the iteration is dependent upon the initial va... We have deduced incremental harmonic balance an iteration scheme in the (IHB) method using the harmonic balance plus the Newton-Raphson method. Since the convergence of the iteration is dependent upon the initial values in the iteration, the convergent region is greatly restricted for some cases. In this contribution, in order to enlarge the convergent region of the IHB method, we constructed the zeroth-order deformation equation using the homotopy analysis method, in which the IHB method is employed to solve the deformation equation with an embedding parameter as the active increment. Taking the Duffing and the van der Pol equations as examples, we obtained the highly accurate solutions. Importantly, the presented approach renders a convenient way to control and adjust the convergence. 展开更多
关键词 Incremental harmonic balance method Homotopy analysis method Initial value CONVERGENCE
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INCREMENTAL HARMONIC BALANCE METHOD FOR AIRFOIL FLUTTER WITH MULTIPLE STRONG NONLINEARITIES 被引量:1
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作者 蔡铭 刘济科 李军 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第7期953-958,共6页
The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stiffness terms were considered... The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stiffness terms were considered in the flutter equations of two-dimensional airfoil. First, the equations were transferred into matrix form, then the vibration process was divided into the persistent incremental processes of vibration moments. And the expression of their solutions could be obtained by using a certain amplitude as control parameter in the harmonic balance process, and then the bifurcation, limit cycle flutter phenomena and the number of harmonic terms were analyzed. Finally, numerical results calculated by the Runge-Kutta method were given to verify the results obtained by the proposed procedure. It has been shown that the incremental harmonic method is effective and precise in the analysis of strongly nonlinear flutter with multiple structural nonlinearities. 展开更多
关键词 strongly nonlinear flutter incremental harmonic balance method BIFURCATION limit cycle
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Primary resonance of fractional-order Duffing–van der Pol oscillator by harmonic balance method 被引量:1
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作者 Sujuan Li Jiangchuan Niu Xianghong Li 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第12期211-216,共6页
The dynamical properties of fractional-order Duffing–van der Pol oscillator are studied, and the amplitude–frequency response equation of primary resonance is obtained by the harmonic balance method. The stability c... The dynamical properties of fractional-order Duffing–van der Pol oscillator are studied, and the amplitude–frequency response equation of primary resonance is obtained by the harmonic balance method. The stability condition for steady-state solution is obtained based on Lyapunov theory. The comparison of the approximate analytical results with the numerical results is fulfilled, and the approximations obtained are in good agreement with the numerical solutions. The bifurcations of primary resonance for system parameters are analyzed. The results show that the harmonic balance method is effective and convenient for solving this problem, and it provides a reference for the dynamical analysis of similar nonlinear systems. 展开更多
关键词 fractional-order oscillator harmonic balance method primary resonance
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Analysing chaos in fractional-order systems with the harmonic balance method
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作者 吴峥茂 卢俊国 谢剑英 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第6期1201-1207,共7页
In this paper, the fractional-order Genesio-Tesi system showing chaotic behaviours is introduced, and the corresponding one in an integer-order form is studied intensively. Based on the harmonic balance principle, whi... In this paper, the fractional-order Genesio-Tesi system showing chaotic behaviours is introduced, and the corresponding one in an integer-order form is studied intensively. Based on the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, a theoretical approach is used to investigate the conditions of system parameters under which this fractional-order system can give rise to a chaotic attractor. Finally, the numerical simulation is used to verify the validity of the theoretical results. 展开更多
关键词 fractional-order system harmonic balance principle Genesio-Tesi system CHAOS Lur'e system
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A vertical track nonlinear energy sink
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作者 Meng LI Hu DING 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第6期931-946,共16页
Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design ... Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity. 展开更多
关键词 track nonlinear energy sink(TNES) vertical direction GRAVITY nonlinear stiffness harmonic balance method(HBM) vibration control
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时域谐波平衡求解器中非物理解出现根源探析
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作者 张森 王丁喜 《风机技术》 2024年第2期44-50,共7页
The time domain harmonic balance method is an attractive reduced order method of analyzing unsteady flow for turbomachines. However, the method can admit non-physical solutions. Non-physical solutions were encountered... The time domain harmonic balance method is an attractive reduced order method of analyzing unsteady flow for turbomachines. However, the method can admit non-physical solutions. Non-physical solutions were encountered from a three-blade-row compressor configuration in a time domain harmonic balance analysis. This paper aims to investigate the root cause of the non-physical solutions. The investigation involves several strategies, which include increasing the number of harmonics, increasing the number of time instants, including scattered modes,including the rotor-rotor interaction, and the use of a new method-the approximate time domain nonlinear harmonic method. Numerical analyses pertinent to each strategy are presented to reveal the root cause of the non-physical solution. It is found that the nonlinear interaction of unsteady flow components with different fundamental frequencies is the cause of the non-physical solution. The non-physical solution can be eliminated by incorporating extra scattered modes or using the approximate time domain nonlinear harmonic method. 展开更多
关键词 The Time Domain harmonic balance Method Non-physical Solution Turbomachinery Blade Row Interaction
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Subharmonic resonance of a clamped-clamped buckled beam with 1:1 internal resonance under base harmonic excitations
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作者 Junda LI Jianliang HUANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2020年第12期1881-1896,共16页
The subharmonic resonance and bifurcations of a clamped-clamped buckled beam under base harmonic excitations are investigated.The nonlinear partial integrodifferential equation of the motion of the buckled beam with b... The subharmonic resonance and bifurcations of a clamped-clamped buckled beam under base harmonic excitations are investigated.The nonlinear partial integrodifferential equation of the motion of the buckled beam with both quadratic and cubic nonlinearities is given by using Hamilton’s principle.A set of second-order nonlinear ordinary differential equations are obtained by spatial discretization with the Galerkin method.A high-dimensional model of the buckled beam is derived,concerning nonlinear coupling.The incremental harmonic balance(IHB)method is used to achieve the periodic solutions of the high-dimensional model of the buckled beam to observe the nonlinear frequency response curve and the nonlinear amplitude response curve,and the Floquet theory is used to analyze the stability of the periodic solutions.Attention is focused on the subharmonic resonance caused by the internal resonance as the excitation frequency near twice of the first natural frequency of the buckled beam with/without the antisymmetric modes being excited.Bifurcations including the saddle-node,Hopf,perioddoubling,and symmetry-breaking bifurcations are observed.Furthermore,quasi-periodic motion is observed by using the fourth-order Runge-Kutta method,which results from the Hopf bifurcation of the response of the buckled beam with the anti-symmetric modes being excited. 展开更多
关键词 nonlinear vibration buckled beam incremental harmonic balance method BIFURCATION subharmonic resonance
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1/3 SUBHARMONIC SOLUTION OF ELLIPTICAL SANDWICH PLATES
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作者 李银山 张年梅 杨桂通 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第10期1147-1157,共11页
The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elli... The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected. 展开更多
关键词 elliptical sandwich plate superpositive-iterative harmonic balance (SIHB) method 1/3 subharmonic solution BIFURCATION
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VISCO—ELASTIC SYSTEMS UNDER BOTH DETERMINISTIC HARMONIC AND RANDOM EXCITATION
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作者 徐伟 戎海武 方同 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第1期61-67,共7页
The response of visco_elastic system to combined deterministic harmonic and random excitation was investigated. The method of harmonic balance and the method of stochastic averaging were used to determine the response... The response of visco_elastic system to combined deterministic harmonic and random excitation was investigated. The method of harmonic balance and the method of stochastic averaging were used to determine the response of the system. The theoretical analysis was verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increase, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions and jumps may exist. 展开更多
关键词 visco_elastic system method of harmonic balance method of stochastic averaging
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Adjacent mode resonance of a hydraulic pipe system consisting of parallel pipes coupled at middle points 被引量:2
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作者 Xin FAN Changan ZHU +1 位作者 Xiaoye MAO Hu DING 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第3期363-380,共18页
The coupling vibration of a hydraulic pipe system consisting of two pipes is studied.The pipes are installed in parallel and fixed at their ends,and are restrained by clips to one bracket at their middle points.The pi... The coupling vibration of a hydraulic pipe system consisting of two pipes is studied.The pipes are installed in parallel and fixed at their ends,and are restrained by clips to one bracket at their middle points.The pipe subjected to the basement excitation at the left end is named as the active pipe,while the pipe without excitation is called the passive pipe.The clips between the two pipes are the bridge for the vibration energy.The adjacent natural frequencies will enhance the vibration coupling.The governing equation of the coupled system is deduced by the generalized Hamilton principle,and is discretized to the modal space.The modal correction is used during the discretization.The investigation on the natural characters indicates that the adjacent natural frequencies can be adjusted by the stiffness of the two clips and bracket.The harmonic balance method(HBM)is used to study the responses in the adjacent natural frequency region.The results show that the vibration energy transmits from the active pipe to the passive pipe swimmingly via the clips together with a flexible bracket,while the locations of them are not node points.The adjacent natural frequencies may arouse wide resonance curves with two peaks for both pipes.The stiffness of the clip and bracket can release the vibration coupling.It is suggested that the stiffness of the clip on the passive pipe should be weak and the bracket should be strong enough.In this way,the vibration energy is reflected by the almost rigid bracket,and is hard to transfer to the passive pipe via a soft clip.The best choice is to set the clips at the pipe node points.The current work gives some suggestions for weakening the coupled vibration during the dynamic design of a coupled hydraulic pipe system. 展开更多
关键词 hydraulic pipe system coupling vibration adjacent mode coupling parallel pipe conveying fluid harmonic balance method(HBM)
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A novel way for vibration control of FGM fluid-conveying pipes via NiTiNOL-steel wire rope 被引量:1
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作者 Jian ZANG Ronghuan XIAO +1 位作者 Yewei ZHANG Liqun CHEN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第6期877-896,共20页
In this study,a coupling model of fluid-conveying pipes made of functionally graded materials(FGMs)with NiTiNOL-steel(NiTi-ST)for vibration absorption is investigated.The vibration responses of the FGM fluid-conveying... In this study,a coupling model of fluid-conveying pipes made of functionally graded materials(FGMs)with NiTiNOL-steel(NiTi-ST)for vibration absorption is investigated.The vibration responses of the FGM fluid-conveying pipe with NiTi-ST are studied by the Galerkin truncation method(GTM)and harmonic balance method(HBM).The harmonic balance solutions and the numerical results are consistent.Also,the linearized stability of the structure is determined.The effects of the structure parameters on the absorption performance are also studied.The results show that the NiTi-ST is an effective means of vibration absorption.Furthermore,in studying the effect of the NiTi-ST,a closed detached response(CDR)is first observed.It is noteworthy that the CDR may dramatically change the vibration amplitude and that the parameters of the NiTi-ST may determine the emergence or disappearance of the CDR.This vibration absorption device can be extended to offer more general vibration control in engineering applications. 展开更多
关键词 NiTiNOL-steel(NiTi-ST) functionally graded material(FGM)fluid-conveying pipe vibration absorption harmonic balance method(HBM) closed detached response(CDR)
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Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations 被引量:16
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作者 Fei Fang Guanghui Xia Jianguo Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第3期561-577,共17页
The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Eul... The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed- parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold. 展开更多
关键词 Parametric and external excitations Nonlinear distributed parameter model Nonlinear dynamic response Energy harvesting harmonic balance method
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Periodic response analysis of a misaligned rotor system by harmonic balance method with alternating frequency/time domain technique 被引量:6
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作者 LI HongLiang CHEN YuShu +1 位作者 HOU Lei ZHANG ZhiYong 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2016年第11期1717-1729,共13页
A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Pe... A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain(HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the Floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems. 展开更多
关键词 rotor system coupling misalignment harmonic balance method with alternating frequency/time domain(HB-AFT) technique Floquet theory stability BIFURCATION
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Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory 被引量:7
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作者 Shaowu YANG Yuxin HAO +2 位作者 Wei ZHANG Li YANG Lingtao LIU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2021年第7期981-998,共18页
In this study,the first-order shear deformation theory(FSDT)is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite(FG-GPLRC).The vi... In this study,the first-order shear deformation theory(FSDT)is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite(FG-GPLRC).The vibration analyses of the FG-GPLRC truncated conical shell are presented.Considering the graphene platelets(GPLs)of the FG-GPLRC truncated conical shell with three different distribution patterns,the modified Halpin-Tsai model is used to calculate the effective Young’s modulus.Hamilton’s principle,the FSDT,and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell.The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell.Then,the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method.The effects of the weight fraction and distribution pattern of the GPLs,the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed.This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell. 展开更多
关键词 nonlinear free vibration harmonic balance method functionally graded graphene platelet-reinforced composite(FG-GPLRC) truncated conical shell chaos
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NES cell 被引量:6
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作者 Hu DING Yufei SHAO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2022年第12期1793-1804,共12页
A broadband adaptive vibration control strategy with high reliability and flexible versatility is proposed.The high vibration damping performance of nonlinear energy sink(NES)has attracted attention.However,targeted e... A broadband adaptive vibration control strategy with high reliability and flexible versatility is proposed.The high vibration damping performance of nonlinear energy sink(NES)has attracted attention.However,targeted energy transfer may cause severe vibration of NES.Besides,it is difficult to realize pure nonlinear stiffness without the linear part.As a result,the reliability of NES is not high.The low reliability of NES has hindered its application in engineering.In addition,the performance of NES depends on its mass ratio of the primary system,and NES lacks versatility for different vibration systems.Therefore,this paper proposes the concept of NES cell.The advantages of the adaptive vibration control of NES are applied to cellular NES.By applying a large number of NES cells in parallel,the reliability of NES and its versatility to complex vibration structures are improved.An elastic beam is used as the primary vibration structure,and a limited NES is used as the cell.The relationship between the vibration suppression effect of NES cells and the number of NES cell is studied.In addition,the effect of the distribution of NES cells on the multi-mode resonance suppression of the beam is also studied.In summary,the mode of the primary structure can be efficiently controlled by a large number of lightweight NES cell.Therefore,the lightweight NES cell is flexible for vibration control of complex structures.In addition,it improves the reliability of NES applications.Therefore,the distributed application of NES cells proposed in this paper is a valuable vibration suppression strategy. 展开更多
关键词 VIBRATION nonlinear energy sink(NES) NES cell vibration control clamped beam harmonic balance method(HBM)
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