SYMMETRIC AND ANTISYMMETRIC NORMAL MODES OF A CANTILEVER RECTANGULAR PLATE: EFFECT OF POISSON'S RATIO AND A CONCENTRATED MASS

1996 ◽  
Vol 195 (1) ◽  
pp. 142-148 ◽  
Author(s):  
R.E. Rossi ◽  
P.A.A. Laura
Keyword(s):  
Rectangular Plate ◽  
Poisson’S Ratio ◽  
Normal Modes ◽  
Poisson's Ratio ◽  
Concentrated Mass ◽  
Cantilever Rectangular Plate

scholarly journals The bending of a centrally-loaded Isotropic rectangular plate supported at two opposite edges

1928 ◽  
Vol 118 (780) ◽  
pp. 427-440 ◽  
Keyword(s):  
Rectangular Plate ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Isotropic Material ◽  
Flexural Rigidity ◽  
Middle Surface ◽  
Poisson's Ratio ◽  
Uniform Thickness ◽  
Isotropic Rectangular Plate

1. The plate will be taken to be of uniform isotropic material, the elastic quality of which is specified by its Young’s modulus E and Poisson’s ratio σ, and it will be taken to be of small uniform thickness 2 h . The flexural rigidity D of the plate is then given by the formula D = 2/3 E h 3 /(1 - σ 2 ). (1) The initially plane middle surface of the plate will be taken as the plane of rectangular cartesian co-ordinates x , y , and the edges of the plate will be taken to cut this plane in segments of the lines x = ± a , y = ± b , so that the length of the plate is 2 a , and the breadth 2 b .

scholarly journals Effect of linear variation in density and circular variation in Poisson’s ratio on time period of vibration of rectangular plate

2018 ◽  
Vol 21 ◽  
pp. 14-19 ◽  
Author(s):  
Amit Sharma ◽  
Anup Kumar ◽  
Neeraj Lather ◽  
Reeta Bhardwaj ◽  
Naveen Mani
Keyword(s):  
Rectangular Plate ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Linear Variation ◽  
Time Period

Vibrations of a Rectangular Plate With Concentrated Mass, Spring, and Dashpot

1963 ◽  
Vol 30 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Y. C. Das ◽  
D. R. Navaratna
Keyword(s):  
Rectangular Plate ◽  
Composite System ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Double Series ◽  
Concentrated Mass ◽  
Orthogonal Functions ◽  
Isotropic Rectangular Plate ◽  
Mass Spring

An analytical method, developed by Young [1], is here extended to the determination of the natural frequencies of a composite system which consists of an isotropic rectangular plate with a concentrated mass, spring, and dashpot attached at any point of the plate. This method makes use of a double series expansion in terms of two sets of orthogonal functions which represent the normal modes of the vibration of the plate alone. Numerical examples for a square plate with (a) a combined concentrated mass and spring, (b) two concentrated masses, and (c) an attached dashpot have been presented.

The Model for Calculating Elastic Modulus and Poisson's Ratio of Coal Body

2013 ◽  
Vol 6 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Ai Chi ◽  
Li Yuwei
Keyword(s):  
Elastic Modulus ◽  
Poisson’S Ratio ◽  
Fractured Rock ◽  
Rock Block ◽  
Poisson's Ratio ◽  
Linear Elastic ◽  
Study Results ◽  
The Face ◽  
Block Face ◽  
Coal Rock

Coal body is a type of fractured rock mass in which lots of cleat fractures developed. Its mechanical properties vary with the parametric variation of coal rock block, face cleat and butt cleat. Based on the linear elastic theory and displacement equivalent principle and simplifying the face cleat and butt cleat as multi-bank penetrating and intermittent cracks, the model was established to calculate the elastic modulus and Poisson's ratio of coal body combined with cleat. By analyzing the model, it also obtained the influence of the parameter variation of coal rock block, face cleat and butt cleat on the elastic modulus and Poisson's ratio of the coal body. Study results showed that the connectivity rate of butt cleat and the distance between face cleats had a weak influence on elastic modulus of coal body. When the inclination of face cleat was 90°, the elastic modulus of coal body reached the maximal value and it equaled to the elastic modulus of coal rock block. When the inclination of face cleat was 0°, the elastic modulus of coal body was exclusively dependent on the elastic modulus of coal rock block, the normal stiffness of face cleat and the distance between them. When the distance between butt cleats or the connectivity rate of butt cleat was fixed, the Poisson's ratio of the coal body initially increased and then decreased with increasing of the face cleat inclination.

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