Exponential solutions for a longitudinally vibrating inhomogeneous rod
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
Journal of Mechanics of Materials and Structures
Publication Status
Version of Record
Abstract
A special class of closed form solutions for inhomogeneous rods is investigated, arising from the following problem: for a given distribution of the material density, find the axial rigidity of an inhomogeneous rod so that the exponential mode shape serves as the vibration mode. Specifically, for a rod clamped at one end and free at the other, the exponentially varying vibration mode is postulated and the associated semi-inverse problem is solved. This yields distributions of axial rigidity which, together with a specific law of material density, satisfy the governing eigenvalue problem. The results obtained can be used in the context of functionally graded materials for vibration tailoring, that is, for the design of a rod with a given natural frequency according to a postulated vibration mode.
First Page
1251
Last Page
1256
DOI
10.2140/jomms.2009.4.1251
Publication Date
1-1-2009
Recommended Citation
Caliò, Ivo and Elishakoff, Isaac, "Exponential solutions for a longitudinally vibrating inhomogeneous rod" (2009). Faculty Scholarship. 396.
https://digitalcommons.fau.edu/faculty_papers/396