Response of infinite length rods and beams with periodically varying area
| Autor: | Benjamin A. Cray, Andrew J. Hull |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Acoustics and Ultrasonics
business.industry Differential equation Mechanical Engineering Mathematical analysis Equations of motion Moment of inertia Condensed Matter Physics Displacement (vector) Optics Mechanics of Materials Displacement field Series expansion business Fourier series Beam (structure) Mathematics |
| Zdroj: | Journal of Sound and Vibration. 333:4960-4976 |
| ISSN: | 0022-460X |
| DOI: | 10.1016/j.jsv.2014.04.041 |
| Popis: | This paper develops a solution method for the longitudinal motion of a rod or the flexural motion of a beam of infinite length whose area varies periodically. The conventional rod or beam equation of motion is used with the area and moment of inertia expressed using analytical functions of the longitudinal (horizontal) spatial variable. The displacement field is written as a series expansion using a periodic form for the horizontal wavenumber. The area and moment of inertia expressions are each expanded into a Fourier series. These are inserted into the differential equations of motion and the resulting algebraic equations are orthogonalized to produce a matrix equation whose solution provides the unknown wave propagation coefficients, thus yielding the displacement of the system. An example problem of both a rod and beam are analyzed for three different geometrical shapes. The solutions to both problems are compared to results from finite element analysis for validation. Dispersion curves of the systems are shown graphically. Convergence of the series solutions is illustrated and discussed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect