Adjustable parameter method for vibration of polar orthotropic plates
About: This article is published in Journal of Sound and Vibration.The article was published on 1987-07-01. It has received 2 citations till now. The article focuses on the topics: Orthotropic material.
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TL;DR: In this paper, the authors proposed a solution to the titled problem by solving the posed semi-inverse problem with the aid of the semidefinite formulation of the problem.
1 citations
Cites methods from "Adjustable parameter method for vib..."
...Consider now the alternative quartic mode shape: WðrÞ ¼ R4 4r3Rþ 3r4 ð99Þ Note that this function was utilized in (Elishakoff, 1987) as a trial function in the context of the approximate, Rayleigh–Ritz method....
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...The Garlerkin method was applied by Prathap and Varadan (1976), while the Rayleigh–Ritz method was employed by Elishakoff (1987)....
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TL;DR: In this paper, 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.
Abstract: 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.
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TL;DR: In this paper, an analysis of the vibration of a cylindrically aeolotropic circular plate with circular stiffeners was carried out, where the effective elastic compliances had been determined in previous investigation.
Abstract: Equations for the determination of the frequencies of flexural vibration and corresponding modal shapes for cylindrically aeolotropic circular plates are presented. A considerable analysis has been made of the case of symmetric vibrations, and results are tabulated. The theory is exemplified by an analysis of the vibration of a circular plate with circular stiffeners for which the effective elastic compliances had been determined in a previous investigation. Nodal patterns and corresponding frequencies were experimentally determined for the first five symmetric modes and the first four asymmetric modes of a simply supported stiffened plate. Comparison between the theoretical and experimental results for the first three symmetric modes is provided. Finally, some discussion given for the important problem of approximating plates with attached stiffeners by equivalent homogeneous uniformly thick aeolotropic plates.
33 citations
31 citations
31 citations
TL;DR: In this paper, the authors generalized the Rayleigh-Ritz direct variational method for the determination of constant coefficients of assumed shape functions by the introduction of arbitrary parameters in the shape functions and illustrated by several simple examples of freely vibrating beams and a plate.
Abstract: The so-called Rayleigh-Ritz direct variational method for the determination of constant coefficients of assumed shape functions has been generalized by the introduction of arbitrary parameters in the shape functions and then illustrated by means of several simple examples of freely vibrating beams and a plate. The arbitrary parameters are determined by minimizing the natural frequency by the rules of differential calculus or by a number of trial calculations, in difficult problems. Although the calculational labor is greater in the applications of the proposed technique than in the common Rayleigh-Ritz method, the technique offers some advantages in regard to accuracy and flexibility. The proposed technique can also be used for estimating Saint-Venant's torques, bifurcation loads on columns and plates, and other eigenvalues.
30 citations
18 citations