Computation of the Eigenvalues of Wave Propagation in Periodic Substructural Systems

1993 ◽  
Vol 115 (4) ◽  
pp. 422-426 ◽  
Author(s):  
F. W. Williams ◽  
Zhong Wanxie ◽  
P. N. Bennett
Keyword(s):  
Wave Propagation ◽  
Timoshenko Beam ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Periodic Structures ◽  
Dynamic Stiffness ◽  
Finite Element Program ◽  
Element Program ◽  
Simple Supports ◽  
Phase Propagation

The wave propagation constants of periodic structures are computed using the exact dynamic stiffness matrix of a typical substructure. The approach used is to show that wave propagation and the natural vibration eigenproblem are similar to such an extent that methods used to find the natural frequencies of a structure can be applied to find its wave propagation constants. The Wittrick-Williams algorithm has been incorporated into a finite element program, JIGFEX, in conjunction with exact dynamic member stiffnesses, to ensure that no phase propagation eigenvalues are missed during computation. The accuracy of the present approach is then demonstrated by comparing the results that it gives to analytically determined wave propagation curves for a Timoshenko beam on periodic simple supports. Finally, phase propagation curves are given for a complex Timoshenko beam structure of a type that would be very difficult to analyze analytically.

Wave Propagation in Periodic Stiffened Shells: Spectral Finite Element Modeling and Experiments

2003 ◽  
Vol 9 (9) ◽  
pp. 1057-1081 ◽  
Author(s):  
G. Solaroli ◽  
Z. Gu ◽  
A. Baz ◽  
M. Ruzzene
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Periodic Structures ◽  
Dynamic Stiffness ◽  
Geometrical Parameters ◽  
Pass Band ◽  
Matrix Formulation ◽  
Stiffened Shell ◽  
Stiffened Shells ◽  
Spectral Finite Element

The capability of periodic structures to act as filters for propagating waves is used to control the propagation of waves in thin shells. The shells are stiffened by periodically placed rings in order to generate periodic discontinuities in the stiffness and inertial spatial distribution along the longitudinal axes of these shells. Such discontinuities result in attenuation of the wave propagation over certain frequency bands called stop bands. A distributed-parameter approach is used to derive a spectral finite element model of the periodically stiffened shell. The model accurately describes the dynamic behavior of the shell using a small number of elements. The stiffening rings, modeled using the curved beam theory, are considered as lumped elements whose mass and stiffness matrices are combined with those of the shell. The resulting dynamic stiffness matrix of the ring-stiffened shell element is used to predict the wave propagation dynamics in the structure. In particular, the shell propagation constants are determined by solving a polynomial eigenvalue problem, as a numerically robust alternative to the traditional transfer matrix formulation. The study of the propagation constants shows that the discontinuity introduced by the stiffeners generates the typical stop/pass band pattern of periodic structures. The location and width of the stop bands depend on the spacing and geometrical parameters of the rings. The existence of the stop bands, as predicted from the analysis of the propagation constants, is verified experimentally. Excellent agreement between theoretical predictions and experimental results is achieved. The presented theoretical and experimental techniques provide viable means for designing periodically stiffened shells with desired attenuation and filtering characteristics.

scholarly journals Dynamic Stiffness Analysis of Curved Thin-Walled Beams

1993 ◽  
Vol 1 (1) ◽  
pp. 77-88 ◽  
Author(s):  
A.Y.T. Leung ◽  
W.E. Zhou
Keyword(s):  
Present Method ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
High Accuracy ◽  
Stiffness Analysis ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Out Of Plane ◽  
Thin Walled

The natural vibration problem of curved thin-walled beams is solved by the dynamic stiffness method. The dynamic stiffness of a curved open thin-walled beam is given. The computed natural frequencies of the beam are compared with those obtained by a completely analytical method to show the high accuracy of the present method. The interaction of in-plane and out-of-plane modes is emphasized.

Analysis of the Natural Vibration Properties of a Timoshenko Beam Supported by Springs (by Finite Integral Transform Method)

1999 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura ◽  
Kunisato Seto
Keyword(s):  
Timoshenko Beam ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Integral Transform ◽  
Frequency Equation ◽  
Transform Method ◽  
Vibration Problem ◽  
Vibration Properties ◽  
Finite Integral ◽  
Integral Transform Technique

Abstract This paper presents analytical results of transverse vibration of a Timoshenko beam supported by spring-spring which stiffness is variable, that is a simplified model of magnetically levitated vehicle body’s vibration problem and magnetic bearings support shaft’s vibration problem. By applying the finite integral transform technique, the analytical solution of this dynamic model is successfully obtained. Especially, by investigating the frequency equation, the effect of the stiffness of two supporting-springs to the natural frequencies is clarified. From the results, it is cleared that the natural frequencies of the beam system can be effectively controlled by changing the supporting-spring’s stiffness.

Property determination and wave propagation in a block of Barre granite

1977 ◽  
Vol 67 (1) ◽  
pp. 87-102 ◽  
Author(s):  
Werner Goldsmith ◽  
J. L. Sackman ◽  
R. L. Taylor
Keyword(s):  
Wave Propagation ◽  
Finite Element Program ◽  
In Situ Calibration ◽  
Propagation Analysis ◽  
Principal Axes ◽  
Element Program ◽  
Principal Directions ◽  
Calibration Techniques ◽  
Barre Granite ◽  
The Impact

abstract The principal axes of a 666.8 by 609.6 by 489.0 mm (2614 in by 24 in by 1914 in) block of Barre granite, treated as an orthotropic elastic material were determined from measured pulse velocities along directions connecting 160 pairs of surface points, encompassing the entire spectrum of possible orientations. The elastic moduli of the rock were ascertained by Hopkinson bar tests involving rods cored from other samples along their principal directions; this was required for the execution of a wave-propagation analysis in the block treated as a half-space. Construction and insertion techniques were developed for transducers to be embedded in the rock at 14 locations. External and internal calibration procedures were devised to permit interpretation of the data transmitted from the interior of the sample. Transients in the block were generated by the impact of 6.35-mm (14 in) diameter steel spheres on loading bars sandwiching a thin quartz disk, serving as an input transducer, against the specimen. The wave patterns sensed by the transducers were displayed and photographed on oscillographic screens. A finite element program capable of handling arbitrary anisotropy was developed and employed for comparing the experimental results with analytical predictions based on the measured input as the boundary condition. For those stations where computations were performed, the correlation ranged from good to qualitative. It is concluded that better transducer embedment and in situ calibration techniques are required for internal transducers used in hard rocks of this type.

Influence of Loading on Mode Localization in Periodic Structures

1995 ◽  
Vol 48 (11S) ◽  
pp. S132-S137 ◽  
Author(s):  
Reyolando M. L. R. F. Brasil ◽  
Carlos E. N. Mazzilli
Keyword(s):  
Small Parameter ◽  
Periodic Structures ◽  
Computer Code ◽  
Vibration Modes ◽  
Finite Element Program ◽  
Mode Localization ◽  
Element Program ◽  
The Masses ◽  
Lumped Masses ◽  
Two Degree Of Freedom

This paper addresses the problem of the presence of a slightly disordered loading in otherwise ordered periodic structures as an element to trigger the phenomenon of vibration mode localization due to its effect in their stiffness. The sample structures are basically cantilever columns supporting the loads due to large lumped masses in their top which may vary according to a disorder related small parameter. They are connected by very flexible springs. A first series of results deals with a two-degree-of-freedom model where localization is achieved due to loading disorder. The frequencies and displacements show very sharp and nonlinear variation when the small parameter changes slightly around its zero value. The results for this simple model compare well with those of a finite element program developed by the authors. For a more complex example, another model of a rank of six columns is analyzed by the same computer code. A pseudo-random variation of the masses is considered and the resulting vibration modes are compared to those of the ordered structure, which are global in nature and present a sinusoidal spatial distribution. Again, due to mode localization, motions in the perturbed structure are found to be restricted largely to one of the masses.

Finite Element Analysis of Natural Vibration Frequency for Unbounded Prestressed Concrete Beams

2013 ◽  
Vol 351-352 ◽  
pp. 1034-1037
Author(s):  
Feng Ge Li ◽  
Yan Zhao
Keyword(s):  
Finite Element ◽  
Vibration Frequency ◽  
Prestressed Concrete ◽  
Natural Vibration ◽  
Concrete Beams ◽  
Variable Stiffness ◽  
Natural Vibration Frequency ◽  
Element Analysis ◽  
Finite Element Program ◽  
Element Program

An experimental investigation on the dynamic characteristics of unbounded prestressed concrete simply support beams is presented. A total of 5 unbounded prestressed concrete simply support beams were constructed and tested. The influence of prestressing on natural vibration frequency of concrete beams is studied by applying prestress gradually. A model of variable stiffness is proposed to calculate the natural vibration frequency of unbounded prestressed concrete beams. The finite element program Sap2000 is used to calculate the frequency of unbounded prestressed concrete beams. The results show that the calculating results agree well with experimental ones.

ROTOR RESONANCES ANALYSES OF HIGH-SPEED HIGH POWER PERMANENT-MAGNET ELECTRICAL MACHINES

2021 ◽  
pp. 95-108
Author(s):  
Wedad Alsadiq Alhawil ◽  
Ali A. Mehna ◽  
Asheraf Eldieb ◽  
Tarak Assaleh
Keyword(s):  
Finite Element ◽  
Permanent Magnet ◽  
High Speed ◽  
Natural Frequencies ◽  
Design Stage ◽  
Design Parameters ◽  
Element Analysis ◽  
Finite Element Program ◽  
Element Program ◽  
The Impact

High-speed electric machines (HSEMs) have been widely used in many of today’s applications.  For high-speed machines, in particular, it is very important to accurately predict natural frequencies of the rotor at the design stage to minimize the likelihood of failure. The main goal of this study is examine the design issues and performance of high-speed machines. For permanent-magnet synchronous motors (PMSM) driven by high-frequency drives, the rotor speed is normally above 30 000 rpm and it may exceed 100 000 rpm.  This study examined a 7-kw permanent magnet synchronous machine at 200,000 rpm. 3D finite element analysis (ANSYS WORKBENCH 15) was conducted to determine the natural frequencies and rotor patterns of a synchronous high-speed permanent magnetic motor, to assess the impact of leading design parameters, such as length, column diameter, span, bearings, material properties, and to compare the results of the finite element program with the results of analytical methods (i.e. critical speed).

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