On the approximate determination of natural frequencies and modes of cantilever beams

1970 ◽  
Vol 9 (1-2) ◽  
pp. 109-120 ◽  
Author(s):  
B. H. Karnopp ◽  
J. C. Fung
Keyword(s):  
Natural Frequencies ◽  
Approximate Determination ◽  
Cantilever Beams ◽  
Natural Frequencies And Modes

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.

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.

Numerical Determination of Natural Frequencies and Modes of the Vibrations of a Thick-Walled Cylindrical Shell

2018 ◽  
Vol 54 (1) ◽  
pp. 75-84 ◽  
Author(s):  
A. Ya. Grigorenko ◽  
M. Yu. Borisenko ◽  
E. V. Boichuk ◽  
A. P. Prigoda
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Numerical Determination ◽  
Natural Frequencies And Modes

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.

Vibration of Elastically Coupled Cantilever Beams using Greens's Functions

2003 ◽  
Vol 9 (11) ◽  
pp. 1303-1324
Author(s):  
Abdel-Salaam Mohamad ◽  
Abdulghaffar A N Al-Jawi
Keyword(s):  
Natural Frequencies ◽  
Forced Vibrations ◽  
Cantilever Beams ◽  
Finite Element Code ◽  
Mode Localization ◽  
Free Wave ◽  
Finite Difference Equations ◽  
Free Mode ◽  
Free Wave Propagation

The dynamic characteristics of cantilever beams, elastically coupled into linear and cyclic chains are considered theoretically, using Green's functions. This leads to finite difference equations, which can be solved easily for the tuned structure, or to tri-diagonal and cyclic tri-diagonal matrices for the linear and cyclic chains respectively, when mistuning is present, which can be inverted by standard routines. Free wave propagation and forced vibrations are both studied. Propagation constants for the tuned problem are presented and discussed. Mode localization factors are determined using Monte Carlo simulation when mistuning is introduced. The finite element code (ABAQUS) is also applied in the determination of natural frequencies and the study of free mode localization.

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