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 ...
Chen, Y-H. (1987), "General Dynamic-Stiffness Matrix of a Timoshenko Beam for Transverse Vibrations," Earthquake Engineering and Structural Dynamics, Vol. 15, pp. 391-402.CHEN, Y-H. (1987). General dynamic-stiffness matrix of a Timoshenko beam for transverse vibrations. Earthquake Engineering...
A method for calculating the dynamic transfer and stiffness matrices for a straight Timoshenko shear beam is presented. The method is applicable to beams with arbitrarily shaped cross sections and places no restrictions on the orientation of the element coordinate system axes in the plane of the cro...
Analytical expressions for the coupled bending-torsional dynamic stiffness matrix terms of an axially loaded uniform Timoshenko beam element are derived in an exact sense by solving the governing differential equations of motion of the element. The symbolic computing package REDUCE has been used to gene...
IyticaIexpressionsofdynamicstiffnessmatrixofpIanebeamfortransversevibrationwithconsideringthesheardistortionandrotaryinertiaofmassarepresentedbydirectIysoIvingmotiondifferentiaIe uationsofauniformTimoshenkobeam.SecondIy,thefre uencycharacteristice uationissoIvedbythebisectionmethodandWittrick-WiIIiamsaIgorithm.FinaIIy,the...
Each layer of the beam is idealised by the Timoshenko beam theory and the combined system is reduced to a tenth-order system using symbolic computation. An exact dynamic stiffness matrix is then developed by relating amplitudes of harmonically varying loads to those of the responses. The resulting...
For various temperature loads (homogeneous, linear and non-linear), thermal stresses are converted to mechanical stresses and then the thermal rigidity matrix is combined with the stiffness matrix of the beam. After verification of the method, the novel findings of the interaction of the moving ...
In this work, we present a semi-analytical approach to predict the forced response of a multi-cracked Timoshenko beam traversed by a moving harmonic load with constant speed. The beam is fully or partially supported by the viscoelastic foundation, where the normal stiffness and shear modulus of ...
A finite thin circular beam element for out-of-plane vibration analysis of curved beams A finite thin circular beam element for the out-of-plane vibration analysis of curved beams is presented in this paper. Its stiffness matrix and mass matri... YK Bo,CB Kim,SG Song,... - 《Journal of...
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 ...