M Rezaiee-Pajand - Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
A Aftabi Sani - Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
S.M Hozhabrossadati - Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

This study is concentrated on the natural frequencies and mode shapes of a simple three-member space frame coupled with a dynamic vibration absorber. The dynamic vibration absorber is modeled as a sixdegree- of-freedom mass-spring system. For the first time, the free vibration of an elastic structure with a six-degree-of-freedom mass-spring system is found. Each member of the space frame has uniform mechanical and geometrical properties, but these may differ from one member to another one. Theexact result of this complex problem is obtained via analytical scheme and finite element method. All effects of the axial and torsional deformations and also in- and out-of-plane bending are taken into account. This formulation includes eighteen differential equations along with thirty six boundary and compatibility conditions. Comparison of the obtained results by both mentioned approaches, illustrates the accuracy of the authors solutions. Findings are useful benchmarks for the natural frequencies andmode shapes of the space frame coupled with a dynamic vibration absorber

Space Frame,Dynamic Vibration Absorber,Vibration Analysis,Six-Degree-of-freedom Mass-spring System,Exact Solution,Finite Element Solution