The Effect of Welding Self-Equilibrating Stresses on the Natural Frequencies of Thin Rectangular Plate With Edges Rotational Flexibility

2005 ◽  
Author(s):  
Albert E. Yousif ◽  
Shakir Al-Samarrai ◽  
A. Salam Al-Ammri
Keyword(s):  
Residual Stresses ◽  
Rectangular Plate ◽  
Energy Method ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Thin Rectangular Plate ◽  
Special Solutions ◽  
General Frequency ◽  
Elastically Restrained ◽  
Good Agreement

An investigation has been made into the effect of residual stresses on the vibration characteristics of a thin rectangular plate elastically restrained against rotation along all edges using an energy method. General frequency equations with and without the effect of residual stresses have been obtained. Exact frequency equations with and without the effect of residual stresses for the cases: C-C-C-C, S-S-S-S, S-S-C-S, C-S-C-S, S-S-C-C, C-C-C-S have also been obtained. Exact equations were derived including the effect of the position of welding along the width of the plate for all cases considered. The validity of the equations obtained was checked with available special solutions with a good agreement.

The Effect of Welding Self-Equilibrating Stresses on the Natural Frequencies of Thin Rectangular Clamped Plate

2006 ◽  
Author(s):  
A. Salam Al-Ammri
Keyword(s):  
Residual Stresses ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Clamped Plate ◽  
Special Solutions ◽  
General Frequency ◽  
Good Agreement

In this paper an investigation has been made into the effect of residual stresses on the vibration characteristics of thin rectangular clamped plate. General frequency equations with and without the effect of residual stresses due to multi-lines of heating or welding along the length and width of the plate have been obtained. The validity of the equations obtained was checked with available special solutions with a good agreement.

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

2020 ◽  
Vol 30 (5-6) ◽  
pp. 217-225
Author(s):  
Samir Deghboudj ◽  
Wafia Boukhedena ◽  
Hamid Satha
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Rectangular Plate ◽  
Analytical Approach ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
The Finite Element Method ◽  
Thin Rectangular Plate ◽  
Good Agreement

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.

scholarly journals Vibrations of Circular Plates with Elastically Restrained Edge against Translation and Resting on Elastic Foundation

2016 ◽  
Vol 13 (2) ◽  
pp. 187
Author(s):  
L.B. Rao ◽  
C.K. Rao
Keyword(s):  
Elastic Foundation ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Vibration Characteristics ◽  
Graphical Form ◽  
Winkler Foundation ◽  
Stiffness Ratio ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Elastically Restrained

The present paper deals with exact solutions for the free vibration characteristics of thin circular plates elastically restrained against translation and resting on Winkler-type elastic foundation based on the classical plate theory. Parametric investigations are carried out for estimating the influence of edge restraint against translation and stiffness of the elastic foundation on the natural frequencies of circular plates. The elastic edge restraint against translation and the presence of elastic foundation has been found to have a profound influence on vibration characteristics of the circular plate undergoing free transverse vibrations. Computations are carried out for natural frequencies of vibrations for varying values of translational stiffness ratio and stiffness parameter of Winkler-type foundation. Results are presented for twelve modes of vibration both in tabular and graphical form for use in design. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates. 

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

2021 ◽  
Vol 16 ◽  
pp. 198-205
Author(s):  
Jacob Nagler
Keyword(s):  
Rectangular Plate ◽  
Energy Method ◽  
Strain Energy ◽  
Euler Method ◽  
General View ◽  
Thin Rectangular Plate ◽  
Transverse Loads ◽  
Buckling Stress ◽  
Strain Energy Method ◽  
Plate Width

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.

Study of Vibration Characteristics of Cantilever Rectangular Plate with Side Crack

2012 ◽  
Vol 226-228 ◽  
pp. 113-118 ◽  
Author(s):  
Li Hua Chen ◽  
Yue Sun ◽  
Wei Zhang
Keyword(s):  
Rectangular Plate ◽  
Theoretical Basis ◽  
Natural Frequencies ◽  
Engineering Application ◽  
Vibration Characteristics ◽  
Combination Method ◽  
Relevant Study ◽  
Crack Location ◽  
Cantilever Rectangular Plate ◽  
Side Crack

In this paper, the vibration characteristics of the cantilever rectangular plate with side crack are studied in the way of analysis, which including natural frequency and mode shape. The influences of different parameters of crack, such as the locations and lengths of crack, to the vibration characteristics of the cantilever rectangular plate are investigated. The modal function of the crack plate consists two parts, which are (1) the modal function of intact cantilever rectangular plate from beam functions combination method and (2) corner functions presenting the discontinuity of displacement and slope along the crack. The natural frequencies and modal shapes can be obtained when taking the modal function into the method of Ritz. At last, the effects of the crack location and crack length on the vibration characteristics are investigated, and it could provide the theoretical basis for engineering application and the relevant study.

scholarly journals Vibration Characteristics Research of Sandwich Structure with Octet-truss Lattice Core

2021 ◽  
Vol 2125 (1) ◽  
pp. 012059
Author(s):  
Nan Wei ◽  
Hongling Ye ◽  
Xing Zhang ◽  
Jicheng Li ◽  
Boshuai Yuan
Keyword(s):  
Natural Frequencies ◽  
Sandwich Beam ◽  
Vibration Characteristics ◽  
Thin Sheets ◽  
Truss Core ◽  
Octet Truss ◽  
The Face ◽  
Lattice Core ◽  
Truss Member ◽  
Good Agreement

Abstract Lattice sandwich beams are often subjected to vibrations when they are used. The aim of this study was to explore the vibration characteristics of the octet-truss lattice core sandwich beam by translating discrete octet-truss core to the continuous homogenization material. The natural frequencies of which are obtained by theoretical calculation and numerical simulation. The theoretical solutions are in good agreement with the numerical results. It demonstrates that the theoretical approach is effective to compute the natural frequency. Furthermore, the influences of truss member radius and thin sheets ply on the natural frequencies are also discussed. The outcomes indicate that the octet-truss lattice core sandwich beam’s natural frequencies are controlled via selecting the appropriate truss member radius and the face sheets thickness.

scholarly journals Vibrations of Circular Plates Resting on Elastic Foundation with Elastically Restrained Edge Against Translation

2018 ◽  
Vol 13 (1) ◽  
pp. 14
Author(s):  
L.B. Rao ◽  
C.K. Rao
Keyword(s):  
Elastic Foundation ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Vibration Characteristics ◽  
Graphical Form ◽  
Winkler Foundation ◽  
Stiffness Ratio ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Elastically Restrained

The present paper deals with exact solutions for the free vibration characteristics of thin circular plates resting on Winkler-type elastic foundation based on the classical plate theory elastically restrained against translation. Parametric investigations are carried out for estimating the influence of edge restraint against translation and stiffness of the elastic foundation on the natural frequencies of circular plates. The elastic edge restraint against translation and the presence of elastic foundation has been found to have a profound influence on vibration characteristics of the circular plate undergoing free transverse vibrations. Computations are carried out for natural frequencies of vibrations for varying values of translational stiffness ratio and stiffness parameter of Winkler-type foundation. Results are presented for twelve modes of vibration both in tabular and graphical form for use in the design. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates.  

Scattering from a Thin Rectangular Plate at Glancing Incidence

2001 ◽  
Vol 21 (2) ◽  
pp. 147-163 ◽  
Author(s):  
Hirohide Serizawa ◽  
Kohei Hongo ◽  
Hirokazu Kobayashi
Keyword(s):  
Rectangular Plate ◽  
Thin Rectangular Plate

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

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