𝔖 Bobbio Scriptorium
✦   LIBER   ✦

NATURAL FREQUENCIES OF RECTANGULAR PLATES USING A SET OF STATIC BEAM FUNCTIONS IN RAYLEIGH-RITZ METHOD

✍ Scribed by Zhou Ding

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
302 KB
Volume
189
Category
Article
ISSN
0022-460X

No coin nor oath required. For personal study only.

✦ Synopsis

A fast converging series consisting of a set of static beam functions, which is a combination of sine series and polynomials, is developed and these functions are used as the basis functions in the Rayleigh-Ritz method to study the vibrational characteristics of thin, isotropic rectangular plates. In applications, a relatively small number of functions are required, and consequently, a modest amount of computation is necessary. The approach is very simple and straightforward. Some numerical results are given for rectangular plates with various aspect ratios and boundary conditions. Good accuracy and fast convergence of the method are demonstrated by comparisons with available results. Complicating factors (orthotropic properties, in-plane forces, etc.) can also be taken into account without formal difficulties.

📜 SIMILAR VOLUMES

The Free Vibrations of Tapered Rectangul
The Free Vibrations of Tapered Rectangular Plates Using a New Set of Beam Functions with the Rayleigh–Ritz Method
✍ K.Y Cheung; D Zhou 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 365 KB

In this paper, the free vibrations of a wide range of non-uniform rectangular plates in one or two directions are considered. The domain of the plate is bounded by x = a 1 a, a and y = b 1 b, b in rectangular co-ordinates. The thickness of the plate is continuously varying and proportional to the po

COMMENTS ON THE NATURAL FREQUENCIES OF R
COMMENTS ON THE NATURAL FREQUENCIES OF RECTANGULAR PLATES DERIVED FROM THE RAYLEIGH–RITZ METHOD
✍ R.S. Groves; R.L. Clark 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 129 KB

The study of the transverse vibrations of rectangular plates is among the most widely studied topics in structural dynamics, and the application of the assumed modes/Rayleigh-Ritz method to derive models of this vibration for various sets of boundary conditions has been employed for nearly the entir

VIBRATION OF RECTANGULAR PLATES USING PL
VIBRATION OF RECTANGULAR PLATES USING PLATE CHARACTERISTIC FUNCTIONS AS SHAPE FUNCTIONS IN THE RAYLEIGH–RITZ METHOD
✍ C. Rajalingham; R.B. Bhat; G.D. Xistris 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 411 KB

The plate characteristic functions are used to express the deflection shapes in the Rayleigh-Ritz method to study rectangular plate vibrations. Since the plate characteristic functions are reasonable approximations to the vibration modes, they are found to improve the convergence of vibration freque

FREE VIBRATION OF LINE SUPPORTED RECTANG
FREE VIBRATION OF LINE SUPPORTED RECTANGULAR PLATES USING A SET OF STATIC BEAM FUNCTIONS
✍ D. Zhou; Y.K Cheung 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 191 KB

The free vibration of thin orthotropic rectangular plates, which may be continuous over a number of intermediate line supports in one or two directions, is analyzed by the Rayleigh ± Ritz method. A new set of admissible functions which are the static solutions of a point supported beam under a serie