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Steady state response of an infinite beam on a viscoelastic foundation with moving distributed mass and load

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Science China(Physics,Mechanics & Astronomy) 2020年第8期63卷 71-85页

作者： Yin Zhang State Key Laboratory of Nonlinear Mechanics(LNM) Institute of MechanicsChinese Academy of SciencesBeijing 100190China School of Engineering Science University of Chinese Academy of SciencesBeijing 100049China

Compared with the moving concentrated load model,it is more realistic and proper to use the moving distributed mass and load model to simulate the dynamics of a train moving along a railway *** the problem of a moving concentrated load,there is only one critical velocity,which divides the load moving velocity into two categories:subcritical and *** locus of a concentrated load demarcates the space into two parts:the waves in these two domains are called the front and rear waves,*** comparison,in the problem of moving distributed mass and load,there are two critical velocities,which results in three categories of the distributed mass moving *** to the presence of the distributed mass and load,the space is divided into three domains,in which three different waves *** richer and different variation patterns of wave shapes arise in the problem of the moving distributed mass and *** mechanisms responsible for these variation patterns are systematically studied.A semi-analytical solution to the steady-state is also obtained,which recovers that of the classical problem of a moving concentrated load when the length of the distributed mass and load approaches zero.

关键词： steady state beam viscoelastic foundation moving distributed mass

Vibration of axially moving beam supported by viscoelastic foundation

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Applied Mathematics and Mechanics(English Edition) 2017年第2期38卷 161-172页

作者： Haijuan ZHANG Jian MA Hu DING Liqun CHEN Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China School of Mechanical Engineering Anhui University of Technology Maanshan 243032 Anhui Province China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Shanghai 200072 China Department of Mechanics College of Sciences Shanghai University Shanghai 200444 China

In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton＇s principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.

关键词： axially moving beam viscoelastic foundation complex modal analysis,natural frequency forced vibration

Solving Nonlinear Differential Equation Governing on the Rigid Beams on viscoelastic foundation by AGM

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Journal of Marine Science and Application 2015年第1期14卷 30-38页

作者： M. R. Akbari D. D. Ganji A. K. Rostami M. Nimafar Department of Civil Engineering and Chemical Engineering University of Tehran P.O. Box 11155-4563 Tehran Iran Department of Mechanical Engineering Babol University of Technology P.O. Box 484 Babol Iran Department of Mechanical and Aerospace Engineering Politecnico di Torino 24-10129 Turin Italy

In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji＇s method （AGM）. AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method （Runk45） and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration （A）, the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure Therefore, AGM can be considered as a significant progress in nonlinear sciences.

关键词： nonlinear differential equation Akbari-Ganji's method(AGM) rigid beam viscoelastic foundation vibrating system damping ratio energy lost per cycle

Dynamic analysis of buried pipeline with and without barrier system subjected to underground detonation

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Defence Technology（防务技术） 2023年第11期29卷 95-105页

作者： Chaidul Haque Chaudhuri Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology BombayMumbai400076India

Failure of pipe networks due to blast loads resulting from terrorist attacks or construction facilities, may cause economic loss, environmental pollution, source of firing or even it may lead to a disaster. The present work develops a closed-form solution of buried pipe with barrier system subjected to subsurface detonation. The solution is derived based on the concept of double-beam system. Euler Bernoulli's beams are used to simulate the buried pipe and the barrier system. Soil is idealized as viscoelastic foundation along with shear interaction between discrete Winkler springs(advanced soil model). The finite SineFourier transform is employed to solve the coupled partial differential equations. The solution is validated with past studies. A parametric study is conducted to investigate the influence of TNT charge weight, pipe material, damping ratio and TNT offset on the response of buried pipe with and without barrier system. Further a statistical analysis is carried out to get the significant soil and pipe input parameters. It is perceived that peak pipe displacements for both the cases(with and without barrier) are increases with increasing the weight of TNT charge and decreases with increasing the damping ratio and TNT offset. The deformation of pipe also varies with pipe material. Pipe safety against blast loads can be ensured by providing suitable barrier layer. The present study can be utilized in preliminary design stage as an alternative to expensive numerical analysis or field study.

关键词： Buried pipeline Subsurface detonation Analytical solution viscoelastic foundation Protective barrier

On wave dispersion of rotating viscoelastic nanobeam based on general nonlocal elasticity in thermal environment

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Applied Mathematics and Mechanics(English Edition) 2023年第9期44卷 1577-1596页

作者： A.RAHMANI S.FAROUGHI M.SARI Mechanical Engineering Faculty Urmia University of TechnologyUrmia ***Iran Mechanical and Maintenance Engineering Department German Jordanian UniversityAmman 11180Jorda

The present research focuses on the analysis of wave propagation on a rotating viscoelastic nanobeam supported on the viscoelastic foundation which is subject to thermal gradient effects.A comprehensive and accurate model of a viscoelastic nanobeam is constructed by using a novel nonclassical mechanical *** on the general nonlocal theory(GNT),Kelvin-Voigt model,and Timoshenko beam theory,the motion equations for the nanobeam are *** the GNT,material hardening and softening behaviors are simultaneously taken into account during wave *** analytical solution is utilized to generate the results for torsional(TO),longitudinal(LA),and transverse(TA)types of wave ***,the effects of nonlocal parameters,Kelvin-Voigt damping,foundation damping,Winkler-Pasternak coefficients,rotating speed,and thermal gradient are illustrated and discussed in detail.

关键词： temperature effect general nonlocal theory(GNT) Kelvin-Voigt model viscoelastic foundation wave propagation rotating viscoelastic nanobeam

Deformation response of roof in solid backfilling coal mining based on viscoelastic properties of waste gangue

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International Journal of Mining Science and Technology 2021年第2期31卷 279-289页

作者： Peng Huang Jixiong Zhang Xingjie Yan Anthony John Spencer Spearing Meng Li Shiwei Liu School of Mines China University of Mining and TechnologyXuzhou 221116China State Key Laboratory of Coal Resources and Safe Mining China University of Mining and TechnologyXuzhou 221116China School of Mathematics China University of Mining and TechnologyXuzhou 221116China National Engineering Laboratory For Surface Transportation Weather Impacts Prevention Broadvision Engineering ConsultantsKunming 650041China

Solid backfill mining(SBM)is a form of green mining,the core of which is to control and minimize the deformation and movement of strata above longwall coal *** a mechanical model that can reliably describe roof deformation by considering the viscoelastic properties of waste gangue is important as it assists in improving mine designs and reducing the environmental impact on the *** this paper,the time-dependent deformation characteristics of gangue under different stress levels were obtained by using lateral confinement compression,that reliably represents the compaction of *** viscoelastic foundation model for gangue mechanical response is different from the traditionally used elastic foundation model,as it considers the time factor and viscoelasticity.A mechanical model using a thin plate on a fractional viscoelastic foundation was established,and the roof deflection,bending moment,time-dependent,viscous and other characteristics of SBM were included and *** with the existing elastic foundation model,the proposed fractional order viscoelastic foundation model has higher accuracy with laboratory *** plate deflection increases by 50.9%and the bending moment increases by 37.9%after 100 days,which the elastic model would not have been able to predict.

关键词： SBM Fractional order Thin plate Time factor viscoelastic foundation Roof deflection and bending moment

Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation

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Applied Mathematics and Mechanics(English Edition) 2023年第1期44卷 35-52页

作者： Zhaonian LI Juan LIU Biao HU Yuxing WANG Huoming SHEN Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province School of Mechanics and Aerospace EngineeringSouthwest Jiaotong UniversityChengdu 610031China

This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric(FGP) nanoplates deposited in a viscoelastic *** is assumed that(i) the material parameters of the nanoplates obey a power-law variation in thickness and(ii) the uniform porosity exists in the *** combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined higher-order shear deformation *** scale effects of the nanoplates are captured by employing nonlocal strain gradient theory(NSGT).The motion equations are calculated in accordance with Hamilton’s ***,the dispersion characteristics of the nanoplates are numerically determined by using a harmonic *** results indicate that the nonlocal parameters(NLPs) and length scale parameters(LSPs) have exactly the opposite effects on the wave *** addition,it is found that the effect of porosity volume fractions(PVFs) on the wave frequency depends on the gradient indices and damping *** these two values are small,the wave frequency increases with the volume *** contrast,at larger gradient index and damping coefficient values,the wave frequency decreases as the volume fraction increases.

关键词： scale effect functionally graded material(FGM) dispersion characteristic piezoelectric nanoplate viscoelastic foundation

Dynamics of vehicle-pavement coupled system based on a revised flexible roller contact tire model

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中国科学:技术科学 2010年第3期 341-341页

作者： YANG ShaoPu,LI ShaoHua & LU YongJie School of Mechanical Engineering,Shijiazhuang Railway Institute,Shijiazhuang 050043,China

A revised flexible roller contact tire model (RFRC tire model) is proposed,which considers not only the geometric and flexible filtering effect,but also tire damping and pavement displacement.A vehicle-pavement coupled system is modeled as a two DOF oscillator moving along a simply supported beam on a linear viscoelastic *** using the Galerkin’s and Direct Integral method,dynamical responses of the vehicle-pavement coupled system are obtained based on the RFRC tire model and the traditional single point contact tire model (SPC tire model).The simulation results are compared with test data and the validity of the proposed RFRC tire model is *** between the two models are also *** is found that the dynamical behaviors for both models agree with each other quite well when road surface roughness is a long harmonic *** the other hand,they are different under short harmonic wave or impulse road *** the RFRC tire model should be used to compute the tire force and investigate dynamical responses of vehicle and pavement.

关键词： tire model dynamics flexible roller contact vehicle-pavement coupled system viscoelastic foundation