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nonlinear vibration of the Flexoelectric Nanoplate with Surface Elastic Electrodes Under Active Electric Loading

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Acta Mechanica Solida Sinica 2020年第6期33卷 864-878页

作者： Yanmei Yue Department of Engineering Mechanics Shijiazhuang Tiedao UniversityShijiazhuang 050043Chino

This paper mainly studies the effects of surface elastic electrodes and electric loading on the nonlinear vibration of flexoelectric nanoplate.The governing equations are derived based on the von Karman type strain-displacement relations and the flexoelectricity theory.The nonlinear vibration equation is solved by an approximate method.Numerical results reveal that the surface elastic electrodes and the length-width ratio of flexoelectric nanoplate have a more significant effect on the nonlinear resonant frequency of simply-supported nanoplate than that of the all-edge-clamped nanoplate.Meanwhile,the effect of the graphene electrode on the nonlinear resonant frequency is more notable than that of the A1 electrode.Additionally,the applied electric loading can significantly affect the nonlinear resonant frequency of the flexoelectric nanoplate.For the nanoplates with different boundary conditions,the applied electric loading has different effects on the nonlinear resonant frequency.This study has certain research significance in the structure design and examination of the flexoelectric nanoplate with electrodes.

关键词： Flexoelectric naxDplate Surface elastic electrode nonlinear vibration Multilayered model

nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium using DQM

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Applied Mathematics and Mechanics(English Edition) 2015年第8期36卷 1033-1044页

作者： A.G.ARANI G.S.JAFARI Faculty of Mechanical Engineering University of Kashan Institute of Nanoscience & Nanotechnology University of Kashan

The nonlocal nonlinear vibration analysis of embedded laminated micro- plates resting on an elastic matrix as an orthotropic Pasternak medium is investigated. The small size effects of micro/nano-plate are considered based on the Eringen nonlocal theory. Based on the orthotropic Mindlin plate theory along with the von Kármán geo- metric nonlinearity and Hamilton＇s principle, the governing equations are derived. The differential quadrature method （DQM） is applied for obtaining the nonlinear frequency of system. The effects of different parameters such as nonlocal parameters, elastic me- dia, aspect ratios, and boundary conditions are considered on the nonlinear vibration of the micro-plate. Results show that considering elastic medium increases the nonlinear frequency of system. F^lrthermore, the effect of boundary conditions becomes lower at higher nonlocal parameters.

关键词： nonlinear vibration laminated micro-plate orthotropic Pasternak medium,differential quadrature method

nonlinear vibration FOR MODERATE THICKNESS RECTANGULAR CRACKED PLATES INCLUDING COUPLED EFFECT OF ELASTIC FOUNDATION

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Applied Mathematics and Mechanics(English Edition) 2005年第8期26卷 963-972页

作者： XIAO Yong-gang（肖勇刚） FU Yi-ming（傅衣铭） ZHA Xu-dong（查旭东） Department of Engineering Mechanics Hunan UniversityChangsha 410082 P. R. China College of Bridge and Structure Engineering Changsha University of Science and Technology Changsha 410076 P. R. China

Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack＇s continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.

关键词： moderate thickness rectangular plate elastic foundation crack nonlinear vibration

nonlinear vibration OF THIN SHALLOW CONIC SHELLS UNDER COMBINED ACTION OF PERIPHERAL MOMENT AND TRANSVERSE LOADS

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Applied Mathematics and Mechanics(English Edition) 2003年第12期24卷 1381-1389页

作者：赵永刚王新志叶开沅 School of Sciences Lanzhou University of Technology Physical College Lanzhou University

Based on the variation and harmonic equations and by taking the maximum amplitude of the shell center as the perturbation parameter, nonlinear vibration of thin shallow conic shells under combined action of peripheral moment and transverse loads was solved. The linear natural frequency can be got by the first_order approximation and the more accurate nonlinear frequency is got by the second_order approximation under the action of static loads. Meanwhile the third_order approximate analytic expression is given for describing the nonlinear relation between nature frequency and peripheral moment,transverse loads, amplitude, base angle under the small deformation. Within some range, the complex and regularity of the nonlinear relation can be directly observed from the numeric results.

关键词： perturbation variation method nonlinear vibration natural frequency thin shallow conical shell

nonlinear vibration OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD

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Applied Mathematics and Mechanics(English Edition) 2006年第10期27卷 1417-1424页

作者：杜国君马建青 Yanshan University Qinhuangdao 066004Hebei ProvinceP.R.China

Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.

关键词： sandwich plate nonlinear vibration critical load buckling amplitude frequency-load characteristic relation

nonlinear vibration and buckling of circular sandwich plate under complex load

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Applied Mathematics and Mechanics(English Edition) 2007年第8期28卷 1081-1091页

作者：杜国君马建青 College of Architecture Engineering and Mechanics Yanshan University Qinhuangdao 066004Hebei ProvinceP.R.China

The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.

关键词： circular sandwich plate nonlinear vibration buckling complex load amplitude frequency-load characteristic relation

nonlinear vibration OF BEAMPLATES WITH A DELAMINATION

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Acta Mechanica Solida Sinica 2000年第4期13卷 353-362页

作者： Fu Yiming Zhang Yunliang Hunan Univ Dept Engn Mech Changsha 410082 Peoples R China

The problem of beam-plates with a delamination located at anarbitrary site undergoing non- linear free vibration without damp isinvestigated. For this problem, nonlinear governing equations as wellas the continuity, equilibrium and compatibility conditions areestablished. The Galerkin method and harmonic balance method areemployed to find solutions. Finally, in some examples,amplitude-frequency curves of the delaminated structure are presentedin order to reveal some special dynamic features.

关键词： delamination beam-plate nonlinear vibration

nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

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Nanotechnology and Precision Engineering 2024年第1期7卷 44-54页

作者： Reza Ebrahimi Mechanical Engineering Faculty of EngineeringYasouj UniversityYasouj 75918-74831Iran

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousﬂuid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefﬁcients,ﬂuid viscosity,and amplitude and frequency of the external force inﬂuence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

关键词： nonlinear vibration Carbon nanotubes Nonlocal effect Viscousﬂuid nonlinear elastic medium

Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

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Applied Mathematics and Mechanics(English Edition) 2024年第5期45卷 779-794页

作者： Lele REN Wei ZHANG Ting DONG Yufei ZHANG State Key Laboratory of Mechanical System and vibration Shanghai Jiao Tong UniversityShanghai 200240China Department of Mechanics Guangxi UniversityNanning 530004China Beijing Key Laboratory of nonlinear vibrations and Strength of Mechanical Structures College of Mechanical EngineeringBeijing University of TechnologyBeijing 100124China School of Mechanical Engineering Beijing Institute of TechnologyBeijing 100081China

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.

关键词： bistable composite laminated cantilever shell snap-through behavior nonlinear vibration nonlinear stiffness characteristic chaos and bifurcation