@article{(Open Science Index):https://publications.waset.org/pdf/10001326,
	  title     = {Out-of-Plane Free Vibrations of Circular Rods},
	  author    = {Faruk Fırat Çalım and  Nurullah Karaca and  Hakan Tacettin Türker},
	  country	= {},
	  institution	= {},
	  abstract     = {In this study, out-of-plane free vibrations of a circular
rods is investigated theoretically. The governing equations for
naturally twisted and curved spatial rods are obtained using
Timoshenko beam theory and rewritten for circular rods. Effects of
the axial and shear deformations are considered in the formulations.
Ordinary differential equations in scalar form are solved analytically
by using transfer matrix method. The circular rods of the mass matrix
are obtained by using straight rod of consistent mass matrix. Free
vibrations frequencies obtained by solving eigenvalue problem. A
computer program coded in MATHEMATICA language is prepared.
Circular beams are analyzed through various examples for free
vibrations analysis. Results are compared with ANSYS results based
on finite element method and available in the literature.},
	    journal   = {International Journal of Civil and Environmental Engineering},
	  volume    = {9},
	  number    = {5},
	  year      = {2015},
	  pages     = {812 - 815},
	  ee        = {https://publications.waset.org/pdf/10001326},
	  url   	= {https://publications.waset.org/vol/101},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 101, 2015},
	}