Influence of thermal gradient on natural frequency of rectangular plate vibration
TL;DR: In this article, the dynamic free response of thin rectangular plates subjected to steady state one dimensional and two dimensional temperature distributions satisfying the Laplace equation is analyzed by using the finite difference method and finite element method.
About: This article is published in Nuclear Engineering and Design.The article was published on 1979-03-01. It has received 5 citations till now. The article focuses on the topics: Finite difference method & Finite element method.
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TL;DR: In this paper, the free vibration behavior of laminated composite plates subjected to varying temperature and moisture was investigated using both experimental and numerical analysis. But the results were limited to the case of a simple lamin...
Abstract: The present study deals with both experimental and numerical investigation on the free vibration behavior of laminated composite plates subjected to varying temperature and moisture. A simple lamin...
60 citations
TL;DR: In this article, an analytical study on the dynamic characteristics of a laminated plate under temperature gradient is carried out, where theoretical formulations are derived with the first order shear deformation theory and von Karman nonlinear strain displacement relationship considering the effect of temperature gradient.
28 citations
Cites methods from "Influence of thermal gradient on na..."
...The dynamic free response of thin rectangular plates subjected to one and two dimensional steady state temperature distributions satisfying Laplace’s equation was investigated by using the finite difference method and finite element method [18,19]....
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TL;DR: In this paper, the effect of temperature change on the natural frequencies of glass fiber reinforced polymer (GFRP) composites has been analyzed using a nonlinear finite element (FE) model.
12 citations
TL;DR: In this article, the effect of temperature dependent Young's moduli on the transverse vibration of polar orthotropic circular plates is considered, and two aspects are considered: the effect upon the flexural aspect of the plate and the geometric stiffness resulting from the more complicated form of the radial stress distribution.
5 citations
Dissertation•
01 Jan 2012
TL;DR: In this paper, the effects of various parameters such as number of layers, aspect ratios, side-to thickness ratios, ply orientations, static load factors, lamination angle and the degree of orthotropic are studied.
Abstract: Composite materials are increasingly used in aerospace, naval and high performance civil engineering structures such as aerospace, submarines, automobiles. The structural components, subjected to in-plane harmonic loads may undergo parametric resonance or dynamic stability due to certain combinations of the applied in-plane forcing parameters and natural frequency of transverse vibration. The parametric instability itself requires investigation of vibration and buckling of structures. The present study deals with free vibration, buckling and parametric resonance behavior of laminated composite plates under in-plane periodic loading under varying temperatureand moisture. In this analysis, the effects of various parameters such as number of layers, aspect ratios, side-to thickness ratios, ply orientations, static load factors, lamination angle and the degree of orthotropic are studied. A simple laminated plate model based on the first order shear deformation theory (FSDT) is developed for the free vibration, buckling and parametric instability effects of composite plates subjected to hygrothermal loading. The principal instability regions are obtained using Bolotin’s approach employing finite element method (FEM). An eight-node isoparametric quadratic element is employed in the present analysis with five degree of freedom per node. The element is modified to accommodate the laminated composite plates under hygrothermal environment, considering the effects of transverse shear deformation and rotary inertia. The element stiffness matrix, geometric stiffness matrix due to residual stresses, element mass matrix, geometric stiffness matrix due to applied in-plane loads and nodal load vector of the element are derived using the principle of minimum potential energy. They are evaluated using the Gauss quadrature numerical integration technique. Reduced integration technique is applied to avoid the possible shear locking. A computer program based on FEM in MATLAB environment is developed to perform all necessary computations. The basic vibration and buckling experiments are performed on the industry driven woven fiber Glass/Epoxy specimens subjected to hygrothermal environment. The specimens were hygrothermally conditioned in a humidity cabinet where the conditions were maintained at temperatures of 300K-425K and relative humidity (RH) ranging from 0-1.0% for moisture concentrations. The numerical and experimental results show that there is reduction in natural frequencies and buckling loads with increasing temperature and moisture concentration for laminates both for simply supported and clamped boundary conditions. The dynamic instability study using FEM revealed that, due to the static component of load, the instability regions tend to shift to lower frequencies. The onset of instability occurs earlier and the width of dynamic instability regions increases with rise in temperature and moisture concentration for different parameters. With increase in lamination angle, the width of the instability region becomes smaller. The onset of instability occurs later for square plates than rectangular plates with wider instability region with increase of aspect ratio. The ply orientation significantly affects the onset of instability. It is observed that the excitation frequency increases with introduction of curvatures from flat panel to doubly curved panel in hygrothermal environments. Thus the instability behaviour of laminated composite panels is influenced by increase in number of layers, aspect ratio, side to thickness ratio, increase in static and dynamic load factor, geometry, material, ply lay-up and its orientation. This can be utilized to tailor the design of laminated composite panels in hygrothermal environment.
2 citations
References
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Book•
01 Jan 1960
TL;DR: Theory of thermal stresses, Theory of Thermal Stresses, this paper, Theory of thermal stress, and thermal stresses theory, thermal stresses and thermal stress theory in literature, 2015.
Abstract: Theory of thermal stresses , Theory of thermal stresses , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
2,319 citations
Book•
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TL;DR: The fundamental equation of classical plate theory can be found in this article, where anisotropic and variable-thickness versions of the classical plates are considered, as well as other considerations.
Abstract: : Contents: Fundamental Equations of Classical Plate Theory; Circular Plates; Elliptical Plates; Rectangular Plates; Parallelogram Plates; Other Quadrilateral Plates; Triangular Plates; Plates of Other Shapes; Anisotropic Plates; Plates With Inplane Forces; Plates With Variable Thickness; and Other Considerations.
2,137 citations
2,034 citations
TL;DR: In this paper, the method is based on the following theorem: if A is a positive definite matrix of band form such that A = 0, then there exists a real non-singular lower triangular matrix L such that L{L^T} = A,
Abstract: The method is based on the following theorem. If A is a positive definite matrix of band form such that
$${a_{ij}} = 0{\rm{ (|}}i - j| >m{\rm{)}}$$
(1)
then there exists a real non-singular lower triangular matrix L such that
$$L{L^T} = A,{\rm{ where }}{l_{ij}} = 0{\rm{ (}}i - j >m{\rm{)}}{\rm{.}}$$
(2)
76 citations
75 citations