scholarly journals Analysis of nonlinear dynamic responses for functionally graded beams resting on tensionless elastic foundation under thermal shock

2016 ◽  
Vol 142 ◽  
pp. 272-277 ◽  
Author(s):  
Jun Zhong ◽  
Yiming Fu ◽  
Yang Chen ◽  
Yingli Li
Keyword(s):  
Thermal Shock ◽  
Elastic Foundation ◽  
Nonlinear Dynamic ◽  
Functionally Graded ◽  
Dynamic Responses

scholarly journals Nonlinear static and dynamic buckling of eccentrically stiffened functionally graded cylindrical shells under axial compression surrounded by an elastic foundation

2014 ◽  
Vol 36 (1) ◽  
pp. 27-47 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dao Huy Bich ◽  
Dao Van Dung
Keyword(s):  
Elastic Foundation ◽  
Axial Compression ◽  
Nonlinear Dynamic ◽  
Linear Time ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Buckling Load ◽  
Dynamic Responses ◽  
Nonlinear Buckling

This paper presents an analytical approach to investigate the nonlinear buckling of imperfect eccentrically stiffened functionally graded thin circular cylindrical shells subjected to axial compression and surrounded by an elastic foundation. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, initial geometrical imperfection, the smeared stiffeners technique and Pasternak’s two-parameter elastic foundation, the governing equations of eccentrically stiffened functionally graded cylindrical shells are derived. The functionally graded cylindrical shells are reinforced by homogeneous ring and stringer stiffener system on internal and (or) external surface. The resulting equations are solved by the Galerkin method to obtain the explicit expression of static critical buckling load, post-buckling load-deflection curve and nonlinear dynamic motion equation. The nonlinear dynamic responses are found by using fourth order Runge-Kutta method. The dynamic critical buckling loads of shells are considered for step loading of infinite duration and linear-time compression. The obtained results show the effects of foundation, stiffeners and input factors on the nonlinear buckling behavior of these structures. 

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.

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.

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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