0
TECHNICAL PAPERS

Dynamic Stiffness Formulation and Its Application for a Combined Beam and a Two Degree-of-Freedom System

[+] Author and Article Information
J. R. Banerjee

School of Engineering and Mathematical Sciences, City University, Northampton Square, London EC1V OHBe-mail: j.r.banerjee@city.ac.uk

J. Vib. Acoust 125(3), 351-358 (Jun 18, 2003) (8 pages) doi:10.1115/1.1569943 History: Received May 01, 2002; Revised December 01, 2002; Online June 18, 2003
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.

References

Chen,  Y., 1963, “On the Vibration of Beams or Rods Carrying a Concentrated Mass,” ASME J. Appl. Mech., 30, pp. 310–311.
Pan,  H. H., 1965, “Transverse Vibration of an Euler Beam Carrying a System of Heavy Bodies,” ASME J. Appl. Mech., 32, pp. 434–437.
Laura,  P. A. A., Pombo,  J. L., and Susemihl,  E. A., 1974, “A Note on the Vibration of a Clamped-Free Beam with a Mass at the Free End,” J. Sound Vib., 37, pp. 161–168.
Parnell,  L. A., and Cobble,  M. H., 1976, “Lateral Displacements of a Vibrating Cantilever Beam with a Concentrated Mass,” J. Sound Vib., 44, pp. 499–511.
Gurgoze,  M., 1984, “A Note on the Vibrations of Restrained Beams and Rods with Point Masses,” J. Sound Vib., 96, pp. 461–468.
Burch,  J. C., and Mitchell,  T. P., 1987, “Vibration of a Mass-Loaded Clamped-Free Timoshenko beam,” J. Sound Vib., 114, pp. 341–345.
Laura,  P. A. A., Filipich,  C. P., and Cortinez,  V. H., 1987, “Vibrations of Beams and Plates Carrying Concentrated Masses,” J. Sound Vib., 117, pp. 459–465.
Wu,  J. S., and Lin,  T. L., 1990, “Free Vibration Analysis of a Uniform Cantilever Beam with Point Masses by an Analytical-and-Numerical-Combined Method,” J. Sound Vib., 136, pp. 201–213.
Abramovich,  H., and Hamburger,  O., 1991, “Vibration of a Cantilever Timoshenko Beam with a Tip Mass,” J. Sound Vib., 148, pp. 162–170.
Massalas,  C., and Soldatos,  K., 1978, “Free Vibration of a Beam Subjected to Elastic Constraints,” J. Sound Vib., 57, pp. 607–608.
Davies,  H. G., and Rogers,  R. J., 1979, “The Vibration of Structures Elastically Constrained at Discrete Points,” J. Sound Vib., 63, pp. 437–447.
Lau,  J. H., 1981, “Fundamental Frequency of a Constrained Beam,” J. Sound Vib., 78, pp. 154–157.
Verniere,  P., Ficcadenti,  G., and Laura,  P. A. A., 1984, “Dynamic Analysis of a Beam with an Intermediate Elastic Support,” J. Sound Vib., 96, pp. 381–389.
Lau,  J. H., 1984, “Vibration Frequencies and Mode Shapes for a Constrained Cantilever,” ASME J. Appl. Mech., 51, pp. 182–187.
Maurizi,  M. J., and Bambill de Rossit,  D. V., 1987, “Free Vibration of a Clamped-Clamped Beam with an Intermediate Elastic Support,” J. Sound Vib., 119, pp. 173–176.
Rao,  C. K., 1989, “Frequency Analysis of Clamped-Clamped Uniform Beams with Intermediate Elastic Support,” J. Sound Vib., 133, pp. 502–509.
Jacquot,  R. G., and Gibson,  J. D., 1972, “The Effects of Discrete Masses and Elastic Supports on Continuous Beam Natural Frequencies,” J. Sound Vib., 23, pp. 237–244.
Laura,  P. A. A., Maurizi,  M. J., and Pombo,  J. L., 1975, “A Note on the Dynamic Analysis of an Elastically Restrained-Free Beam with a Mass at the Free End,” J. Sound Vib., 41, pp. 397–405.
Laura,  P. A. A., Susemihl,  E. A., Pombo,  J. L., Luisoni,  L. E., and Gelos,  R., 1977, “On the Dynamic Behavior of Structural Elements Carrying Elastically Mounted, Concentrated Masses,” Appl. Acoust., 10, pp. 121–145.
Bapat,  C. N., and Bapat,  C., 1987, “Natural Frequencies of a Beam with Nonclassical Boundary Conditions and Concentrated Masses,” J. Sound Vib., 112, pp. 177–182.
Ercoli,  L., and Laura,  P. A. A., 1987, “Analytical and Experimental Investigation on Continuous Beams Carrying Elastically Mounted Masses,” J. Sound Vib., 114, pp. 519–533.
Larrondo,  H., Avalos,  D., and Laura,  P. A. A., 1992, “Natural Frequencies of a Bernoulli Beam Carrying an Elastically Mounted Concentrated Mass,” Ocean Eng., 19, pp. 461–468.
Abramovich,  H., and Hamburger,  O., 1992, “Vibration of a Cantilever Timoshenko Beam with Translational and Rotational Springs and with Tip Mass,” J. Sound Vib., 154, pp. 67–80.
Rossi,  R. E., Laura,  P. A. A., Avalos,  D. R., and Larrondo,  H. O., 1993, “Free Vibrations of Timoshenko Beams Carrying Elastically Mounted, Concentrated Masses,” J. Sound Vib., 165, pp. 209–223.
Gurgoze,  M., 1996, “On the Eigenfrequencies of a Cantilever Beam with Attached Tip Mass and a Spring-Mass System,” J. Sound Vib., 190, pp. 149–162.
Jen,  M. U., and Magrab,  E. B., 1993, “Natural Frequencies and Mode Shapes of Beams Carrying a Two-Degree-of-Freedom Spring-Mass System,” ASME J. Vibr. Acoust., 115, pp. 202–209.
Wu,  J. S., and Huang,  C. G., 1995, “Free and Forced Vibrations of a Timoshenko Beam with any Number of Translational and Rotational Springs and Lumped Masses,” Int. J. Commun. Num. Meth. Eng., 11, pp. 743–756.
Chang,  T. P., and Chang,  C. Y., 1998, “Vibration Analysis of Beams with a Two Degree-of-Freedom Spring-Mass System,” Int. J. Solids Struct., 35, pp. 383–401.
Wu,  J. S., and Chou,  H. M., 1998, “Free Vibration Analysis of a Cantilever Beam Carrying any Number of Elastically Mounted Pointed Masses with the Analytical-and-Numerical-Combined Method,” J. Sound Vib., 213, pp. 317–332.
Wu,  J. S., and Chou,  H. M., 1999, “A New Approach for Determining the Natural Frequencies and Mode Shapes of a Uniform Beam Carrying any Number of Sprung Masses,” J. Sound Vib., 220, pp. 451–468.
Wu,  J. J., and Whittaker,  A. R., 1999, “The Natural Frequencies and Mode Shapes of a Uniform Beam with Multiple Two-DOF Spring-Mass Systems,” J. Sound Vib., 227, pp. 361–381.
Dowell,  E. H., 1979, “On Some General Properties of Combined Dynamical Systems,” ASME J. Appl. Mech., 46, pp. 206–209.
Nicholson,  J. W., and Bergman,  L. A., 1986, “Free Vibration of Combined Dynamical Systems,” J. Eng. Mech., 112, pp. 1–13.
Howson,  W. P., and Williams,  F. W., 1977, “Compact Computation of Natural Frequencies and Buckling Loads for Plane Frames,” Int. J. Numer. Methods Eng., 11, pp. 1067–1081.
Howson,  W. P., Banerjee,  J. R., and Williams,  F. W., 1983, “Concise Equations and Program for Exact Eigensolutions of Plane Frames including Member Shear,” Adv. Eng. Software, 5, pp. 137–141.
Kolousek, V., 1973, Dynamics in Engineering Structures, Butterworths, London.
Wittrick,  W. H., and Williams,  F. W., 1971, “A General Algorithm for Computing Natural Frequencies of Elastic Structures,” Q. J. Mech. Appl. Math., 24, pp. 263–284.
Anderson, M. S., Williams, F. W., Banerjee, J. R., Durling, B. J., Herstrom, C. L., Kennedy D., and Warnaar, D. B., 1986, “User Manual BUNVIS-RG: An Exact Buckling and Vibration Program for Lattice Structures, with Repetitive Geometry and Substructuring option,” NASA Tech. Memo. 87669.
Cheng,  F. Y., 1970, “Vibration of Timoshenko Beams and Frameworks,” J. Struct. Div. ASCE, 96, pp. 551–571.
Wang,  T. M., and Kinsman,  T. A., 1971, “Vibration of Frame Structures According to the Timoshenko Theory,” J. Sound Vib., 14, pp. 215–227.
Howson,  W. P., and Williams,  F. W., 1973, “Natural Frequencies of Frames with Axially Loaded Timoshenko Members,” J. Sound Vib., 26, pp. 503–515.
Cheng,  F. Y., and Tseng,  W. H., 1973, “Dynamic Stiffness Matrix of Timoshenko Beam Columns,” J. Struct. Div. ASCE, 99, 527–549.
Banerjee,  J. R., 1996, “Dynamic Stiffness Formulation for Structural Elements: A General Approach,” Comput. Struct., 63, pp. 101–103.
Clough, R. W., and Penzien, J., 1975, Dynamics of Structures, McGraw-Hill, Singapore.

Figures

Grahic Jump Location
Amplitudes of displacements and forces at the ends of a Bernoulli-Euler Beam in free vibration
Grahic Jump Location
A two degree-of-freedom system kinematically connected to a beam element
Grahic Jump Location
A clamped-clamped beam carrying a two degree-of-freedom spring-mass system
Grahic Jump Location
The first three natural frequencies and mode shapes of the clamped-clamped beam carrying a two degree-of-freedom shown in Fig. 3
Grahic Jump Location
The effect of spring stiffness on the fundamental natural frequency of the clamped-clamped beam carrying a two degree-of-freedom shown in Fig. 3
Grahic Jump Location
A plane frame carrying a two degree-of-freedom spring mass system
Grahic Jump Location
Coordinate system and notation for a Bernoulli-Euler beam
Grahic Jump Location
End conditions for a Bernoulli-Euler beam in free vibration

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In