Natural Modes and Natural Frequencies of Uniform, Circular, Free-Edge Plates

1979 ◽  
Vol 46 (2) ◽  
pp. 448-453 ◽  
Author(s):  
K. Itao ◽  
S. H. Crandall
Keyword(s):  
Circular Plate ◽  
Isotropic Material ◽  
Natural Frequencies ◽  
Free Edge ◽  
Poisson's Ratio ◽  
Thin Circular Plate ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Homogeneous Isotropic Material ◽  
Free Edges

The natural modes and natural frequencies for the first 701 modes of vibration of a uniform thin circular plate with free edges are tabulated for a homogeneous isotropic material with Poisson’s ratio ν = 0.330.

Modal Analysis of Circular Plates

2014 ◽  
Vol 611 ◽  
pp. 245-251
Author(s):  
Jozef Bocko ◽  
Peter Sivák ◽  
Ingrid Delyová ◽  
Štefánia Šelestáková
Keyword(s):  
Circular Plate ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Engineering Practice ◽  
Structural Elements ◽  
Circular Plates ◽  
Structural Element ◽  
Thin Circular Plate ◽  
Outer Periphery ◽  
Modes Of Vibration

In engineering practice, some of the structural elements take the form of a thin planar plate. For such elements, it is sometimes important to consider dangerous condition of resonance. A structural element cannot operate in the range of resonant frequencies. It is therefore necessary to determine natural frequencies and normal modes of vibration of such structural elements. Parts of the paper are the results of the analysis of natural frequencies and normal modes of vibration using FEM program Cosmos. The subject of the analysis was a thin flat circular plate considered in three modifications, i.e. free thin circular plate without hole, a thin circular plate without hole, clamped on the outer periphery, a thin circular plate with a hole, clamped on the outer and inner circumference. At the same time, Chladni patterns were obtained. They were created using the Matlab system and extraction of the outputs of the Cosmos program.

Free Vibrations of Constrained Beams

1952 ◽  
Vol 19 (4) ◽  
pp. 471-477
Author(s):  
Winston F. Z. Lee ◽  
Edward Saibel
Keyword(s):  
Natural Frequencies ◽  
Degree Of Approximation ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Continuous Beam ◽  
Concentrated Mass ◽  
Simple Manner ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Rigid Supports

Abstract A general expression is developed from which the frequency equation for the vibration of a constrained beam with any combination of intermediate elastic or rigid supports, concentrated masses, and sprung masses can be found readily. The method also is extended to the case where the constraint is a continuous elastic foundation or uniformly distributed load of any length. This method requires only the knowledge of the natural frequencies and natural modes of the beam supported at the ends in the same manner as the constrained beam but not subjected to any of the constraints between the ends. The frequency equation is obtained easily and can be solved to any desired degree of approximation for any number of modes of vibration in a quick and simple manner. Numerical examples are given for a beam with one concentrated mass, for a beam with one sprung mass, and a continuous beam with one sprung mass.

Node Control of Uniform Beams Subject to Various Boundary Conditions

1992 ◽  
Vol 59 (4) ◽  
pp. 983-990 ◽  
Author(s):  
L. Weaver ◽  
L. Silverberg
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Controlled System ◽  
Free Boundary Conditions ◽  
Various Boundary Conditions ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Control Forces ◽  
Direct Feedback

This paper introduces node control, whereby discrete direct feedback control forces are placed at the nodes of the N+1th mode (the lowest N modes participate in the response). Node control is motivated by the node control theorem which states, under certain conditions, that node control preserves the natural frequencies and natural modes of vibration of the controlled system while achieving uniform damping. The node control theorem is verified for uniform beams with pinned-pinned, cantilevered, and free-free boundary conditions, and two cases of beams with springs on the boundaries. A general proof of the node control theorem remains elusive.

Normal Vibrations of a Uniform Plate Carrying Any Number of Finite Masses

1959 ◽  
Vol 26 (2) ◽  
pp. 210-216
Author(s):  
W. F. Stokey ◽  
C. F. Zorowski
Keyword(s):  
Natural Frequencies ◽  
Physical Characteristics ◽  
Normal Vibrations ◽  
Simply Supported ◽  
Numerical Example ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
General Method

Abstract A general method is presented for determining approximately the natural frequencies of the normal vibrations of a uniform plate carrying any number of finite masses. Its application depends on knowing the frequencies and natural modes of vibration of the unloaded plate and the physical characteristics of the mass loadings. A numerical example is presented in detail in which this method is applied to a simply supported plate carrying two masses. Results also are included of experimentally measured frequencies for this configuration and several additional cases along with the frequencies computed using this method for comparison.

Numerical Analysis of Forced Vibrations of Beams

1953 ◽  
Vol 20 (1) ◽  
pp. 53-56
Author(s):  
N. O. Myklestad
Keyword(s):  
Natural Frequencies ◽  
Driving Forces ◽  
Bending Moments ◽  
Internal Damping ◽  
Shear Forces ◽  
Natural Modes ◽  
Tabular Method ◽  
Modes Of Vibration ◽  
The One ◽  
Phase Angles

Abstract In this paper a simple tabular method is developed by which the vibration amplitudes, bending moments, and shear forces of a beam of variable but symmetrical cross section, carrying any number of concentrated masses and acted on by any number of harmonically varying forces, can be found. The driving forces must all have the same frequency but the phase angles may be different. The method is an extension of the one employed by the author to find natural modes of vibration of beams, but in the case of forced vibration only one application of the tabular calculations is necessary, making it essentially a far simpler problem than that of finding the natural modes. Internal damping of the beam material is easily considered and should always be taken into account if there is any danger that the forced frequency is near any one of the natural frequencies.

scholarly journals Dynamic testing of a modern concrete bridge

1979 ◽  
Vol 6 (3) ◽  
pp. 447-455 ◽  
Author(s):  
J. H. Rainer ◽  
G. Pernica
Keyword(s):  
Natural Frequencies ◽  
Dynamic Testing ◽  
Dynamic Properties ◽  
Mode Shapes ◽  
Total Width ◽  
Concrete Bridge ◽  
Reinforced Concrete Bridge ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Good Agreement

A posttensioned reinforced concrete bridge, slated for demolition, was tested to obtain its dynamic properties. The 10 year old bridge consisted of a continuous flat slab deck of variable thickness having a total width of 103 ft (31.39 m) and spans of 28 ft 6 in. (8.69 m), 71 ft 0 in. (21.64 m), and 42 ft 6 in. (12.95 m). The entire bridge was skewed 10°50′ and the deck was slightly curved in plan.The mode shapes, natural frequencies, and damping ratios for the lowest five natural modes of vibration were determined using sinusoidal forcing functions from an electrohydraulic shaker. These modes, located at 5.7, 6.4, 8.7, 12.0, and 17.4 Hz, were found to be highly dependent on the lateral properties of the bridge deck. Damping ratios were determined from the widths of resonance peaks. The modal properties from the steady state excitation were compared with those obtained from measurements of traffic-induced vibrations and good agreement was found between the two methods.

On the Nature of Natural Control

1989 ◽  
Vol 111 (4) ◽  
pp. 412-422 ◽  
Author(s):  
L. Silverberg ◽  
M. Morton
Keyword(s):  
Control Systems ◽  
Structural Control ◽  
Natural Frequencies ◽  
Dynamic Performance ◽  
Natural Control ◽  
Space Truss ◽  
Natural Modes ◽  
Modal Damping ◽  
Modes Of Vibration ◽  
Control Forces

This paper examines families of structural control systems and reveals inherent properties that provide the essential motivation behind the theory of Natural Control. It is determined that the associated fuel consumed by the controls is near minimal when the natural frequencies are identical to the controlled modal frequencies, and when the natural modes of vibration are identical to the controlled modes of vibration. Also, by casting the objective to suppress vibration in the form of an exponential stability condition, it is found that vibration is most efficiently suppressed when the modal damping rates are identical to a designer chosen decay rate. The use of a limited number of control forces over distributed control is characterized by a change in fuel consumed by the controls and by a deterioration in the dynamic performance reflected by changes in the modal damping rates. The Natural Control of a space truss demonstrates the results.

Stress and Vibrational Analysis of an Indian Railway RCF Bogie

2018 ◽  
Vol 9 (5) ◽  
Author(s):  
Rakesh Chandmal Sharma ◽  
Srihari Palli ◽  
Ramji Koona
Keyword(s):  
Finite Element ◽  
Transient Analysis ◽  
Natural Frequencies ◽  
Vibrational Analysis ◽  
Railway Vehicle ◽  
Dynamic Finite Element ◽  
Natural Modes ◽  
Dynamic Analyses ◽  
Modes Of Vibration ◽  
Indian Railway

In the present work, static and dynamic finite element analyses are carried out on an Indian railway 6 ton RCF sleeper bogie. The geometrical CAD model of railway vehicle has been developed in UG-NX7.5 and has been exported to ANSYS12.1 package where finite element modelling and the required static and dynamic analyses have been performed. For dynamic response, modal, harmonic and transient dynamic analyses are carried out. First few natural modes of vibration of the bogie are extracted in Eigen frequency analysis and it is observed that the roll mode attained at a frequency which is well matched with the fundamental natural frequency calculated analytically. The harmonic peaks obtained are matching well with the natural frequencies obtained in modal analysis. Response to the ground excitation when the bogie passes over a bump is simulated in transient analysis.

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