Influence of Poisson's ratio on the lower natural frequencies of transverse vibration of a circular plate of linearly varying thickness and with an edge elastically restrained against rotation

1978 ◽  
Vol 60 (4) ◽  
pp. 587-590 ◽  
Author(s):  
P.A.A. Laura ◽  
R.O. Grossi
Keyword(s):  
Circular Plate ◽  
Transverse Vibration ◽  
Poisson’S Ratio ◽  
Natural Frequencies ◽  
Poisson's Ratio ◽  
Varying Thickness ◽  
Elastically Restrained

Bending of a circular plate with an eccentric circular patch symmetrically loaded with respect to its centre

1956 ◽  
Vol 52 (3) ◽  
pp. 584-598 ◽  
Author(s):  
W. A. Bassali ◽  
R. H. Dawoud
Keyword(s):  
Boundary Condition ◽  
Circular Plate ◽  
Complex Variable ◽  
Poisson’S Ratio ◽  
Complex Variable Method ◽  
Variable Method ◽  
Poisson's Ratio ◽  
General Boundary ◽  
General Boundary Condition ◽  
Circular Patch

ABSTRACTThe complex variable method is applied to obtain solutions for the deflexion of a supported circular plate with uniform line loading along an eccentric circle under a general boundary condition including the clamped boundary , a boundary with zero peripheral couple , a boundary with equal boundary cross-couples , a hinged boundary and a boundary for which , η being Poisson's ratio. These solutions are used to obtain the deflexion at any point of a circular plate having an eccentric circular patch symmetrically loaded with respect to its centre. Expressions for the slope and cross-couples over the boundary and the deflexions at the centres of the plate and the loaded patch are obtained.

Natural Modes and Natural Frequencies of Uniform, Circular, Free-Edge Plates

1979 ◽  
Vol 46 (2) ◽  
pp. 448-453 ◽  
Author(s):  
K. Itao ◽  
S. H. Crandall
Keyword(s):  
Circular Plate ◽  
Isotropic Material ◽  
Natural Frequencies ◽  
Free Edge ◽  
Poisson's Ratio ◽  
Thin Circular Plate ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Homogeneous Isotropic Material ◽  
Free Edges

The natural modes and natural frequencies for the first 701 modes of vibration of a uniform thin circular plate with free edges are tabulated for a homogeneous isotropic material with Poisson’s ratio ν = 0.330.

Free, Transverse Vibrations of a Solid Elastic Mass in an Infinitely Long, Rigid, Circular-Cylindrical Tank

1960 ◽  
Vol 27 (4) ◽  
pp. 663-668 ◽  
Author(s):  
J. H. Baltrukonis
Keyword(s):  
Natural Frequency ◽  
Poisson’S Ratio ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
Poisson's Ratio ◽  
Cylindrical Tank ◽  
Field Equations ◽  
Displacement Fields ◽  
Transverse Vibrations

Making use of the field equations of elasticity, the frequency equation is derived for the free, transverse vibrations of a solid elastic mass contained by an infinitely long, rigid, circular-cylindrical tank. This frequency equation relates the natural circular frequencies and Poisson’s ratio. This relationship is plotted revealing a very interesting steplike variation of the natural frequency with Poisson’s ratio. Displacement fields are plotted for two natural frequencies in each of the first three modes.

The Deflection of a Uniformly Loaded Circular Plate Supported by a Concentric Ring

1963 ◽  
Vol 67 (631) ◽  
pp. 452-454
Author(s):  
S. A. Urry
Keyword(s):  
Circular Plate ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Slight Variation ◽  
Concentric Ring ◽  
Ring Radius ◽  
Supporting Ring

SummaryFor a given plate and loading the optimum supporting ring radius is shown to be approximately 0·677a, there being a slight variation with Poisson’s ratio.The “edge square” condition, i.e. zero slope at the circumference of the plate, is also investigated. It is satisfied by a ring radius of , a result which is independent of Poisson’s ratio.Macaulay’s brackets are used in the analysis as an example of their value in circular plate problems.

Vibration Transmission Loss of Auxetic Lattices

2015 ◽  
Vol 797 ◽  
pp. 282-289
Author(s):  
Eligiusz Idczak ◽  
Tomasz Strek
Keyword(s):  
Dynamic Behavior ◽  
Poisson’S Ratio ◽  
Natural Frequencies ◽  
Transmission Loss ◽  
Dynamic Properties ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Vibration Transmission ◽  
Auxetic Structures ◽  
Negative Poisson's Ratio

The auxetic lattices are structures, which have the negative Poisson’s ratio. When material has negative Poisson’s ratio, has also auxetic properties - during process of stretching, are made wider and during compressing are made narrower. This structures are cellular and negative Poisson’s ratio is depending on the geometry of single auxetic cell. When geometry of the cell is slightly changed also Poisson’s ratio is different. Auxetics have attracted attention of researchers because of their superior dynamic properties. The lattice auxetic structures at one of their natural frequencies exhibit the deformed geometry. It’s can be exploit as resonance to optimization of the power required for the occurrence localized deformations. The dynamic behavior of auxetic and their transmission of the vibration, which is circumscribed by the parameter VTL (Vibration Transmission Loss) will be analyzed in this article.

scholarly journals Vibration and Flutter of a Honeycomb Sandwich Plate with Zero Poisson’s Ratio

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2528
Author(s):  
Junhua Zhang ◽  
Zhaochen Yan ◽  
Lili Xia
Keyword(s):  
Poisson’S Ratio ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Geometric Parameters ◽  
Poisson's Ratio ◽  
Honeycomb Core ◽  
Honeycomb Sandwich ◽  
Honeycomb Sandwich Plate ◽  
Honeycomb Cores

A honeycomb is a kind of excellent lightweight structure and a honeycomb sandwich plate with zero Poisson’s ratio (ZPR) core is used widely in morphing structures. In this paper, a sandwich plate composed of a honeycomb core with zero Poisson’s ratio is analyzed for free vibrations and flutter under supersonic airflows. The equivalent elastic parametric formulas of the honeycomb core for zero Poisson’s ratio are proposed. The models are compared for their natural frequencies by theoretical and finite element methods respectively, which verifies the validity of the equivalent elastic parametric formulas and the model for the honeycomb sandwich plate with zero Poisson’s ratio. The influence of the geometric parameters of the honeycomb plate on the vibration frequencies is obtained. Three kinds of honeycomb cores, namely, regular hexagon, auxetic and hybrid with zero Poisson’s ratio, are compared through natural frequencies of the sandwich plate. It is found that the frequency of the zero Poisson’s ratio honeycomb sandwich plate is the second one when the other parameters are the same. The flutter of the honeycomb plate is analyzed by using the first order piston theory under supersonic flows. The critical flutter velocity of the plate is obtained, and the influence of geometric parameters of the honeycomb plate on the critical flutter velocities is obtained.

Circular Elastic Plates on Elastic Unilateral Edge Supports

1988 ◽  
Vol 55 (3) ◽  
pp. 624-628 ◽  
Author(s):  
Zekai Celep ◽  
Dog˘an Turhan ◽  
Rajeh Zaid Al-Zaid
Keyword(s):  
Circular Plate ◽  
Poisson’S Ratio ◽  
Spring Constant ◽  
Poisson's Ratio ◽  
Elastic Plates ◽  
Circular Arc ◽  
Elastic Circular Plate

The response of an elastic circular plate supported unilaterally by elastic springs along its edge is studied. A load which is uniformly distributed along a circular arc of the plate is considered. The loss of the contact along the edge of the plate, the variations of deflections and those of reactions are presented. The influences of the position of loading, the spring constant, and Poisson’s ratio are shown in various figures.

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