Natural frequencies and modes of vibration of spherical shells with attached masses

1987 ◽  
Vol 23 (9) ◽  
pp. 852-856
Author(s):  
V. N. Revutskii ◽  
A. I. Telalov
Keyword(s):  
Natural Frequencies ◽  
Spherical Shells ◽  
Natural Frequencies And Modes ◽  
Modes Of Vibration

Natural frequencies of cooling tower shells

1967 ◽  
Vol 2 (2) ◽  
pp. 127-133 ◽  
Author(s):  
B G Neal
Keyword(s):  
Cooling Tower ◽  
Natural Frequencies ◽  
Support Condition ◽  
Theoretical Determination ◽  
Electro Deposition ◽  
Horizontal Fracture ◽  
Natural Frequencies And Modes ◽  
Modes Of Vibration ◽  
Hyperbolic Cooling Tower

A theoretical determination of the lowest natural frequencies of inextensional vibrations of hyperbolic cooling tower shells is first presented. It is shown that inextensional behaviour is only possible for certain types of support condition at the base, one of which consists of four pairs of inclined columns evenly spaced round the circumference which, at their points of attachment, only permit displacements normal to the plane of the shell. Experiments to determine the natural frequencies and modes of vibration of a model shell are then described. This model, which was made by the electro-deposition of copper on a Perspex mould, could be supported at its base by up to forty pairs of inclined columns. Using only four evenly spaced pairs of columns the lowest natural frequencies of inextensional vibrations were first determined, and found to agree well with the theoretical values. The natural frequencies and modes of the extensional vibrations which occurred when the shell was supported by forty pairs of columns were then explored. Finally, the effect of removing some of the supports, thereby simulating a horizontal fracture in part of the shell, was studied. The possibility of wind-induced vibrations occurring in practice is then considered. It is concluded that these are unlikely to occur unless the shell has already suffered damage, as for example by experiencing a horizontal fracture over part of its circumference near the base.

Effect of a Change in Position of a Support on the Natural Frequencies and Modes of Vibration of a System

1965 ◽  
Vol 7 (3) ◽  
pp. 271-278 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Torsional Vibration ◽  
Simple Formula ◽  
Natural Frequencies ◽  
Static Deflection ◽  
Deflection Curve ◽  
Natural Frequencies And Modes ◽  
Method Of Solution ◽  
Modes Of Vibration ◽  
Frequency Changes ◽  
Small Change

The effect of a small change in position of one of the supports on the natural frequencies and modes of a structure, which is ‘continuous’ over a number of supports, is examined in this paper. Using energy and receptance methods a simple formula is obtained for the change in natural frequency of a beam when the support displacement is infinitesimal. The corresponding displacements of other nodal points are also obtained. When the support displacement is finite, but not large, changes in mode and frequency are determined by iteration. The method of solution is extended to the coupled flexural and torsional vibration of a non-symmetrical beam. In the case of a rectangular plate with stiffeners parallel to an edge, frequency changes due to the change in position of a stiffener may be determined by the same method. Alternative approximate formulae, based on the static deflection curve, are derived for the change of fundamental frequency.

Vibrations of Orthogonally Stiffened Panels

1978 ◽  
Vol 22 (02) ◽  
pp. 100-109 ◽  
Author(s):  
Niels FI. Madsen
Keyword(s):  
Numerical Method ◽  
Cross Section ◽  
Natural Frequencies ◽  
Axial Deformation ◽  
Linear Combinations ◽  
Stiffened Panels ◽  
Natural Frequencies And Modes ◽  
Modes Of Vibration

A general numerical method for the determination of natural frequencies and modes of vibration for orthogonally stiffened panels is presented. The panel is considered as an assembly of prismatic beams and plate strips rigidly connected along their longitudinal edges and transversely stiffened by beams of varying cross section. The modes of vibration are approximated by linear combinations of the analytically calculated modes of vibration for the prismatic panel, resulting from neglecting the transverse stiffening and assuming simple end supports. For the transverse stiffening, the effects of shear deflection, axial deformation, and St. Venant torsion are taken into account. As a practical example, the natural frequencies of a deep girder in a tanker have been calculated.

scholarly journals Vibrations of Complete Spherical Shells With Imperfections

2007 ◽  
Vol 129 (3) ◽  
pp. 363-370 ◽  
Author(s):  
Thomas A. Duffey ◽  
Jason E. Pepin ◽  
Amy N. Robertson ◽  
Michael L. Steinzig ◽  
Kimberly Coleman
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Spherical Shells ◽  
The Past ◽  
Dynamic Holography ◽  
Theoretical Investigations ◽  
Modes Of Vibration ◽  
Geometrical Imperfections ◽  
Theoretical Results

Numerous theoretical investigations on the natural frequencies for complete spherical shells have been reported over the past four decades. However, attempts at correlating the theoretical results with either experimental or simulated results (both for axisymmetric and nonaxisymmetric modes of vibration) are almost completely lacking. In this paper, natural frequencies and mode shapes obtained from axisymmetric and nonaxisymmetric theories of vibration of complete spherical shells and from finite element computer simulations of the vibrations, with and without geometrical imperfections, are presented. Modal tests reported elsewhere on commercially available, thin spherical marine floats (with imperfections) are then utilized as a basis for comparison of frequencies to both the theoretical and numerical results. Because of the imperfections present, “splitting” of frequencies of nonaxisymmetric modes is anticipated. The presence of this frequency splitting phenomenon is demonstrated. In addition, results of a “whole field” measurement on one of the imperfect shells using dynamic holography are presented.

The Natural Frequencies and Modes of Vibration of a Rotating Beam

1954 ◽  
Vol 58 (525) ◽  
pp. 652-654
Author(s):  
H. S. Liner
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Matrix Form ◽  
Rotating Beam ◽  
Bending Vibrations ◽  
Natural Frequencies And Modes ◽  
Modes Of Vibration ◽  
Frequency Diagram

This note presents in matrix form the equations of motion of a rotating and vibrating beam. The natural frequencies of the system are obtained by plotting an impedance-frequency diagram and noting the frequencies at which the impedance vanishes. Uncoupled bending vibrations are considered but the analysis can easily be extended to include coupled bending-torsion vibrations. The arrangement of the method for solution on a digital computor is quite straight-forward.

On the Determination of the Dynamic Characteristics of a Vibrating System

1967 ◽  
Vol 71 (683) ◽  
pp. 793-796 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Experimental Investigations ◽  
Aircraft Industry ◽  
Natural Frequencies And Modes ◽  
Vibrating System ◽  
Modes Of Vibration

The natural frequencies and modes of vibration of a structure may be obtained more or less directly from experiments. The generalised masses and stiffnesses, however, are usually obtained indirectly from experimental investigations of the dynamic behaviour of the system. One of the techniques widely used for this purpose in the aircraft industry is known as the method of displaced frequenciesm.Stated briefly, the method consists of observing the changes in the natural frequencies caused by the addition of one or more small masses to the vibrating system.

Bending, Buckling and Vibration of Orthotropic Plate-Beam Structures

1968 ◽  
Vol 12 (04) ◽  
pp. 249-268 ◽  
Author(s):  
C. S. Smith
Keyword(s):  
Orthotropic Plate ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Elastic Buckling ◽  
Lateral Loads ◽  
Orthotropic Plates ◽  
Approximate Methods ◽  
Buckling Loads ◽  
Natural Frequencies And Modes ◽  
Modes Of Vibration

A method is described of estimating elastic deflections and stresses in systems of interconnected rectangular orthotropic plates and single-direction beams, under distributed or concentrated lateral loads combined with compressive or tensile stresses applied either normal to or in the direction of the beams. The effects of initial deformation of beams and plates are included. Elastic buckling loads and modes and natural frequencies and modes of vibration may be computed. The methods described have been incorporated in a family of FORTRAN IV computer programs which are used to obtain a number of illustrative solutions, including:(/) deflections and stresses in an orthogonally stiffened, three-dimensional ship compartment; these are compared with results computed by an alternative finite element method; (//) buckling loads and modes and natural frequencies and modes of vibration for a typical deck structure; these are compared with results calculated by more approximate methods commonly used in design.

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