THE HARMONIC RESPONSE OF UNIFORM BEAMS ON MULTIPLE LINEAR SUPPORTS - A FLEXURAL WAVE ANALYSIS

Date

1990-09-22

Author

MEAD, DJ
Yaman, Yavuz

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

264
views

0
downloads

A wave approach is developed for the exact analysis of the harmonic response of uniform finite beams on multiple supports. The beam may be excited by single or multi-point harmonic forces or moments; its supports may have general linear characteristics which may include displacement-rotation coupling. Use is made of the harmonic response function for an infinite beam subjected to a single-point harmonic force or moment. The unknowns of the finite beam problem are the support reaction forces/moments and the magnitudes of four waves reflected from the ends of the beam. Equations are presented for the response of a single-bay beam with various support conditions and subjected to single-point harmonic excitation. The same equations, but with the simple addition of further straightforward terms on the right-hand side, are used for multi-point excitation. The effects of damping are easily incorporated. Equations for multi-supported beams are also presented together with illustrative computed frequency-response curves. Natural frequencies have been calculated by finding resonance frequencies of very lightly damped beams. These compare impeccably with the results of other investigators.

Subject Keywords

Mechanical Engineering, Acoustics and Ultrasonics, Mechanics of Materials, Condensed Matter Physics

URI

https://hdl.handle.net/11511/38132

Journal

JOURNAL OF SOUND AND VIBRATION

DOI

https://doi.org/10.1016/0022-460x(90)90639-h

Collections

Department of Aerospace Engineering, Article

Suggestions

OpenMETU
Core

THE RESIDUAL VARIABLE METHOD APPLIED TO ACOUSTIC-WAVE PROPAGATION FROM A SPHERICAL SURFACE AKKAS, N; ERDOGAN, F (ASME International, 1993-01-01) The classical wave equation in spherical coordinates is expressed in terms of a residual potential applying the Residual Variable Method. This method essentially eliminates the second derivative of the potential with respect to the radial coordinate from the wave equation. Thus, the dynamic pressure distribution on the surface of a spherical cavity can be studied by considering the cavity surface only. Moreover, the Residual Variable Method, being amenable to ''marching'' solutions in a finite-difference im...
A refined dynamic theory for viscoelastic cylindrical shells and cylindrical laminated composites, Part 2: An application Birlik, G.A.; Mengi, Yalçın (Elsevier BV, 1989-4) In this study, the general approximate theory developed in Part 1 for shells is assessed for axially symmetric elastic waves propagating in a closed circular cylindrical shell (hollow rod). The spectra predicted by zeroth and second order approximate theories are determined for various values of shell thicknesses and the Poisson ratios and they are compared with those of exact theory. It is found that the agreement between the two is good. Approximate and exact cut-off frequencies match almost exactly. The ...
THE HARMONIC RESPONSE OF RECTANGULAR SANDWICH PLATES WITH MULTIPLE STIFFENING - A FLEXURAL WAVE ANALYSIS MEAD, DJ; Yaman, Yavuz (Elsevier BV, 1991-03-22) An exact analytical method is presented for the vibration response of a finite, three-layered, rectangular sandwich plate with a visco-elastic core, subjected to a harmonic line force which varies sinusoidally across the plate. Uniform parallel stiffeners (which may all be different) span the plate between one pair of simply supported edges. The other pair of edges may have any degree or type of uniform constraint. In the analysis the known flexural wave motion in an infinite parallel unstiffened plate subj...
A modal superposition method for non-linear structures Kuran, B; Özgüven, Hasan Nevzat (Elsevier BV, 1996-01-25) The dynamic response of multi-degree of freedom (MDOF) non-linear structures is usually determined by the numerical integration of equations of motion. This is computationally very costly for steady state response analysis. In this study, a powerful and economical method is developed for the harmonic response analysis of non-linear structures. In this method, the equations of motion are first converted into a set of non-linear algebraic equations, and then the number of equations to be solved is reduced by ...
A refined dynamic theory for viscoelastic cylindrical shells and cylindrical laminated composites, Part 1: General theory Birlik, G.A.; Mengi, Yalçın (Elsevier BV, 1989-4) Through the use of a new technique, approximate theories are developed for the dynamic response of viscoelastic cylindrical shells and cylindrical laminated composites (CLC). The new technique eliminates the inconsistencies between the deformation shapes assumed over the thickness of the shell and the boundary or interface conditions to be satisfied on its lateral surfaces. Accordingly, the theory correctly predicts the dynamic behavior of shells or CLC without using any correction factors. Due to its lengt...

Citation Formats

D. MEAD and Y. Yaman, “THE HARMONIC RESPONSE OF UNIFORM BEAMS ON MULTIPLE LINEAR SUPPORTS - A FLEXURAL WAVE ANALYSIS,” JOURNAL OF SOUND AND VIBRATION, pp. 465–484, 1990, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38132.