Vibrations of a Thick-Walled Pipe or a Ring of Arbitrary Shape in Its Plane

1983 ◽  
Vol 50 (4a) ◽  
pp. 757-764 ◽  
Author(s):  
K. Nagaya
Keyword(s):  
Wave Propagation ◽  
Arbitrary Shape ◽  
Fourier Expansion ◽  
Equation Of Motion ◽  
Circular Ring ◽  
Theory Of Elasticity ◽  
Polar Coordinates ◽  
Elliptical Ring ◽  
Vibration Problems ◽  
Plane Strain Assumption

This paper is concerned with a method for solving in-plane vibration problems of thick-walled pipes and rings of arbitrary shape. The solution to the equation of motion based on the theory of elasticity under the plane-strain assumption is obtained exactly by using polar coordinates. The boundary conditions along both the outer and the inner surfaces of the ring of arbitrary shape are satisfied directly by means of the Fourier expansion collocation method which has been developed in the author’s previous reports concerning vibration, dynamic response, and wave propagation problems of plates and rods with various shapes. Numerical calculations have been carried out for a thick elliptical ring, a rectangular ring with rounded corners, and a rectangular ring with a circular inner boundary. To discuss the accuracy of the present analysis, the results of a thick circular ring have also been calculated, and the present results are compared with the previously published ones.

On a Magnetic Damper Consisting of a Circular Magnetic Flux and a Conductor of Arbitrary Shape. Part I: Derivation of the Damping Coefficients

1984 ◽  
Vol 106 (1) ◽  
pp. 46-51 ◽  
Author(s):  
Kosuke Nagaya ◽  
Hiroyuki Kojima
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Magnetic Flux ◽  
Electromagnetic Fields ◽  
Arbitrary Shape ◽  
Fourier Expansion ◽  
Polar Coordinates ◽  
Damping Coefficients ◽  
Theoretical Results ◽  
Good Agreement

Theoretical results for finding the damping coefficients of a magnetic damper consisting of a circular magnetic flux and an arbitrarily shaped conductor have been obtained. In the analysis the exact solution in polar coordinates for the governing equation of the electromagnetic fields is utilized. The boundary condition for arbitrarily shaped boundaries of the conductor is satisfied directly by means of the Fourier expansion collocation method. To discuss the accuracy of the present approximate results, the analysis also has been performed on damper consisting of a circular flux and a circular conductor. The comparison between the present results and the exact ones for the typical damper shows very good agreement.

Time Domain Simulations on a Single Point Moored Submerged Sphere of Variable Radius

2005 ◽  
Author(s):  
Joa˜o M. B. P. Cruz ◽  
Anto´nio J. N. A. Sarmento
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Physical Phenomenon ◽  
Single Point ◽  
Vertical Direction ◽  
Equation Of Motion ◽  
Hydrodynamic Coefficients ◽  
Energy Converter ◽  
Submerged Sphere ◽  
The Time Domain

This paper presents a different approach to the work developed by Cruz and Sarmento (2005), where the same problem was studied in the frequency domain. It concerns the same sphere, connected to the seabed by a tension line (single point moored), that oscillates with respect to the vertical direction in the plane of wave propagation. The pulsating nature of the sphere is the basic physical phenomenon that allows the use of this model as a simulation of a floating wave energy converter. The hydrodynamic coefficients and diffraction forces presented in Linton (1991) and Lopes and Sarmento (2002) for a submerged sphere are used. The equation of motion in the angular direction is solved in the time domain without any assumption about its output, allowing comparisons with the previously obtained results.

scholarly journals V. On the general theory of elastic stability

1914 ◽  
Vol 213 (497-508) ◽  
pp. 187-244 ◽  
Keyword(s):  
General Theory ◽  
Boundary Conditions ◽  
Radial Pressure ◽  
Elastic Stability ◽  
Circular Ring ◽  
Theory Of Elasticity ◽  
Comprehensive Theory ◽  
The Subject ◽  
The Stability ◽  
Straight Rod

Problems which deal with the stability of bodies in equilibrium under stress are so distinct from the ordinary applications of the theory of elasticity that it is legitimate to regard them as forming a special branch of the subject. In every other case we are concerned with the integration of certain differential equations, fundamentally the same for all problems, and the satisfaction of certain boundary conditions; and by a theorem due to Kiechiioff we are entitled to assume that any solution which we may discover is unique. In these problems we are confronted with the possibility of two or more configurations of equilibrium , and we have to determine the conditions which must be satisfied in order that the equilibrium of any given configuration may be stable. The development of both branches has proceeded upon similar lines. That is to say, the earliest discussions were concerned with the solution of isolated examples rather than with the formulation of general ideas. In the case of elastic stability, a comprehensive theory was not propounded until the problem of the straight strut had been investigated by Euler, that of the circular ring under radial pressure by M. Lévy and G. H. Halphen, and A. G. Greenhill had discussed the stability of a straight rod in equilibrium under its own weight, under twisting couples, and when rotating.

Dispersion study of plane-strain vibrations in poroelastic solid bars with polygonal cross-section

2016 ◽  
Vol 22 (1) ◽  
pp. 38-52 ◽  
Author(s):  
Sandhya Rani Bandari ◽  
Malla Reddy Perati ◽  
Gangadhar Reddy Gangu
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Plane Strain ◽  
Cross Section ◽  
Cross Sections ◽  
Fourier Expansion ◽  
Data Phase ◽  
Base Curve ◽  
Symmetric And Antisymmetric Modes ◽  
Relevant Material

This paper studies wave propagation in a poroelastic solid bar with polygonal cross-section under plane-strain conditions. The boundary conditions on the surface of the cylinder whose base curve is polygon are satisfied by means of the Fourier expansion collocation method. The frequency equations are discussed for both symmetric and antisymmetric modes in the framework of Biot’s theory of poroelastic solids. For illustration purposes, sandstone saturated materials and bony material are considered. The numerical results were computed as the basis of relevant material data . Phase velocity is computed against the wavenumber for various cross-sections and results are presented graphically.

A Finite Element Approach to Plate Vibration Problems

1965 ◽  
Vol 7 (1) ◽  
pp. 28-32 ◽  
Author(s):  
D. J. Dawe
Keyword(s):  
Finite Element ◽  
Arbitrary Shape ◽  
Natural Frequencies ◽  
Isotropic Plate ◽  
Uniform Thickness ◽  
Flat Plates ◽  
Finite Element Approach ◽  
Various Boundary Conditions ◽  
Element Approach ◽  
Vibration Problems

A method of computing the natural frequencies of vibration of flat plates of arbitrary shape is outlined in which the plate is considered as an assemblage of elements. Both stiffness and inertia matrices are derived for a rectangular isotropic plate element of uniform thickness, and these matrices are used to find the natural frequencies of square plates subject to various boundary conditions. Comparison of finite element frequencies with known exact, experimental and energy solutions shows the method to give good results even for relatively few elements.

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