Vibration Tailoring of a Polar Orthotropic Circular Plate With a Translational Spring

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Isaac Elishakoff ◽  
Demetris Pentaras
Keyword(s):  
Closed Form ◽  
Circular Plate ◽  
Mode Shape ◽  
Inverse Method ◽  
Closed Form Solution ◽  
Form Solution ◽  
Translational Spring ◽  
Orthotropic Circular Plate ◽  
Polar Orthotropic

In this study, the vibration tailoring problem is analytically solved for the polar orthotropic circular plate with translational spring along its circumference. By using the semi-inverse method and postulating the mode shape as a polynomial, we derive a closed-form solution.

scholarly journals Axisymmetric Large Deflection Elastic Analysis of Hollow Annular Membranes under Transverse Uniform Loading

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1770
Author(s):  
Jun-Yi Sun ◽  
Qi Zhang ◽  
Xue Li ◽  
Xiao-Ting He
Keyword(s):  
Closed Form ◽  
Circular Plate ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Circular Ring ◽  
Form Solution ◽  
Elastic Response ◽  
Geometrically Nonlinear ◽  
Closed Form Solutions ◽  
Annular Membrane

The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.

Polar Orthotropic Inhomogeneous Circular Plates: Vibration Tailoring

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
Demetris Pentaras ◽  
Isaac Elishakoff
Keyword(s):  
Eigenvalue Problem ◽  
Closed Form ◽  
Circular Plate ◽  
Mode Shape ◽  
Fundamental Mode ◽  
Inverse Eigenvalue Problem ◽  
Static Deflection ◽  
Circular Plates ◽  
Inverse Eigenvalue ◽  
Polar Orthotropic

Problem of matching a desired fundamental natural frequency is solved in the closed form for the polar-orthotropic inhomogeneous circular plate, which is clamped along its circumference. The vibration tailoring is performed by posing a semi-inverse eigenvalue problem. To do this, the fundamental mode shape is postulated. Namely, the analytical expression due to Lekhnitskii, and pertaining to the static deflection of the homogeneous circular plate is demanded to serve as an exact mode shape of the inhomogeneous plate. The analytical and numerical results are reported for several ratios of orthotropic coefficient.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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