Free and Forced Vibrations of Monolithic and Composite Rectangular Plates With Interior Constrained Points

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Arka P. Chattopadhyay ◽  
Romesh C. Batra
Keyword(s):  
Forced Vibration ◽  
Plate Theory ◽  
Translational Motion ◽  
Orientation Angle ◽  
Stationary Points ◽  
Width Ratio ◽  
Rectangular Plates ◽  
Fiber Reinforced ◽  
Mode Localization ◽  
Unidirectional Fiber

The restriction of deformations to a subregion of a system undergoing either free or forced vibration due to an irregularity or discontinuity in it is called mode localization. Here, we study mode localization in free and forced vibration of monolithic and unidirectional fiber-reinforced rectangular linearly elastic plates with edges either simply supported (SS) or clamped by using a third-order shear and normal deformable plate theory (TSNDT) with points on either one or two normals to the plate midsurface constrained from translating in all three directions. The plates studied are symmetric about their midsurfaces. The in-house developed software based on the finite element method (FEM) is first verified by comparing predictions from it with either the literature results or those computed by using the linear theory of elasticity and the commercial FE software abaqus. New results include: (i) the localization of both in-plane and out-of-plane modes of vibration, (ii) increase in the mode localization intensity with an increase in the length/width ratio of a rectangular plate, (iii) change in the mode localization characteristics with the fiber orientation angle in unidirectional fiber reinforced laminae, (iv) mode localization due to points on two normals constrained, and (iv) the exchange of energy during forced harmonic vibrations between two regions separated by the line of nearly stationary points that results in a beats-like phenomenon in a subregion of the plate. Constraining translational motion of internal points can be used to design a structure with vibrations limited to its small subregion and harvesting energy of vibrations of the subregion.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

Nonlinear forced vibration of rectangular plates by modified multiple scale method

2021 ◽  
pp. 095440622110527
Author(s):  
Farzaneh Rabiee ◽  
Ali Asghar Jafari
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Forced Vibration ◽  
Multiple Scales ◽  
Plate Theory ◽  
Multiple Scales Method ◽  
Rectangular Plates ◽  
Partial Differential ◽  
Classical Plate Theory ◽  
Nonlinear Forced Vibration

In the present study, the nonlinear forced vibration of a rectangular plate is investigated analytically using modified multiple scales method for the first time. The plate is subjected to transversal harmonic excitation, and the boundary condition is assumed to be simply supported. The von Karman nonlinear strain displacement relations are used. The extended Hamilton principle and classical plate theory are applied to derive the partial differential equations of motions. This research focuses on resonance case with 3:1 internal resonance. By applying Galerkin method, the nonlinear partial differential equations are transformed into time dependent nonlinear ordinary differential equations, which are then solved analytically by modified multiple scales method. This proposed approach is very simple and straightforward. The obtained results are then compared with both the traditional multiple scales method and previous studies, and excellent compatibility is noticed. The effect of some of the main parameters of the system is also examined.

scholarly journals Analytical solution for vibration characteristics of rotating graphene nanoplatelet-reinforced plates under rub-impact and thermal shock

2020 ◽  
Vol 29 ◽  
pp. 2633366X2093365 ◽  
Author(s):  
Tian Yu Zhao ◽  
Yu Xuan Wang ◽  
Hong Gang Pan ◽  
Xiang Sheng Gao ◽  
Yi Cai
Keyword(s):  
Thermal Shock ◽  
Forced Vibration ◽  
Mechanical Performance ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Weight Fraction ◽  
Vibration Characteristics ◽  
Width Ratio ◽  
Graphene Nanoplatelet ◽  
Pattern Length

This article presents an analytical investigation on vibration characteristics of rotating graphene nanoplatelet (GPL)-reinforced plates subjected to rub-impact and thermal shock. The effective material properties are assumed to vary continuously and smoothly along the thickness direction of the plate and are determined via the Halpin–Tsai micromechanics model together with the rule of mixture. Considering the gyroscopic effect, the equations of motion are derived by adopting the Hamilton’s principle based on the Kirchhoff’s plate theory. Then, the Galerkin method and the small parameter perturbation method are utilized to obtain the free and forced vibration results for the rotating plate. A detailed parametric study is conducted to examine the effects of the GPL weight fraction, GPL distribution pattern, length-to-thickness ratio and length-to-width ratio of GPLs, and the rotating speed on free vibration characteristics of the nanocomposite plate. Attention is also given to the influences of the GPL weight fraction, thermal flow, and friction coefficient on forced vibration responses of the plate. The obtained results can play a role in the design of a rotating GPL-reinforced plate structure to achieve significantly improved mechanical performance.

Prediction of the damping properties of fiber-reinforced polymer composite panels with arbitrary geometries

2016 ◽  
Vol 232 (2) ◽  
pp. 275-283 ◽  
Author(s):  
A Abbaslou ◽  
MR Maheri
Keyword(s):  
Polymer Composite ◽  
Plate Theory ◽  
Mixed Finite Element ◽  
Fiber Reinforced Polymer ◽  
Rectangular Plates ◽  
Fiber Reinforced ◽  
Arbitrary Geometry ◽  
Classical Plate Theory ◽  
Reinforced Polymer ◽  
Arbitrary Geometries

In this work, the modal damping of multilayered, fiber-reinforced polymer composite laminates with an arbitrary geometry have been computed using a mixed finite element-meshless method. The meshless node distribution scheme is used in conjunction with the Lagrangian quadrilateral interpolating functions to ensure the continuity of interelemental displacements. Furthermore, since the distribution of the elements is not confined to the geometry of the problem, any arbitrary geometry can be readily analyzed by using the same node and element distributions. Using the classical plate theory, together with a structural damping model, modal response results have been produced for a number of multilayer fiber-reinforced polymer plate geometries, including triangular and circular as well as rectangular plates with different combinations of free and clamped edges. Comparison of these results with those reported in the literature shows that the proposed method can predict the modal properties of fiber-reinforced polymer laminates with arbitrary geometries and boundary conditions with a good degree of accuracy.

Flexural-Torsional Buckling of Pultruded Fiber-Reinforced Polymer Angle Beams under Eccentric Loading

2020 ◽  
Vol 982 ◽  
pp. 201-206
Author(s):  
Jaksada Thumrongvut ◽  
Natthawat Pakwan ◽  
Samaporn Krathumklang
Keyword(s):  
Buckling Load ◽  
Fiber Reinforced Polymer ◽  
Width Ratio ◽  
Fiber Reinforced ◽  
Torsional Buckling ◽  
Eccentric Load ◽  
Buckling Loads ◽  
Reinforced Polymer ◽  
Cross Sectional Dimension ◽  
Flexural Torsional Buckling

In this paper, the experimental study on the pultruded fiber-reinforced polymer (pultruded FRP) angle beams subjected to transversely eccentric load are presented. A summary of critical buckling load and buckling behavior for full-scale flexure tests with various span-to-width ratios (L/b) and eccentricities are investigated, and typical failure mode are identified. Three-point flexure tests of 50 pultruded FRP angle beams are performed. The E-glass fibre/polyester resin angle specimens are tested to examine the effect of span-to-width ratio of the beams on the buckling responses and critical buckling loads. The angle specimens have the cross-sectional dimension of 76x6.4 mm with span-to-width ratios, ranging from 20 to 40. Also, four different eccentricities are investigated, ranging from 0 to ±2e. Eccentric loads are applied below the horizontal flange in increments until beam buckling occurred. Based upon the results of this study, it is found that the load and mid-span vertical deflection relationships of the angle beams are linear up to the failure. In contrast, the load and mid-span lateral deflection relationships are geometrically nonlinear. The general mode of failure is the flexural-torsional buckling. The eccentrically loaded specimens are failed at critical buckling loads lower than their concentric counterparts. Also, the quantity of eccentricity increases as buckling load decreases. In addition, it is noticed that span-to-width ratio increases, the buckling load is decreased. The eccentric location proved to have considerable influence over the buckling load of the pultruded FRP angle beams.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

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