A CLOSED-FORM APPROXIMATE SOLUTION FOR COUPLED VIBRATIONS OF COMPOSITE THIN-WALLED BEAMS WITH MID-PLANE SYMMETRY
Original scientific paper The purpose of this paper is to develop and present an approximate analysis procedure to estimate the natural frequencies and mode shapes of thin-walled beams with arbitrary open cross-section, made of laminates with mid-plane symmetry. Theory of thin-walled composite beams is based on assumptions consistent with the Vlasov's beam theory and classical lamination theory. The equations of motion for coupled bending-torsional vibrations are derived from the principle of virtual displacements. In the case of simply supported thin-walled beam the frequency equation, given in determinant form, is expanded in an explicit analytical form, which gives the natural frequencies of free harmonic vibrations. For verification, the analytical study by other researchers and the FEM analysis using ANSYS are compared with the current results.
VIBRATION AND BUCKLING OF COMPOSITE THIN-WALLED BEAMS WITH SHEAR DEFORMABILITY
In this paper, a theoretical model is developed for the dynamic analysis of composite thin-walled beams with open or closed cross-sections. The present model incorporates, in a full form, the shear flexibility (bending and warping shear) as well as a state of initial stresses. This allows to study the free vibration and buckling problems in a unified fashion. An analytical solution of the developed equations is obtained for the case of simply supported thin-walled beams. Numerical examples are given to demonstrate the importance of the shear flexibility on the vibration and buckling behavior of the considered structures.
United Nations Convention on the Law of the Sea 1982, A Commentary
Volume VI is the sixth substantive volume to be published in the series. It deals with the work of the First Committee at the Third UN Conference on the Law of the Sea, namely the international seabed area. The volume thus embraces the deep seabed mining regime set out in Part XI of the 1982 Convention on the Law of the Sea together with the 1994 Agreement on its implementation. Completion of this commentary was delayed first by the consultations and negotiations that commenced in 1990 and led to the 1994 Agreement and the entry into force of the Convention. It was further delayed until the Assembly of the International Seabed Authority approved the detailed mining regulations in 2000. Additional supplementary material can be found at UNCLOS 1982 Commentary: Supplementary Documents.