Experimental studies on the dynamic response of thin rectangular plates subjected to moving mass

2020 ◽  
pp. 107754632093313 ◽  
Author(s):  
Sajjad Seifoori ◽  
Ahmad Mahdian Parrany ◽  
Sajjad Darvishinia
Keyword(s):  
Dynamic Response ◽  
Rectangular Plate ◽  
Plate Theory ◽  
Experimental Studies ◽  
Time History ◽  
Moving Mass ◽  
Rectangular Plates ◽  
Classical Plate Theory ◽  
Thin Rectangular Plate ◽  
Expansion Technique

This article presents experimental studies on the dynamic response of a thin rectangular plate with clamped boundary conditions subjected to a moving mass. The designed experimental setup is described in detail, and the obtained experimental results are compared with theoretical solutions. In this regard, the governing motion equation of the thin rectangular plate excited by a moving mass is formulated based on the classical plate theory, and the eigenfunction expansion technique is used to solve the equation. Parametric studies are carried out to investigate the effect of some parameters, including the moving object mass and velocity, as well as the plate’s aspect ratio and thickness, on the dynamic response of the plate based on the time history of the plate’s central point deflection.

Experimental Investigation of Nonlinear Vibration of a Thin Rectangular Plate

2019 ◽  
Vol 11 (06) ◽  
pp. 1950059 ◽  
Author(s):  
Sohayb Abdulkerim ◽  
Athanasios Dafnis ◽  
Hans-G Riemerdes
Keyword(s):  
Rectangular Plate ◽  
Plate Theory ◽  
Plate Thickness ◽  
Extraction Procedure ◽  
Time History ◽  
Laser Vibrometer ◽  
Classical Plate Theory ◽  
Thin Rectangular Plate ◽  
Sinusoidal Input ◽  
History Of

In this paper, the geometrical nonlinear vibrations of a rectangular plate have been investigated experimentally and numerically. The experiment was conducted on a thin rectangular plate. The plate was excited close to the first fundamental natural frequency. The time history of velocities of the central point has been measured by using a laser vibrometer. While the numerical investigation has been carried using the Finite Element Method (FEM), the numerical results are validated by analytical and experimental results. In order to develop and test the extraction procedure of the bifurcation plot of a dynamical system, a chaotic pendulum has been analyzed. Then, the same successful code has been used again for the experimental dynamics of the investigated plate. The plate has been forced with a sinusoidal input at a gradually stepped and increased amplitude. For every step, the phase portrait is determined, and then processed to extract the bifurcation map. The resulted map has shown successfully the linear range where the classical plate theory is adequate, and the boundary at which the transition to nonlinearity has occurred. The bifurcation has occurred when the lateral amplitude has reached 50% of the plate thickness.

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.

Wavelet Multi-Scale Solution for Deflection of Thin Rectangular Plates under Temperature

2012 ◽  
Vol 166-169 ◽  
pp. 2871-2875
Author(s):  
Yan Chang Wang ◽  
Ke Liang Ren ◽  
Yan Dong ◽  
Ming Guang Wu
Keyword(s):  
Differential Equations ◽  
Rectangular Plate ◽  
Thermal Environment ◽  
Operational Matrix ◽  
Rectangular Plates ◽  
Thin Rectangular Plate ◽  
Multi Scale ◽  
Scale Method ◽  
The Matrix ◽  
Operational Matrix Of Integration

To consider the deformation of thin rectangular plate under temperature. In this paper, the wavelet multi-scale method was used to solve the thin plate governing differential equations with four different initial or boundary conditions. An operational matrix of integration based on the wavelet was established and the procedure for applying the matrix to solve the differential equations was formulated, and got the deflection of thin rectangular plates under temperature. The result provides a theoretical reference for solving thin rectangular plate deflection in thermal environment using multi-scale approach.

scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

Forced Flexural Vibrations in a Thin Nonlocal Rectangular Plate with Kirchhoff’s Thin Plate Theory

2020 ◽  
Vol 20 (09) ◽  
pp. 2050107
Author(s):  
Iqbal Kaur ◽  
Parveen Lata ◽  
Kulvinder Singh
Keyword(s):  
Rectangular Plate ◽  
Thin Plate ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Small Scale ◽  
Concentrated Load ◽  
Thin Rectangular Plate ◽  
Flexural Vibrations

This study deals with a novel model of forced flexural vibrations in a transversely isotropic thermoelastic thin rectangular plate (TRP) due to time harmonic concentrated load. The mathematical model is prepared for the thin plate in a closed form with the application of Kirchhoff’s love plate theory for nonlocal generalized thermoelasticity with Green–Naghdi (GN)-III theory of thermoelasticity. The nonlocal thin plate has a nonlocal parameter to depict small-scale effect. The double finite Fourier transform technique has been used to find the expressions for lateral deflection, thermal moment and temperature distribution for simply supported (SS) thin rectangular plate in the transformed domain. The effect of classical thermoelasticity (CTE) theory of thermoelasticity and nonlocal parameters has been shown on the computed quantities. Few particular cases have also been deduced.

Effect of Shear Deformation and Rotatory Inertia on Dynamic Buckling of Elastic Plates

1988 ◽  
Vol 110 (3) ◽  
pp. 282-286
Author(s):  
V. Birman
Keyword(s):  
Dynamic Response ◽  
Shear Deformation ◽  
Plate Theory ◽  
Deformation Mode ◽  
Dynamic Buckling ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Qualitative Effect

The influence of shear deformation and rotatory inertia on dynamic response of elastic rectangular plates subject to in-plane loads increasing with time is discussed using Mindlin’s plate theory. The qualitative effect of those factors on transverse displacements is estimated. It is shown that this effect becomes essential only if the plate is thick and the number of half-waves along the plate axes in the deformation mode is large.

Effect of Shear Deformations on the Bending of Rectangular Plates

1960 ◽  
Vol 27 (1) ◽  
pp. 54-58 ◽  
Author(s):  
V. L. Salerno ◽  
M. A. Goldberg
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Plate Theory ◽  
Order Partial Differential Equation ◽  
Rectangular Plates ◽  
Partial Differential ◽  
Classical Plate Theory ◽  
Simply Supported ◽  
Wide Range

The three partial differential equations derived by Dr. E. Reissner2, 3 have been reduced to a fourth-order partial differential equation resembling that of the classical plate theory and to a second-order differential equation for determining a stress function. The general solution for the two partial differential equations has been applied to a simply supported plate with a constant load p and to a plate with two opposite edges simply supported and the other two edges free. Numerical calculations have been made for the simply supported plate and the results compared with those of classical theory. The calculations for a wide range of parameters indicate that the deviation is small.

scholarly journals The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method

2020 ◽  
pp. 146134842094657
Author(s):  
Xu Liang ◽  
Zeng Cao ◽  
Yu Deng ◽  
Xue Jiang ◽  
Xing Zha ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Analytical Method ◽  
Numerical Solutions ◽  
Thermal Environment ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Fourier Series Expansion ◽  
Pasternak Foundation

This paper carries out the transient behaviors of a thin rectangular plate considering different boundary conditions, Pasternak foundation, and thermal environment simultaneously. The governing differential equations of the system are derived by employing the Kirchhoff’s classical plate theory and Hamilton’s principle. This paper proposes a novel semi-analytical methodology, which integrates Laplace transform, the one-dimensional differential quadrature method, Fourier series expansion technique, and Laplace numerical inversion to analyze plates’ transient response. The proposed method can obtain dynamic response of the rectangular efficiently and accurately, which fills the gap of transient behaviors in semi-analytical method. A comparison between semi-analytical results and numerical solutions from the publication on this subject is presented to verify the method. Specifically, the results also agree well with the data generated by the Navier’s method. The convergence tests indicate that the semi-analytical algorithm is a quick convergence method. The effects of various variables, such as geometry, boundary conditions, temperature, and the coefficients of the Pasternak foundation, are further studied. The parametric studies show that geometry and temperature change are significant factors that affect the dynamic response of the plate.

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