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.
Quadruply coupled linear free vibrations of thin-walled beams with a generic open section
Abstract The coupled vibration of thin-walled beams with a generic open section induced by the boundary conditions is investigated using the finite element method. If the axial displacement of the pin end is restrained at another point rather than the centroid of the asymmetric cross section, the axial vibration, two bending vibrations, and torsional vibration may be all coupled. The element developed here has two nodes with seven degrees of freedom per node. The shear center axis is chosen to be the reference axis and the element nodes are chosen to be located at the shear centers of the end cross sections of the beam element. Different sets of element nodal degrees of freedom corresponding to different pin ends are considered here. The relation between element matrices referred to different sets of element nodal degrees of freedom is derived. Numerical examples are presented to demonstrate the accuracy of the proposed method and to investigate the effects of different pin ends on the coupled vibrations of the thin-wall beam.
Suitability and water quality criteria of an open drainage municipal sewage water at Coimbatore, used for irrigation.
Sanganur canal is the major open drainage system which has intricate linkage with storm water supply, domestic sewage and industrial effluent disposal. Water samples from various stations were collected and analysed for physicochemical parameters to assess the water quality of the Sanganur canal system. The study revealed that physicochemical parameters like pH, EC, TDS, DO, BOD, COD exceeded the permissible limit, clearly indicating the need of proper treatment of waste water before discharge into the Noyyal river.