Forced Vibration of a Damped Combined Linear System

1985 ◽  
Vol 107 (3) ◽  
pp. 275-281 ◽  
Author(s):  
L. A. Bergman ◽  
J. W. Nicholson
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Forced Vibration ◽  
Green's Functions ◽  
Natural Frequencies ◽  
Green’S Functions ◽  
Orthogonality Relation ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
General Method

A new and general method for determining the exact undamped natural frequencies and natural modes of vibration, the orthogonality relation for the natural modes, and the response to arbitrary excitation for both damped and undamped combined linear systems is given. The method, based upon Green’s functions of the vibrating distributed subsystems, is demonstrated for a multiplicity of linear oscillators connected to a simple beam.

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.

AN INTRODUCTORY GUIDE TO GREEN’S FUNCTION METHODS IN NUCLEAR MANY-BODY PROBLEMS

1994 ◽  
Vol 03 (02) ◽  
pp. 523-589 ◽  
Author(s):  
T.T.S. KUO ◽  
YIHARN TZENG
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Model Space ◽  
Many Body ◽  
Diagram Expansion ◽  
Nucleus Scattering ◽  
Many Body Systems ◽  
General Method

We present an elementary and fairly detailed review of several Green’s function methods for treating nuclear and other many-body systems. We first treat the single-particle Green’s function, by way of which some details concerning linked diagram expansion, rules for evaluating Green’s function diagrams and solution of the Dyson’s integral equation for Green’s function are exhibited. The particle-particle hole-hole (pphh) Green’s function is then considered, and a specific time-blocking technique is discussed. This technique enables us to have a one-frequency Dyson’s equation for the pphh and similarly for other Green’s functions, thus considerably facilitating their calculation. A third type of Green’s function considered is the particle-hole Green’s function. RPA and high order RPA are treated, along with examples for setting up particle-hole RPA equations. A general method for deriving a model-space Dyson’s equation for Green’s functions is discussed. We also discuss a method for determining the normalization of Green’s function transition amplitudes based on its vertex function. Some applications of Green’s function methods to nuclear structure and recent deep inelastic lepton-nucleus scattering are addressed.

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.

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.

Thermal Stresses in an Orthotropic Elastic Semispace

1972 ◽  
Vol 39 (1) ◽  
pp. 87-90 ◽  
Author(s):  
A. Y. Ako¨z ◽  
T. R. Tauchert
Keyword(s):  
Temperature Field ◽  
Green's Functions ◽  
Thermal Stresses ◽  
Green’S Functions ◽  
Elastic Solid ◽  
Displacement Boundary ◽  
Steady State Temperature ◽  
Method Of Solution ◽  
Displacement Potentials ◽  
General Method

The thermal stresses in an orthotropic semi-infinite elastic solid subject to plane strain are investigated. A general method of solution based upon displacement potentials is presented for the case of a steady-state temperature field. Results are presented for both stress-free and zero-displacement boundary conditions. The stresses are written in terms of Green’s functions, where the Green’s functions represent stresses induced by a line source of temperature on the bounding plane.

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.

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