Concentrated mass localization in beam-like structures using natural frequencies

2020 ◽  
Author(s):  
Ganggang Sha ◽  
Maciej Radzienski ◽  
Rohan Soman ◽  
Maosen Cao ◽  
Wieslaw Ostachowicz
Keyword(s):  
Natural Frequencies ◽  
Concentrated Mass

A Unified Frequency Equation and the Motion Analysis of a Moving Flexible Beam Carrying a Concentrated Mass

1999 ◽  
Author(s):  
S. Park ◽  
J. W. Lee ◽  
Y. Youm ◽  
W. K. Chung
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Open Loop ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Forcing Function ◽  
The Mathematical Model

Abstract In this paper, the mathematical model of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying an intermediate lumped mass is derived. The equations of motion of the beam-mass-cart system is analyzed utilizing unconstrained modal analysis, and a unified frequency equation which can be generally applied to this kind of system is obtained. The change of natural frequencies and mode shapes with respect to the change of the mass ratios of the beam, the lumped mass and the cart and to the position of the lumped mass is investigated. The open-loop responses of the system by arbitrary forcing function are also obtained through numerical simulations.

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.

Transverse Vibrations of a Free Circular Plate Carrying Concentrated Mass

1951 ◽  
Vol 18 (3) ◽  
pp. 280-282
Author(s):  
R. E. Roberson
Keyword(s):  
Laplace Transform ◽  
Mode Shape ◽  
Natural Frequencies ◽  
Mass Ratio ◽  
Concentrated Mass ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Transverse Vibrations ◽  
The Laplace Transform ◽  
Plate Face

Abstract The plate under consideration carries a concentrated mass at its center, which is struck impulsively in a direction perpendicular to the undisturbed plate face. Only circularly symmetric vibrations are considered. The solution is carried out by the use of the Laplace transform method, treating the concentrated mass as a plate-density impulse. The first four natural frequencies are displayed as functions of mass ratio, and the first mode shape is displayed for three mass ratios. The natural frequencies, particularly the higher, are shown to be very sensitive to changes in mass ratio at small values of the concentrated mass.

Effect of Local Modifications on the Vibration Characteristics of Linear Systems

1968 ◽  
Vol 35 (2) ◽  
pp. 327-332 ◽  
Author(s):  
J. T. Weissenburger
Keyword(s):  
Linear System ◽  
Eigenfunction Expansion ◽  
Natural Frequencies ◽  
Original System ◽  
Vibration Characteristics ◽  
Concentrated Mass ◽  
Linear Eigenvalue Problem ◽  
Local Modification ◽  
Linear Spring ◽  
New System

A method is presented for predicting the effect of a local modification such as the addition or removal of a concentrated mass or linear spring on the vibration characteristics of a linear system. The method, which is mathematically applicable to any linear eigenvalue problem, is rigorous even for large changes and has its basis in an eigenfunction expansion of the solution of the modified system in terms of the eigenfunctions of the unmodified system. Given the natural frequencies and modes of the original system, the characteristic function of the modified system is of such a form that it may be solved with a significant reduction in work as compared with direct treatment of the new system.

Natural frequencies of a Bernoulli beam carrying an elastically mounted concentrated mass

1992 ◽  
Vol 19 (5) ◽  
pp. 461-468 ◽  
Author(s):  
H. Larrondo ◽  
D. Avalos ◽  
P.A.A. Laura
Keyword(s):  
Natural Frequencies ◽  
Bernoulli Beam ◽  
Concentrated Mass

Vibrations of a Clamped Circular Plate Carrying Concentrated Mass

1951 ◽  
Vol 18 (4) ◽  
pp. 349-352
Author(s):  
R. E. Roberson
Keyword(s):  
Circular Plate ◽  
Constant Velocity ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
The Other ◽  
Mass Ratio ◽  
Concentrated Mass ◽  
Resonance Curves

Abstract The vibrations of a circular plate clamped at its edge and carrying a concentrated mass at its center are considered. The plate is excited by a motion of the framing, assumed rigid, to which it is clamped. The first four natural frequencies are displayed graphically as functions of mass ratio, and are calculated more precisely for μ = 0, μ = 0.05, and μ = 0.10. The motions of two subsystems with one degree of freedom are compared, one subsystem being driven by the framing and the other by the concentrated mass on the plate. The plate-mounted subsystem has a response in excess of the response of the framing-mounted subsystem if the framing is suddenly put into motion with constant velocity. Except in the neighborhood of their peaks, whose locations depend upon mass ratio, the subsystem resonance curves are depressed in height by increasing the mass ratio.

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