scholarly journals Fourier series expansion type of spectral nodal Galerkin method for vibration analysis of cylindrical shells: Formulation and trial calculation

2016 ◽  
Vol 37 (5) ◽  
pp. 254-257
Author(s):  
Yozo Araki ◽  
Toshiya Samejima
Keyword(s):  
Fourier Series ◽  
Galerkin Method ◽  
Series Expansion ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Fourier Series Expansion

An Exact Fourier Series Method for the Vibration Analysis of Multispan Beam Systems

2009 ◽  
Vol 4 (2) ◽  
Author(s):  
Wen L. Li ◽  
Hongan Xu
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Series Expansion ◽  
Vibration Analysis ◽  
Series Solution ◽  
Series Representation ◽  
Displacement Function ◽  
Fourier Series Expansion ◽  
Series Method ◽  
Fourier Series Method

An exact Fourier series method is developed for the vibration analysis of multispan beam systems. In this method, the displacement on each beam is expressed as a Fourier series expansion plus an auxiliary closed-form function such as polynomials. The auxiliary function is used to deal with all the possible discontinuities, at the end points, with the original displacement function and its derivatives when they are periodically extended over the entire x-axis as implied by a Fourier series representation. As a result, not only is it always possible to expand the beam displacements into Fourier series under any boundary conditions, but also the series solution will be substantially improved in terms of its accuracy and convergence. Mathematically, the current Fourier series expansion represents an exact solution to a class of beam problems in the sense that both the governing equations and the boundary/coupling conditions are simultaneously satisfied to any specified degree of accuracy. In the multispan beam system model, any two adjacent beams are generally connected together via a pair of linear and rotational springs, allowing a better modeling of many real-world joints. Each beam in the system can also be independently and elastically restrained at its ends so that all boundary conditions including the classical homogeneous boundary conditions at the end and intermediate supports can be universally dealt with by simply varying the stiffnesses of the restraining springs accordingly, which does not involve any modification of basis functions, formulations, or solution procedures. The excellent accuracy and convergence of this series solution is demonstrated through numerical examples.

A SIMPLE MODEL FOR ORIENTATIONAL ORDERING OF A SILVER MONOLAYER ELECTRODEPOSITED ON A C(0001) SURFACE

1995 ◽  
Vol 02 (04) ◽  
pp. 489-494 ◽  
Author(s):  
E.E. MOLA ◽  
A.G. APPIGNANESSI ◽  
J.L. VICENTE ◽  
L. VAZQUEZ ◽  
R.C. SALVAREZZA ◽  
...  
Keyword(s):  
Experimental Data ◽  
Fourier Series ◽  
Simple Model ◽  
Series Expansion ◽  
Unit Cell ◽  
Fourier Series Expansion ◽  
Crystal Formation ◽  
Substrate Potential ◽  
Weber Type ◽  
Orientational Ordering

The model for the angular orientational energy (AOE) has been extended to hexagonal submonolayer domains of Ag electrodeposited at a constant overpotential on a C(0001) surface. These domains which are characterized by an epitaxy angle θ=15±5° and an Ag−Ag distance d Ag−Ag =0.330± 0.016 nm, can be considered as precursors of 3D Ag crystal formation, according to a Volmer-Weber type mechanism. Calculations are based upon a simple Hamiltonian evaluated by introducing the concept of the commensurable unit cell. A Fourier series expansion for the substrate potential was used. Results from the model predict the existence of a commensurable cell in agreement with the experimental data derived from STM imaging.

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