On the Solution to Pre- Buckling of a Thin Rectangular Plate Subjected to a Thick Strip in-plane Loading

The current paper deals with the problem of the simply supported thin rectangular plate subjected to the intermediate strip in-plane loading. Based on the strain energy method (Fourier ansatz), the critical (minimum value) of buckling stress occurrence was determined in a general form dependent only on the strip thickness, strip location, plate width and stress magnitude. Compatible with the classical columns Euler method it was found that the plate stability is decreased with the increasing of the plate width due to larger induced stresses. Also, strip location relative to the support region was found to influence the buckling (same analogy to the Euler buckling theory; consider the strip as a both sides pressed rod). Additionally, the strip width parameter increase is likely to cause larger buckling stress. Moreover, expressions that includes both axial and transverse loads for different extended cases configurations were also derived and examined based on the strain energy method alongside explanation for possible applications (thin aluminum plate welding). In a general view, it was found that the cases of combined axial and perpendicular loading action are less stabilized than cases where only one kind of loading configuration is participated. Finally, the buckling stress was found to agree qualitatively with the cited literature.

Modal Analysis of Orthotropic Thin Rectangular Plate Based on Analytical and Finite Element Approaches

The present work aims to carry out modal analysis of orthotropic thin rectangular plate to determine its natural frequencies and mode shapes by using analytical method based on Rayleigh-Ritz energy approach. To demonstrate the accuracy of this approach, the same plate is discritisated and analyzed using the finite element method. The natural and angular frequencies were computed and determined analytically and numerically by using ABAQUS finite element code. The convergency and accuracy of the numerical solution was examined. The effects of geometrical parameters and boundary conditions on vibrations are investigated. The results obtained showed a very good agreement between the analytical approach and the numerical simulations. Also, the paper presents simulations results of testing of the plate with passive vibration control.

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

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.

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

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.

Modelling Method of Dynamic Characteristics of Marine Thin-Walled Structure

Thin-walled structures are very popular in industries, especially in the field of shipbuilding. There are many types of equipment and structures of ships, which are made up of thin-walled structures such as hull, deck and superstructure. Therefore, the analysis and understanding of the static and dynamic characteristics of a thin-walled structure are very important. In this article, we focus on vibration analysis of a typical thin-walled structure-rectangular plate, a basic structure of the hull. Vibration analysis of a rectangular thin plate is conducted by two methods: numerical modelling method of the finite element on Patran-Nastran software platform and experimental method implemented in the laboratory of Gdynia Maritime University. Thin rectangular plate is fixed one end by four clamping plates and is modelled with finite elements and different meshing densities. The numerical model of thin rectangular plate is divided into four cases. Case 1, thin rectangular plate, and clamping plates are modelled with two-dimensional elements. Case 2, the rectangular thin plate is modelled with two-dimensional elements; the clamping plates are modelled with three-dimensional elements. Case 3, both the rectangular thin plate and clamping plates are modelled with three-dimensional elements. Case 4, the rectangular thin plate, and clamping plates are modelled with three-dimensional elements with larger mesh density to increase the accuracy of the calculation results. After that, the results of vibration analysis according to the numerical modelling method on Patran-Nastran software platform for these cases were compared with the measurement results. From there, assess the accuracy of analysis results of selected numerical model methods and the ability to widely apply this numerical model method to other marine structures.