Boundary-type Ritz method for the analysis of arbitrarily shaped polygonal plates

2021 ◽  
Vol 130 ◽  
pp. 124-134
Author(s):  
Mohammad H. Aljawhary ◽  
Husain J. Al-Gahtani
Keyword(s):  
Ritz Method ◽  
Boundary Type

scholarly journals A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-30 ◽  
Author(s):  
Dongyan Shi ◽  
Yunke Zhao ◽  
Qingshan Wang ◽  
Xiaoyan Teng ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Analysis Model ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Auxiliary Functions ◽  
Arbitrary Boundary Conditions ◽  
Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

A GENERALIZED VARIATIONAL PRINCIPLE FOR TRANSPORT PHENOMENA

1958 ◽  
Vol 36 (10) ◽  
pp. 1308-1318 ◽  
Author(s):  
G. E. Tauber
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Ritz Method ◽  
Transport Coefficients ◽  
Distribution Functions ◽  
Generalized Variational Principle ◽  
Lattice Vibrations ◽  
Arbitrary Direction ◽  
Energy Surfaces ◽  
Thermomagnetic Phenomena

A generalized variational principle has been formulated which takes the phonon distribution functions and the external magnetic field into account, is valid for an arbitrary direction of the electric field and polarization of the lattice vibrations, and does not depend on any special form of the energy surfaces. The various transport coefficients, for both thermoelectric and thermomagnetic phenomena, are obtained by the Ritz method in terms of infinite determinants without requiring an explicit solution of the transport equations.

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