Natural Frequencies Formula for Simply Supported Mindlin Plates

1994 ◽  
Vol 116 (4) ◽  
pp. 536-540 ◽  
Author(s):  
C. M. Wang
Keyword(s):  
Exact Solutions ◽  
Explicit Formula ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Kirchhoff Plate ◽  
Vibration Frequencies ◽  
Simply Supported ◽  
Plate Shape

This paper presents an explicit formula for the vibration frequencies of simply supported Mindlin plates in terms of the corresponding thin (Kirchhoff) plate frequencies. The formula has been obtained from an exact vibration analysis of simply supported rectangular Mindlin plates. When the formula was applied to other simply supported plate shapes such as skew plates, circular and annular sectorial plates, it was found to give almost exact solutions. It appears that the formula can be used to predict the frequencies accurately for any simply supported plate shape and thus should be valuable to designers as Mindlin vibration solutions are scarce.

Relationship Between Vibration Frequencies of Reddy and Kirchhoff Polygonal Plates With Simply Supported Edges

1997 ◽  
Vol 122 (1) ◽  
pp. 77-81 ◽  
Author(s):  
C. M. Wang ◽  
S. Kitipornchai ◽  
J. N. Reddy
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Kirchhoff Plate ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Third Order ◽  
Simply Supported ◽  
Kirchhoff Plate Theory ◽  
The Relationship ◽  
Exact Relationship

This paper presents an exact relationship between the natural frequencies of Reddy third-order plate theory and those of classical Kirchhoff plate theory for simply supported, polygonal isotropic plates, including rectangular plates. The relationship for the natural frequencies enables one to obtain the solutions of the third-order plate theory from the known Kirchhoff plate theory for the same problem. As examples, some vibration frequencies for rectangular and regular polygonal plates are determined using this relationship. [S0739-3717(00)01601-9]

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Modeling and Free Vibration Analysis of a Complex Cable-Stayed Bridge

2012 ◽  
Author(s):  
D. Q. Cao ◽  
M. T. Song ◽  
W. D. Zhu
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Longitudinal Vibrations ◽  
Simply Supported ◽  
Cable Stayed Bridge ◽  
Linear Partial Differential Equations ◽  
Localized Mode ◽  
Linearized Model

A complex cable-stayed bridge that consists of a simply-supported four-cable-stayed deck beam and two rigid towers is studied. The nonlinear and linear partial differential equations that govern the motions of the cables and segments of the deck beam, respectively, are derived, along with their boundary and matching conditions. The undamped natural frequencies and mode shapes of the linearized model of the cable-stayed bridge, which includes both the transverse and longitudinal vibrations of the cables, are determined. Numerical analysis of the natural frequencies and mode shapes of the cable-stayed bridge is conducted for a symmetrical case with regards to the sizes of the components of the bridge and the initial sags of the cables. The results show that there are very close natural frequencies and localized mode shapes.

Free Vibration Analysis of Circular FGM Plate Having Variable Thickness Under Axisymmetric Condition by Finite Element Method

2005 ◽  
Author(s):  
M. Nikkhah-Bahrami ◽  
Abazar Shamekhi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Thickness Variation ◽  
Simply Supported ◽  
Element Method

This study presents the free vibration analysis of circular plate having variable thickness made of functionally-graded material. The boundary conditions of the plate is either simply supported or clamped. Dynamic equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander’s non-linear strain-displacement relation for thin plates. The finite element method is used to determine the natural frequencies. The results obtained show good agreement with known analytical data. The effects of thickness variation and Poisson’s ratio are investigated by calculating the natural frequencies. These effects are found not to be the same for simply supported and clamped plates.

scholarly journals Vibration Analysis of Simply Supported Rectangular Tank Partially Filled with Water

2018 ◽  
Vol 210 ◽  
pp. 04003 ◽  
Author(s):  
Kamila Kotrasová
Keyword(s):  
Free Surface ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Fluid Motion ◽  
Simply Supported ◽  
Horizontal Acceleration ◽  
Rectangular Container ◽  
Rectangular Tank ◽  
Tank Bottom ◽  
Sloshing Pressure

Ground-supported tanks are used as fluid storage. One of the phenomena associated with the seismic response of liquid-filled tanks is the fluid motion occurring that causes “sloshing” at the top of free surface. This paper presents the theoretical of fluid response of rectangular tank due to horizontal acceleration of tank bottom, the impulsive and convective (sloshing) pressure and the fluid natural frequencies. The vibration analysis of fluid filled rectangular container was monitored and was evaluated in experiment for purpose to evaluation of the first frequency mode and vibration response of fluid were analysed by using FEM.

Exact Solutions for Vibration of Multi-Span Rectangular Mindlin Plates

2002 ◽  
Vol 124 (4) ◽  
pp. 545-551 ◽  
Author(s):  
Y. Xiang ◽  
G. W. Wei
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Analytical Approach ◽  
Solution Method ◽  
Plate Boundary ◽  
Vibration Frequencies ◽  
Type Solution ◽  
Simply Supported ◽  
Space Technique ◽  
Benchmark Solutions

This paper presents the first-known exact solutions for the vibration of multi-span rectangular Mindlin plates with two opposite edges simply supported. The Levy type solution method and the state-space technique are employed to develop an analytical approach to deal with the vibration of rectangular Mindlin plates of multiple spans. Exact vibration frequencies are obtained for two-span square Mindlin plates with varying span ratios and two-, three- and four-equal-span rectangular Mindlin plates. The influence of the span ratios, the number of spans and plate boundary conditions on the vibration behavior of square and rectangular Mindlin plates is examined. The presented exact vibration results may serve as benchmark solutions for such plates.

BUCKLING AND VIBRATION OF STEPPED, SYMMETRIC CROSS-PLY LAMINATED RECTANGULAR PLATES

2001 ◽  
Vol 01 (03) ◽  
pp. 385-408 ◽  
Author(s):  
Y. XIANG ◽  
J. N. REDDY
Keyword(s):  
Solution Method ◽  
Natural Frequencies ◽  
Laminated Plates ◽  
The Other ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Buckling Loads ◽  
Simply Supported ◽  
Step Thickness ◽  
Thickness Variations

This paper presents the exact buckling loads and vibration frequencies of multi-stepped symmetric cross-ply laminated rectangular plates having two opposite edges simply supported while the other two edges may have any combination of free, simply supported, and clamped conditions. An analytical method that uses the Lévy solution method and the domain decomposition technique is proposed to determine the buckling loads and natural frequencies of stepped laminated plates. Buckling and vibration solutions are obtained for symmetric cross-ply laminated rectangular plates having two-, three- and four-step thickness variations.

scholarly journals Free vibration of a microbeam resting on Pasternak’s foundation via the Green–Naghdi thermoelasticity theory without energy dissipation

2016 ◽  
Vol 35 (4) ◽  
pp. 303-311 ◽  
Author(s):  
Ashraf M Zenkour
Keyword(s):  
Energy Dissipation ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Generalized Thermoelasticity ◽  
Frequency Equation ◽  
Vibration Frequencies ◽  
Simply Supported ◽  
Thermoelasticity Theory ◽  
Foundation Parameters ◽  
Without Energy Dissipation

This article investigates the effect of length-to-thickness ratio and elastic foundation parameters on the natural frequencies of a thermoelastic microbeam resonator. The generalized thermoelasticity theory of Green and Naghdi without energy dissipation is used. The governing frequency equation is given for a simply supported microbeam resting on Winkler–Pasternak elastic foundations. The influences of different parameters are all demonstrated. Natural vibration frequencies are graphically illustrated and some tabulated results are presented for future comparisons.

Static Analysis for Exact Vibration Analysis of Clamped Plates

2015 ◽  
Vol 15 (08) ◽  
pp. 1540030 ◽  
Author(s):  
Moshe Eisenberger ◽  
Aharon Deutsch
Keyword(s):  
Static Analysis ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Point Load ◽  
Vibration Frequencies ◽  
Concentrated Load ◽  
Simply Supported ◽  
Winkler Elastic Foundation ◽  
Isotropic Rectangular Plate

Presented herein is a new method for the analysis of plates with clamped edges. The solutions for the natural frequencies of the plates are found using static analysis. The starting are the equations of motion of an isotropic rectangular plate supported on Winkler elastic foundation, with a positive or negative value. In either case, one can solve the displacements of such a plate under a given concentrated load. This deflection will be infinite if the plate losses its stiffness, or in other words, the generalized foundation is causing the plate to be unstable. The solution for the vibration frequencies of the plate is equivalent to finding the values of the negative elastic foundation that will yield infinite deflection under a point load on the plate. The solution for a clamped plate is decomposed as the sum of three cases of plates resting on elastic foundation: simply supported plate with a concentrated load, and two cases of distributed moments along opposite edges. The solution for simply supported plates with elastic foundation is found using Navier's method. For zero force, the vibration frequencies are found up to the desired accuracy by careful calculations at the neighborhood of the roots.

Exact Solutions for Free-Vibration Analysis of Rectangular Plates Using Bessel Functions

2005 ◽  
Vol 74 (6) ◽  
pp. 1247-1251 ◽  
Author(s):  
Jiu Hui Wu ◽  
A. Q. Liu ◽  
H. L. Chen
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Exact Solutions ◽  
Thin Plate ◽  
Vibration Analysis ◽  
Bessel Functions ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Edge Conditions

A novel Bessel function method is proposed to obtain the exact solutions for the free-vibration analysis of rectangular thin plates with three edge conditions: (i) fully simply supported; (ii) fully clamped, and (iii) two opposite edges simply supported and the other two edges clamped. Because Bessel functions satisfy the biharmonic differential equation of solid thin plate, the basic idea of the method is to superpose different Bessel functions to satisfy the edge conditions such that the governing differential equation and the boundary conditions of the thin plate are exactly satisfied. It is shown that the proposed method provides simple, direct, and highly accurate solutions for this family of problems. Examples are demonstrated by calculating the natural frequencies and the vibration modes for a square plate with all edges simply supported and clamped.

Sign in / Sign up

Export Citation Format

Share Document