Axisymmetric Free Vibration of Shallow Spherical Shells With a Circular Rigid Insert

1993 ◽  
Vol 115 (2) ◽  
pp. 207-209
Author(s):  
D. Y. Hwang ◽  
W. A. Foster
Keyword(s):  
Free Vibration ◽  
Mode Shape ◽  
Vibrational Frequency ◽  
Bessel Functions ◽  
Frequency Equation ◽  
Third Order ◽  
Spherical Shells ◽  
Fundamental Vibrational Frequency ◽  
Rigid Insert ◽  
The Relationship

A general solution for the third-order partial differential equations for the axisymmetric free vibration of thin isotropic shallow spherical shells with a rigid insert is presented in this paper. The frequency equation in terms of Bessel functions as well as modified Bessel functions is solved for the fundamental vibrational frequency and mode shape. Both linear and non-linear boundary conditions are applied and the results are compared. The relationship between the vibrational frequency, mode shape and the size of the rigid insert is discussed.

scholarly journals Free Vibration Frequency of Thick FGM Spherical Shells Based on a Third-order Shear Deformation Theory

2020 ◽  
Vol 13 (4) ◽  
pp. 766-778
Author(s):  
Mohammad Zannon ◽  
Abdullah Abu-Rqayiq ◽  
Ammar Al-bdour
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Spherical Shells ◽  
Free Vibration Frequency ◽  
Vibration Problems

In this paper, we consider free vibration problems of functionally graded thick spherical shells. The analysis performs by collecting the radial basis functions, according to the Third Order Shear Deformation Theory that accounts for through the thickness deformation using the principle of virtual work. Numerical results include spherical shell panels with all edges clamped or simply supported to demonstrate the accuracy of the present approach.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

2012 ◽  
Vol 67 (12) ◽  
pp. 665-673 ◽  
Author(s):  
Kourosh Parand ◽  
Mehran Nikarya ◽  
Jamal Amani Rad ◽  
Fatemeh Baharifard
Keyword(s):  
Viscous Flow ◽  
Flat Plate ◽  
Numerical Algorithm ◽  
Bessel Functions ◽  
Nonlinear Ordinary Differential Equation ◽  
Finite Domain ◽  
Algebraic Equations ◽  
Infinite Domain ◽  
Third Order ◽  
Domain Truncation

In this paper, a new numerical algorithm is introduced to solve the Blasius equation, which is a third-order nonlinear ordinary differential equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on ℝ and is convergent for any x ∊ℝ. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

scholarly journals Dynamic Response of Laminated FRP Composite Made Cracked Spherical Shells Subjected to Free Vibration

2014 ◽  
Vol 6 ◽  
pp. 1580-1587 ◽  
Author(s):  
R.R. Das ◽  
A. Chakraborty ◽  
A. Guchhait ◽  
A. Singla
Keyword(s):  
Free Vibration ◽  
Dynamic Response ◽  
Spherical Shells ◽  
Frp Composite

Thermal Error Modeling of Precision Positioning Stage

2013 ◽  
Vol 694-697 ◽  
pp. 767-770
Author(s):  
Jing Shu Wang ◽  
Ming Chi Feng
Keyword(s):  
Thermal Deformation ◽  
Thermal Error ◽  
Error Modeling ◽  
Precision Positioning ◽  
Third Order ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Positioning Stage ◽  
Order Polynomial ◽  
The Relationship

As the thermal deformation significantly impacts the accuracy of precision positioning stage, it is necessary to realize the thermal error. The thermal deformation of the positioning stage is simulated by the finite element analysis. The relationship between the temperature variation and thermal error is fitted third-order polynomial function whose parameters are determined by genetic algorithm neural network (GANN). The operators of the GANN are optimized through a parametric study. The results show that the model can describe the relationship between the temperature and thermal deformation well.

scholarly journals Application of Laplace Transform to the Free Vibration of Continuous Beams

2017 ◽  
Vol 63 (1) ◽  
pp. 163-180 ◽  
Author(s):  
H.B. Wen ◽  
T. Zeng ◽  
G.Z. Hu
Keyword(s):  
Free Vibration ◽  
Laplace Transform ◽  
Reaction Force ◽  
Bending Moment ◽  
Frequency Equation ◽  
Simplified Model ◽  
Continuous Beam ◽  
Transform Method ◽  
Continuous Beams ◽  
Vibration Problems

AbstractLaplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.

scholarly journals Boundedness and oscillation of third order neutral differential equations

2009 ◽  
Vol 43 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Božena Mihalíková ◽  
Eva Kostiková
Keyword(s):  
Differential Equations ◽  
Third Order ◽  
Neutral Differential Equations ◽  
The Third ◽  
The Relationship ◽  
Oscillation Of Solutions

Abstract The relationship between boundedness and oscillation of solutions of the third order neutral differential equations are presented.

Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

An Indirect Method for Estimating the Weight of Glaze on Wires

1955 ◽  
Vol 36 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Robert W. Lenhard
Keyword(s):  
Indirect Method ◽  
Daily Precipitation ◽  
Meteorological Data ◽  
Power Lines ◽  
Daily Maximum ◽  
Third Order ◽  
Precipitation Total ◽  
Climatological Station ◽  
Temperature Variable ◽  
The Relationship

The relationship between the weight of glaze on power lines and common meteorological variables is examined. The icing data used are those collected by the Pennsylvania Electric Association; the meteorological data are those available in third-order climatological station records. A graphical correlation between ice weight, daily precipitation total and a derived temperature variable is obtained. In addition, the regression of ice weight on daily precipitation is explored and the probability of occurrence of daily maximum and minimum temperatures associated with glaze storms is given. These two relations are suggested as alternative estimating tools.

A numerical method for analysis of free vibration of spherical shells.

AIAA Journal ◽  
1967 ◽  
Vol 5 (7) ◽  
pp. 1256-1261 ◽  
Author(s):  
M. S. ZARGHAMEE ◽  
A. R. ROBINSON
Keyword(s):  
Free Vibration ◽  
Numerical Method ◽  
Spherical Shells
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