Nonlinear dynamic responses of functionally graded tubes subjected to moving load based on a refined beam model

2017 ◽  
Vol 88 (2) ◽  
pp. 1441-1452 ◽  
Author(s):  
Yang Chen ◽  
Yiming Fu ◽  
Jun Zhong ◽  
Yingli Li
Keyword(s):  
Nonlinear Dynamic ◽  
Moving Load ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Beam Model

scholarly journals Dynamic Behavior of a Bidirectional Functionally Graded Sandwich Beam under Nonuniform Motion of a Moving Load

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Dinh Kien Nguyen ◽  
An Ninh Thi Vu ◽  
Ngoc Anh Thi Le ◽  
Vu Nam Pham
Keyword(s):  
Dynamic Response ◽  
Dynamic Behavior ◽  
Moving Load ◽  
Sandwich Beam ◽  
Point Load ◽  
Functionally Graded ◽  
Beam Model ◽  
Material Distribution ◽  
Aspect Ratios ◽  
Nonuniform Motion

A bidirectional functionally graded Sandwich (BFGSW) beam model made from three distinct materials is proposed and its dynamic behavior due to nonuniform motion of a moving point load is investigated for the first time. The beam consists of three layers, a homogeneous core, and two functionally graded face sheets with material properties varying in both the thickness and longitudinal directions by power gradation laws. Based on the first-order shear deformation beam theory, a finite beam element is derived and employed in computing dynamic response of the beam. The element which used the shear correction factor is simple with the stiffness and mass matrices evaluated analytically. The numerical result reveals that the material distribution plays an important role in the dynamic response of the beam, and the beam can be designed to meet the desired dynamic magnification factor by appropriately choosing the material grading indexes. A parametric study is carried out to highlight the effects of the material distribution, the beam layer thickness and aspect ratios, and the moving load speed on the dynamic characteristics. The influence of acceleration and deceleration of the moving load on the dynamic behavior of the beam is also examined and highlighted.

Nonlinear Dynamics of Temperature-Dependent FG-GRC Laminated Beams Resting on Visco-Pasternak Foundations

2019 ◽  
Vol 20 (01) ◽  
pp. 2050012 ◽  
Author(s):  
Yin Fan ◽  
Y. Xiang ◽  
Hui-Shen Shen
Keyword(s):  
Nonlinear Dynamic ◽  
Thermal Environment ◽  
Perturbation Technique ◽  
Beam Theory ◽  
Md Simulations ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Laminated Beams ◽  
Nonlinearity Effect ◽  
Beam Motion

This paper studies the nonlinear dynamic responses of graphene-reinforced composite (GRC) beams in a thermal environment. It is assumed that a laminated beam rests on a Pasternak foundation with viscosity and consists of GRC layers with various volume fractions of graphene reinforcement to construct a functionally graded (FG) pattern along the transverse direction of the beam. An extended Halpin–Tsai model which is calibrated against the results from molecular dynamics (MD) simulations is used to evaluate the material properties of GRC layers. The mechanical model of the beam is on the establishment of a third-order shear deformation beam theory and includes the von-Kármán nonlinearity effect. The model also considers the foundation support and the temperature variation. The two-step perturbation technique is first applied to solve the beam motion equations and to derive the nonlinear dynamic load–deflection equation of the beam. Then a Runge–Kutta numerical method is applied and the solutions for this nonlinear equation are obtained. The influence of FG patterns, visco-elastic foundation, ambient temperature and applied load on transient response behaviors of simply supported FG-GRC laminated beams is revealed and examined in detail.

Nonlinear Dynamics of Simple-Supported Beam under Concentrated Moving Load

2012 ◽  
Vol 226-228 ◽  
pp. 541-545 ◽  
Author(s):  
Dong Xing Cao ◽  
Bao Chen ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Double Layer ◽  
Vibration Suppression ◽  
Structural Parameters ◽  
Moving Load ◽  
Equations Of Motion ◽  
Single Layer ◽  
Dynamic Responses ◽  
Beam Model ◽  
Layer Model

The dynamic responses of two kinds of simple-supported beams with single layer and double-layer under a moving load were analyzed based on the theory of nonlinear dynamics. The equations of motion are derived by using Hamilton’s principle and von Karman type equations for the two models. Galerkin’s method was employed to obtain the ordinary differential equations of motion. First we obtain the periodic motion waveforms in the mid-point of the beams at the same initial velocity, and the result show that the amplitude of the double-layer model is much smaller then that of the single-layer model. Then for the two models, the vibration response and critical velocity were studied considering the effect of the structural parameters, the magnitude and velocity of moving load. The results of numerical simulation show that double-layer beam model has better vibration suppression performance than single-layer beam model.

Nonlinear dynamic responses of beamlike truss based on the equivalent nonlinear beam model

2021 ◽  
Vol 194 ◽  
pp. 106197
Author(s):  
Mei Liu ◽  
Dengqing Cao ◽  
Xiaoyun Zhang ◽  
Jin Wei ◽  
Dongfang Zhu
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Responses ◽  
Beam Model ◽  
Nonlinear Beam

Dynamic Responses of Functionally Graded Sandwich Beams Resting on Elastic Foundation Under Harmonic Moving Loads

2018 ◽  
Vol 18 (09) ◽  
pp. 1850112 ◽  
Author(s):  
Wachirawit Songsuwan ◽  
Monsak Pimsarn ◽  
Nuttawit Wattanasakulpong
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Moving Load ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Harmonic Load ◽  
Sandwich Beams

This paper investigates the free vibration and dynamic response of functionally graded sandwich beams resting on an elastic foundation under the action of a moving harmonic load. The governing equation of motion of the beam, which includes the effects of shear deformation and rotary inertia based on the Timoshenko beam theory, is derived from Lagrange’s equations. The Ritz and Newmark methods are employed to solve the equation of motion for the free and forced vibration responses of the beam with different boundary conditions. The results are presented in both tabular and graphical forms to show the effects of layer thickness ratios, boundary conditions, length to height ratios, spring constants, etc. on natural frequencies and dynamic deflections of the beam. It was found that increasing the spring constant of the elastic foundation leads to considerable increase in natural frequencies of the beam; while the same is not true for the dynamic deflection. Additionally, very large dynamic deflection occurs for the beam in resonance under the harmonic moving load.

Nonlinear vibration and active control of functionally graded beams with piezoelectric sensors and actuators

2011 ◽  
Vol 22 (18) ◽  
pp. 2093-2102 ◽  
Author(s):  
Yiming Fu ◽  
Jianzhe Wang ◽  
Yiqi Mao
Keyword(s):  
Active Control ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Sensors And Actuators ◽  
Nonlinear Dynamic Equations ◽  
Piezoelectric Layers

Employing higher order shear deformation theory, geometric nonlinear theory, and Hamilton’s principle, a set of nonlinear governing equations for the functionally graded beams with surface-bonded piezoelectric layers is derived. Then, the negative velocity feedback algorithm coupling the direct and inverse piezoelectric effect is used to control the piezoelectric functionally graded beams actively. Using the finite difference method and Newmark method synthetically, the numerical solutions for the nonlinear dynamic equations of functionally graded beams with piezoelectric patches are obtained iteratively. In the numerical examples, the effects of the volume fraction exponent on the nonlinear dynamic responses and amplitude–frequency curves are investigated, and the active control responses of the functionally graded beams with piezoelectric layers under different control gains and volume fraction exponents are analyzed. Some meaningful solutions have been presented.

scholarly journals Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

2021 ◽  
Vol 3 (11) ◽  
Author(s):  
Hesam Nazari ◽  
Masoud Babaei ◽  
Faraz Kiarasi ◽  
Kamran Asemi
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Differential Quadrature Method ◽  
Moving Load ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Linear And Nonlinear ◽  
Generalized Differential

Abstract In this study, we present a numerical solution for geometrically nonlinear dynamic analysis of functionally graded material rectangular plates excited to a moving load based on first-order shear deformation theory (FSDT) for the first time. To derive the governing equations of motion, Hamilton’s principle, nonlinear Von Karman assumptions and FSDT are used. Finally, the governing equations of motion are solved by employing the generalized differential quadratic method as a numerical solution. Natural frequencies, dynamic bending behavior and stresses of the plate for linear and nonlinear type of geometrically strain–displacement relations and different factors, including the magnitude and velocity of moving load, length ratio, power law exponent and various edge conditions are obtained and compared. Article highlights Developing generalized differential quadrature method (GDQM) solution based on FSDT for dynamic analysis of FGM plate excited by a moving load for the first time. Comparison of linear and nonlinear dynamic response of plate by considering Von-Karman assumption. Observing considerable difference between linear and nonlinear results

Analysis of nonlinear thermal dynamic responses of sandwich functionally graded cylindrical shells containing fluid

2017 ◽  
Vol 21 (6) ◽  
pp. 1953-1974
Author(s):  
Phu Van Khuc ◽  
Bich Huy Dao ◽  
Doan Xuan Le
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Cylindrical Shells ◽  
Nonlinear Dynamic Analysis ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Effect Of Temperature ◽  
Nonlinear Dynamic Equation ◽  
Graded Material ◽  
The Galerkin Method

Based on the classical shell theory, taking into account the nonlinear geometry of von Karman-Donnell, this article deals with the nonlinear dynamic analysis of Functionally Graded Material (Sandwich-FGM) cylindrical shells containing fluid under mechanical and thermal loads. By using the Galerkin method, the nonlinear dynamic equation is transformed into nonlinear differential equation in terms of time. The investigation of nonlinear dynamic response of sandwich-FGM cylindrical shells containing fluid is established. Numerical results show effect of temperature, fluid, geometric parameters of structure and material parameters (coefficient k) on the dynamic response of structure.

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