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Applied Mathematics and Mechanics(English Edition) 2023年第10期44卷 1761-1776页

作者： Changsong ZHU Xueqian FANG Jinxi LIU State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures Shijiazhuang Tiedao UniversityShijiazhuang 050043China Key Laboratory of Mechanical Behavior Evolution and Control of Traffic Engineering Structures in Hebei Shijiazhuang 050043China School of Environment and Civil Engineering Dongguan University of TechnologyDongguan 523808Guangdong ProvinceChina

In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are *** on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doublycurved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion(LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.

关键词： nonlinear free vibration piezoelectric semiconductor(PS)doubly-curved shell nonlinear drift-diffusion(NLDD)model linearized drift-diffusion(LDD)model

nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

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Applied Mathematics and Mechanics(English Edition) 2022年第8期43卷 1203-1218页

作者： Qingdong CHAI Yanqing WANG Meiwen TENG Key Laboratory of Structural Dynamics of Liaoning Province College of SciencesNortheastern UniversityShenyang110819China Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines Northeastern UniversityShenyang110819China

The aim of the present study is to investigate the nonlinear free vibration of spinning cylindrical shells under spinning and arbitrary boundary *** springs are used to simulate arbitrary boundary ***’shell theory is employed,and von Kármán nonlinear terms are considered in the theoretical *** using Chebyshev polynomials as admissible functions,motion equations are derived with the Ritz ***,a direct iteration method is used to obtain the nonlinear vibration *** effects of the circumferential wave number,the boundary spring stiffness,and the spinning speed on the nonlinear vibration characteristics of the shells are *** is found that there exist sensitive intervals for the boundary spring stiffness,which makes the variation of the nonlinear frequency ratio more *** decline of the frequency ratio caused by the spinning speed is more significant for the higher vibration amplitude and the smaller boundary spring stiffness.

关键词： spinning cylindrical shell nonlinear free vibration arbitrary boundary condition Chebyshev polynomial Sanders’shell theory

nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation

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Applied Mathematics and Mechanics(English Edition) 2018年第12期39卷 1825-1836页

作者： Rong WANG Guohua NIE School of Aerospace Engineering and Applied Mechanics Tongji University

This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.

关键词： nonlinear free vibration reticulated shallow spherical shell transverse shear effect asymptotical iteration method amplitude-frequency relation

nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory

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Applied Mathematics and Mechanics(English Edition) 2021年第7期42卷 981-998页

作者： Shaowu YANG Yuxin HAO Wei ZHANG Li YANG Lingtao LIU College of Mechanical Engineering Beijing Information Science and Technology UniversityBeijing 100192China Beijing Key Laboratory of nonlinear vibrations and Strength of Mechanical Structures College of Mechanical EngineeringBeijing University of TechnologyBeijing 100124China

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 *** 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 ***’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 *** Galerkin method is used to obtain the ordinary differential equations of the truncated conical ***,the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance *** 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 *** study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.

关键词： nonlinear free vibration harmonic balance method functionally graded graphene platelet-reinforced composite(FG-GPLRC) truncated conical shell chaos

Effect of different geometrical non-uniformities on nonlinear vibration of porous functionally graded skew plates: A finite element study

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Defence Technology（防务技术） 2022年第6期18卷 918-936页

作者： H.S.Naveen Kumar Subhaschandra Kattimani Department of Mechanical Engineering National Institute of Technology KarnatakaSurathkal575025India

This article presents the investigation of nonlinear vibration analysis of tapered porous functionally graded skew(TPFGS)plate considering the effects of geometrical non-uniformities to optimize the thickness in the structural *** TPFGS plate is analyzed considering linearly,bi-linearly,and exponentially varying *** plate’s effective material properties are tailor-made using a modified power-law distribution in which gradation varies along the thickness direction of the TPFGS *** the non-linear finite element formulation to develop the kinematic equation’s displacement model for the TPFGS plate is based on the first-order shear deformation theory(FSDT)in conjunction with von Karman’s *** nonlinear governing equations are established by Hamilton’s *** direct iterative method is adopted to solve the nonlinear mathematical relations to obtain the nonlinear *** influence of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the TPFGS plate for different skew angles and variable thicknesses are studied for various geometrical *** influence of taper ratio,variable thickness,skewness,porosity distributions,gradation,and boundary conditions on the plate’s nonlinear vibration is *** nonlinear frequency analysis reveals that the geometrical nonuniformities and porosities significantly influence the porous functionally graded plates with varying thickness than the uniform ***,exponentially and linearly variable thicknesses can be considered for the thickness optimizations of TPFGS plates in the structural design.

关键词： Functionally graded material Shear deformation theory Porosity distributions Variable thickness Geometrical skewness nonlinear free vibration

Energetics and conserved quantity of an axially moving string undergoing three-dimensional nonlinear vibration

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Acta Mechanica Sinica 2008年第2期24卷 215-221页

作者： Liqun Chen C. W. Lim Hu Ding Department of Mechanics Shanghai University Shanghai 200444 China Department of Construction and Building City University of Hong Kong Hong Kong China Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings. The time-rate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way. For a string moving in a constant axial speed and constrained by two fixed ends, a conserved quantity is proved to remain unchanged during three-dimensional vibration, while the string energy is not conserved. An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration. Numerical simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mechanical energy and the invariance of the conserved quantity.

关键词： nonlinear free vibration Axial movingstring Energetics Conserved quantity Stability