The NAVMI Factor and Natural Frequency of a Circular Plate Exposed to Water in Flexural Vibration

2011 ◽  
Vol 199-200 ◽  
pp. 1445-1450
Author(s):  
Hui Juan Ren ◽  
Mei Ping Sheng
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Circular Plate ◽  
Natural Frequencies ◽  
Integration Method ◽  
Flexural Vibration ◽  
The Other ◽  
Additional Mass ◽  
Simply Supported ◽  
Higher Order Modes

The expression of NAVMI factor and the natural frequency of a circular plate, which is placed in a hole of an infinite grid wall with one side exposed to water, are derived from the viewpoint of the additional mass. 10 Nodes Gauss-Legender integration method and the iteration method are employed to obtain the numerical results of the NAVMI factors, AVMI factors and the natural frequencies. It can be found from the results that NAVMI factors of the first two order modes are far bigger than those of the other modes when the boundary condition of a circular plate is certain. The first two order modal NAVMI factors of the circular plate with clamped and simply supported boundary conditions are far bigger than those of the circular plate with free-edged boundary condition, and the NAVMI factors are almost the same for the three order or much higher order modes regardless of the boundary condition. It is also observed that the natural frequencies of the circular plate exposed to water are smaller than those exposed to air, and the natural frequencies of the circular plate exposed to water with both sides are smaller than those of the circular plate exposed to water with one side.

Flexural Vibration of Rectangular Plates with Stiffeners Parallel to the Edges

1963 ◽  
Vol 67 (634) ◽  
pp. 664-668 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Natural Frequencies ◽  
Ritz Method ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Equivalent System ◽  
Simply Supported ◽  
Finite Difference Equations ◽  
Four Corners

SummaryThe basis of the procedure described in the paper is the replacement of the stiffeners by an approximately equivalent system of line springs. One of two methods may then be used to determine the natural frequencies. A rectangular plate with edge stiffeners, point-supported at the four corners, is used to demonstrate the application of the Rayleigh-Ritz method. Numerical results obtained are compared with known approximate solutions based on finite difference equations. A Holzer-type iteration is employed in the case of a plate with parallel stiffeners, where the two edges perpendicular to the stiffeners are simply supported, the other two edges having any combination of conditions.

A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

1962 ◽  
Vol 66 (616) ◽  
pp. 240-241 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Present Note ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Electronic Digital Computer ◽  
Isotropic Plates ◽  
Four Corners ◽  
Square Plate

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

scholarly journals The Vibration of Simply Supported Non-Uniform Cross Sectional Pipe Conveying Fluid Resting on Viscoelastic Foundation

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Natural Frequencies ◽  
Flexural Vibration ◽  
Bernoulli Model ◽  
Viscoelastic Foundation ◽  
Cross Sectional ◽  
Flowing Fluid ◽  
Simply Supported ◽  
Critical Velocities ◽  
Stiffness And Damping ◽  
The Mathematical Model

The induced flexural vibration of slender pipe systems with continuous non uniform cross sectional area containing laminar flowing fluid lying on extended Winkler viscoelastic foundation is considered. The Euler Bernoulli model of the pipe has hinged ends. The inlet flow is considered constant steady that interacts with the wall of the pipe. The mathematical model is developed and its corresponding solution is obtained. The influence of the combination of variation of cross section, foundation stiffness and damping on the critical velocities, complex natural frequencies and stabilization of the system is presented.

Natural Frequency and Vibration Modal Analysis of Composite Laminated Plate

2013 ◽  
Vol 711 ◽  
pp. 396-400
Author(s):  
Long Sheng Zhao ◽  
Jin Wu Wu
Keyword(s):  
Natural Frequency ◽  
Good Accuracy ◽  
Natural Frequencies ◽  
Equation Of Motion ◽  
Theory Method ◽  
Laminated Plate ◽  
Simply Supported ◽  
Composite Laminated Plate ◽  
Experiment Method ◽  
Vibration Modal

In this paper,a layer-wise theory is used to analyze the natural frequency and vibration modal of the composite laminated plate. Layer-wise theory assumes that displacement is continue through thickness direction and has good accuracy to analyze free vibration. The frequency and vibration modal are acquired while building the equation of motion according to layer-wise theory. Through comparing layer-wise theory and other theories, numerical results show that layer-wise theory is credible to analyze composite laminated plate. At the same time, experiment is used in this paper to acquire the natural frequencies and vibration modal of a simply supported composite laminated plate. Lastly, combination of the theory method and experiment method canprobably predict the natural frequencies and vibration modal.

Research on the Natural Frequency Solving Method of the Simply Supported Beam Bridge with Cracks

2013 ◽  
Vol 437 ◽  
pp. 51-55
Author(s):  
Ping Yi Sun ◽  
Yan Hua Wang ◽  
Han Bing Liu ◽  
Guo Jin Tan
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Beam Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Solution Methods ◽  
Element Approach ◽  
Experimental Values ◽  
Beam Bridge

Two kinds of natural frequency solution methods for the simply supported beam bridge with cracks are presented respectively based on the Bernoulli-Euler beam model and the finite element approach. Multiple groups of crack damages are supposed on the experimental simply supported steel I-beam, and the natural frequencies of the experimental beam are measured in all the crack cases. By comparing the calculated natural frequencies respectively obtained by the above two methods with the experimental values, the characteristics of the two kinds of natural frequency solving methods are evaluated.

Bending of an Elastically Restrained Circular Plate Under Normal Loading Over a Sector

1958 ◽  
Vol 25 (1) ◽  
pp. 37-46
Author(s):  
W. A. Bassali ◽  
R. H. Dawoud
Keyword(s):  
Boundary Condition ◽  
Circular Plate ◽  
Complex Variable ◽  
Variable Method ◽  
General Boundary Condition ◽  
Single Treatment ◽  
Normal Loading ◽  
Simply Supported ◽  
Thin Circular Plate ◽  
Elastically Restrained

Abstract The complex variable method is used to find the deflection, bending and twisting moments, and shearing forces at any point of a thin circular plate normally loaded over a sector and supported at its edge under a general boundary condition including the usual clamped and simply supported boundaries. In this way separate treatments for these two cases are avoided and a single treatment is available.

Research on relation between natural frequency and axial stress of round bar with intermediate-supported ends

2017 ◽  
Vol 3 (1) ◽  
pp. 17
Author(s):  
Tsutomu Yoshida ◽  
Takeshi Watanabe ◽  
Kunihiko Sakurada
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Deflection Angle ◽  
Axial Stress ◽  
Continuous Beam ◽  
Theoretical Relation ◽  
Test Device ◽  
Simply Supported ◽  
End Conditions ◽  
Round Bar

In order to make a method be useful to measure an axial stress of a member by a natural frequency, we investigated a relation between a natural frequency and an axial stress of a round bar with intermediate-supported ends, the boundary condition of which was one between a fix-supported end and a simply-supported end. To define an intermediate-supported end condition, we adopted a parameter, a ratio of a moment of a force to a deflection angle at the end. It was shown theoretically that the parameter of an intermediate-supported end could be evaluated by one at a support on a continuous beam consisted of 3 spans. The 3-spanned beam has same vibration characteristics of a beam with intermediate-supported ends. We manufactured a test device of a 3-spanned beam by which we could simulate a vibration under various intermediate-supported end conditions. The theoretical relation and experimental results between a natural frequency and an axial stress agreed for the most part.

Mechanics Mechanism Analysis of Concrete Pavement Resonant Rubblization

2015 ◽  
Vol 667 ◽  
pp. 365-369
Author(s):  
Peng Chen ◽  
Xin Qiu ◽  
Qing Zhu ◽  
Chan Chan Ouyang
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Elastic Foundation ◽  
Thin Plate ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Concrete Pavement ◽  
Mechanism Analysis ◽  
Vibration Theory ◽  
Fundamental Natural Frequency

Based on the assumption of thin plate of elastic foundation and vibration theory, a method for calculating the fundamental natural frequency of cement slab is presented and the certain relationship between the fundamental natural frequency of cement slab and cement slab boundary condition is discussed. As well, according to the analysis results of fundamental natural frequencies of the typical cement pavements of China, the selected proposals of the excitation frequency of the resonant rubblization machine are presented .The research results provide a theory support to popularize resonant rubblization technology in overlaying and rebuilding engineering of the existed cement pavements in China.

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