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nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

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Applied Mathematics and Mechanics(English Edition) 2024年第2期45卷 261-276页

作者： Runqing CAO Zilong GUO Wei CHEN Huliang DAI Lin WANG Department of Engineering Mechanics School of Aerospace EngineeringHuazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment Wuhan 430074China State Key Laboratory of Intelligent Manufacturing Equipment and Technology School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhan 430074China

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

关键词： curved pipe conveying fluid pulsating fluid geometrically exact model(GEM) nonlinear dynamics parametric vibration flutter

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Finite Deformation, Finite Strain nonlinear dynamics and Dynamic Bifurcation in TVE Solids with Rheology

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Applied Mathematics 2024年第1期15卷 108-168页

作者： Karan S. Surana Sri Sai Charan Mathi Department of Mechanical Engineering University of Kansas Lawrence US

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing

关键词： Thermoviscoelasticity Rheology Memory Finite Strain Finite Deformation nonlinear dynamics Dynamic Bifurcation Ordered Rate Theories

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nonlinear dynamics investigation of contact force in a cam–follower system using the Lyapunov exponent parameter,power spectrum analysis,and Poincarémaps

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International Journal of Mechanical System dynamics 2022年第2期2卷 214-230页

作者： Louay S.Yousuf Department of Mechanical Engineering San Diego State UniversitySan DiegoCaliforniaUSA

The aim of this article is to detect the detachment between the cam and the follower using the largest Lyapunov exponent parameter,the power density function of fast Fourier transform,and Poinarémaps due to the nonlinear dynamics phenomenon of the follower.The detachment between the cam and the follower was investigated for different cam speeds and different internal distances of the follower guide from inside.This study focuses on the use of the cam–follower system with a bionic quadruped robot through a linkage mechanism.Multishock absorber(spring–damper–mass)systems at the very end of the follower were used to improve the dynamic performance and to reduce the detachment between the cam and the follower.The SolidWorks program was used in the numerical solution,while a high‐speed camera at the foreground of the OPTOTRAK 30/20 equipment was used to identify the follower position.The friction and impact were considered between the cam and the follower and between the follower and its guide.In general,when the cam and the follower are in permanent contact,there is no loss in potential energy,and no impact or restitution.The detachment between the cam and the follower increases with increasing coefficient of restitution in the presence of the impact.

关键词： nonlinear dynamics Lyapunov exponent non‐periodic motion contact force

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nonlinear dynamics of Nervous Stomach Model Using Supervised Neural Networks

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Computers, Materials & Continua 2022年第7期72卷 1627-1644页

作者： Zulqurnain Sabir Manoj Gupta Muhammad Asif Zahoor Raja N.Seshagiri Rao Muhammad Mubashar Hussain Faisal Alanazi Orawit Thinnukool Pattaraporn Khuwuthyakorn Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Department of Electronics and Communication Engineering JECRC UniversityJaipur(Rajasthan)303905India Future Technology Research Center National Yunlin University of Science and TechnologyYunlin64002Taiwan Department of Applied Mathematics School of Applied Natural SciencesAdama Science and Technology UniversityAdamaEthiopia Department of Mathematics University of PunjabJhelum CampusPakistan Department of Electrical Engineering Prince Sattam Bin Abdulaziz UniversityCollege of EngineeringAl Kharj16278Saudi Arabia Research Group of Embedded Systems and Mobile Application in Health Science College of ArtsMedia and TechnologyChiang Mai UniversityChiang Mai50200Thailand

The purpose of the current investigations is to solve the nonlinear dynamics based on the nervous stomach model(NSM)using the supervised neural networks(SNNs)along with the novel features of Levenberg-Marquardt backpropagation technique(LMBT),i.e.,SNNs-LMBT.The SNNs-LMBT is implemented with three different types of sample data,authentication,testing and training.The ratios for these statistics to solve three different variants of the nonlinear dynamics of the NSM are designated 75%for training,15%for validation and 10%for testing,respectively.For the numerical measures of the nonlinear dynamics of the NSM,the Runge-Kutta scheme is implemented to form the reference dataset.The attained numerical form of the nonlinear dynamics of the NSM through the SNNs-LMBT is implemented in the reduction of the mean square error(MSE).For the exactness,competence,reliability and efficiency of the proposed SNNs-LMBT,the numerical actions are capable using the proportional arrangements through the features of the MSE results,error histograms(EHs),regression and correlation.

关键词： nonlinear dynamics nervous stomach system reference dataset levenberg-marquardt backpropagation technique numerical outcomes

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nonlinear dynamics of electroencephalography study in schizophrenic patients

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Chinese Medical Journal 2013年第15期126卷 2886-2889页

作者： CHEN Xing-shi XU Yi-feng TANG Yun-xiang FANG Yi-ru ZHANG Chen ZHANG Ming-dao LOU Fei-ying LIANG Jian-hua CHEN Chong PAN Xiao YAN Jin CUI Yi Shanghai Jiao Tong Univ Shanghai Mental Hlth Ctr Dept Electrophysiol Shanghai 200030 Peoples R China Shanghai Jiao Tong Univ Shanghai Mental Hlth Ctr Dept Psychiat Shanghai 200030 Peoples R China PLA Mil Med Univ 2 Fac Psychol & Mental Hlth Shanghai 200433 Peoples R China

Background Few characteristic changes of linear electroencephalograph （EEG） have been reported in schizophrenia. The aim of the present study was to investigate the changes in temporal-spatial dimensional properties of EEG under different cognitive tasks in patients with schizophrenia. Methods EEG was recorded by using EEG-1518K system and mapping system （Nihon Kohden Tomioka Corporation, Japan） in 45 schizophrenic patients and 47 healthy adults （normal control, NC） under five states： eyes c^osed, eyes open, mental arithmetic test with eyes closed, memory test with eyes open, and number cancellation test. Correlation dimension （D2） and point-wise correlation dimension （PD2） were calculated for all EEG analyses. Results （1） There were no significant differences of D2 and PD2 between NC and schizophrenic patients under states of eyes open and closed. （2） Compared with NC, schizophrenic patients showed decreased performance of D2 in mental arithmetic test with eyes closed and number cancellation test （mental arithmetic test with eyes closed： Nc 5.9±0.6, Sch 3.0＋0.8; number cancellation test： Nc 6.0±0.6, Sch 4.4±0.7; P 〈0.05 or P 〈0.01）. （3） Schizophrenic patients also showed decrease performance of PD2 in mental arithmetic test with eyes closed, memory test with eyes open, and number cancellation test （mental arithmetic test with eyes closed： Nc 6.9±0.7, Sch 4.0±0.8; memory test with eyes open： Nc 6.6±0.8, Sch 5.0±0.9; number cancellation test： Nc 7.1±0.7, Sch 4.8±0.9; P 〈0.05 or P 〈0.01）. Conclusions nonlinear dynamic analysis provided a new approach in clinical investigation of EEG signals. It was helpful to further understand the cerebral mechanism in schizophrenic cognitive process.

关键词： schizophrenia electroencephalography nonlinear dynamics cognition

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nonlinear dynamics AND SYNCHRONIZATION OF TWO COUPLED PIPES CONVEYING PULSATING FLUID

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Acta Mechanica Solida Sinica 2014年第2期27卷 162-171页

作者： Qiao Ni Zilong Zhang Lin Wang Qin Qian Min Tang Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment Department of Mechanics Huazhong University of Science and Technology

In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.

关键词： pipe conveying pulsating fluid nonlinear dynamics coupled two-pipe system synchronization

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nonlinear dynamics in wurtzite InN diodes under terahertz radiation

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Chinese Physics B 2012年第3期21卷 411-415页

作者：冯伟 Department of Physics Jiangsu University

We carry out a theoretical study of nonlinear dynamics in terahertz-driven n＋nn＋ wurtzite InN diodes by using time-dependent drift diffusion equations. A cooperative nonlinear oscillatory mode appears due to the negative differential mobility effect, which is the unique feature of wurtzite InN aroused by its strong nonparabolicity of the I＂1 valley. The appearance of different nonlinear oscillatory modes, including periodic and chaotic states, is attributed to the competition between the self-sustained oscillation and the external driving oscillation. The transitions between the periodic and chaotic states are carefully investigated using chaos-detecting methods, such as the bifurcation diagram, the Fourier spectrum and the first return map. The resulting bifurcation diagram displays an interesting and complex transition picture with the driving amplitude as the control parameter.

关键词： nonlinear dynamics terahertz radiation wurtzite InN

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nonlinear dynamics MODFLING OF MECHANICAL PERIODICITY OF END DIASTOLIC VOLUME OF LEFT VENTRICLE

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Applied Mathematics and Mechanics(English Edition) 2001年第10期22卷 1183-1191页

作者： XU Shi-xiong(许世雄) MAO Xiao-chun(毛晓春) Mechanics and Engineering Science Department Fudan UniversityShanghai 200433 P R China Mechanics and Engineering Science Department Fudan UniversityShanghai 200433 P R China

The cardiovascular system with a lumped parameter model is treated, in which the Starling model is used to simulate left ventricle and the four-element Burattini & Gnudi model is used in the description of arterial system. Moreover, the feedback action of arterial pressure on cardiac cycle is taken into account. The phenomenon of mechanical periodicity (MP) of end diastolic volume (EDV) of left ventricle is successfully simulated by solving a series of one-dimensional discrete nonlinear dynamical equations. The effects of cardiovascular parameters on MP is also discussed.

关键词： left ventricle end diastolic volume mechanical periodicity nonlinear dynamics

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All-optical nonlinear chiral ultrafast magnetization dynamics driven by circularly polarized magnetic fields

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High Power Laser Science and Engineering 2023年第6期11卷 154-161页

作者： Luis Sánchez-Tejerina Rodrigo Martín-Hernández Rocío Yanes Luis Plaja Luis López-Díaz Carlos Hernández-García Grupo de Investigación en Aplicaciones del Láser y Fotónica Departamento de Física AplicadaUniversidad de SalamancaSalamancaSpain Present address:Departamento de Electricidad y Electrónica Universidad de ValladolidValladolidSpain Departamento de Física Aplicada Universidad de SalamancaSalamancaSpain Unidad de Excelencia en Luz y Materia Estructuradas(LUMES) Universidad de SalamancaSalamancaSpain

Ultrafast laser pulses provide unique tools to manipulate magnetization dynamics at femtosecond timescales,where the interaction of the electric field usually dominates over the magnetic field.Recent proposals using structured laser beams have demonstrated the possibility to produce regions where intense oscillating magnetic fields are isolated from the electric field.In these conditions,we show that technologically feasible tesla-scale circularly polarized high-frequency magnetic fields induce purely precessional nonlinear magnetization dynamics.This fundamental result not only opens an avenue in the study of laser-induced ultrafast magnetization dynamics,but also sustains technological implications as a route to promote all-optical non-thermal magnetization dynamics both at shorter timescales-towards the subfemtosecond regime-and at THz frequencies.

关键词： chiral behavior nonlinear dynamics ultrafast dynamics

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nonlinear dynamics OF LATERAL MICRO-RESONATOR INCLUDING VISCOUS AIR DAMPING

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Chinese Journal of Mechanical Engineering 2007年第3期20卷 75-78页

作者： GAO Rong WANG Xiaojing WANG Min YU Maohua XIE Mingchun School of Mechanical Electronic Engineering and Automation Shanghai University Shanghai 200072 China No. 802 Institute Shanghai Academy of Spaceflight Technology Shanghai 200090 China

The nonlinear dynamics of the lateral micro-resonator including the air damping effect is researched. The air damping force is varied periodically during the resonator oscillating, and the air damp coefficient can not be fixed as a constant. Therefore the linear dynamic analysis which used the constant air damping coefficient can not describe the actual dynamic characteristics of the mi-cro-resonator. The nonlinear dynamic model including the air damping force is established. On the base of Navier-Stokes equation and nonlinear dynamical equation, a coupled fluid-solid numerical simulation method is developed and demonstrates that damping force is a vital factor in micro-comb structures. Compared with existing experimental result, the nonlinear numerical value has quite good agreement with it. The differences of the amplitudes （peak） between the experimental data and the results by the linear model and the nonlinear model are 74.5% and 6% respectively. nonlinear nu-merical value is more exact than linear value and the method can be applied in other mi-cro-electro-mechanical systeme （MEMS） structures to simulate the dynamic performance.

关键词： Air damping nonlinear dynamics Micro-resonator Micro-electro-mechanical systems（MEMS）

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