Banerjee J R,Williams FW.Coupled Bending-torsional Dynamic Stiffness Matrix for Timoshenko Beam Elements.Computers and Structures. 1992Banerjee J.R., Williams F.W.: Coupled bending–torsional dynamic stiffness
In this paper, an exact dynamic stiffness matrix is presented for a composite beam. It includes the effects of shear deformation and rotatory inertia: i.e., it is for a composite Timoshenko beam. The theory accounts for the (material) coupling between the bending and torsional deformations ...
The main novelty of this study is based on combining the dynamic stiffness approach and segmentation of the arch into straight Timoshenko beam segments for free vibration analysis of arch-frames. 2. Model and formulations The arch-frame having 4 joints where each joint has horizontal displacement,...
IyticaIexpressionsofdynamicstiffnessmatrixofpIanebeamfortransversevibrationwithconsideringthe sheardistortionandrotaryinertiaofmassarepresentedbydirectIysoIvingmotiondifferentiaIeuationsof auniformTimoshenkobeam.SecondIy,thefreuencycharacteristiceuationissoIvedbythebisection methodandWittrick-WiIIiamsaIgorithm.FinaIIy,thevib...
In particular, the presented closed-form solutions are exploited to formulate the displacement shape functions of the beam element and the relevant explicit form of the stiffness matrix. The proposed beam element is adopted for a finite element discretization of discontinuous framed structures. In ...
Finite elements are related to continuous elements by means of Simpson’s hypothesis (Sect. 2.8). If the non-essential coordinates (slaves) are eliminated by means of dynamic substructure methods, dynamic stiffnesses result. We shall extend the formulati
whereMis the global mass matrix,Cis the global damping matrix,K(t) is the global stiffness matrix,x(t) is the generalized coordinates of finite element nodes,e(t) refers to the LCMS vector.Fis the external force vector. Hence, the static balance equation of system can be written as ...
The finite element model of the shaft is shown in Figure1. The Timoshenko beam was used, with each shaft consisting of six elements and seven nodes. The motion equation is expressed as follows: mmsqq¨s+(Ωggs+ccs)qq˙s+kksqqs=0, ...
Williams., "Coupled bending-torsional dynamic stiffness matrix of an Axially loaded Timoshenko beam element", Journal of Solids Structures, Elsevier science publishers 31 (1994) 749-762Banerjee J R,Williams F W.Coupled bending-torsional dynamic stiffness matrix of an axially loaded Timoshenko beam ...
An exact dynamic stiffness matrix for a twisted Timoshenko beam is developed in this paper in order to investigate its free vibration characteristics. First the governing differential equations of motion and the associated natural boundary conditions of a twisted Timoshenko beam undergoing free natural vi...