simply supported beamWe investigate the spectrum of frequencies of a nonlocal simply supported Timoshenko beam. When the mass matrix term is nonsingular, we can find the amplitudes of free vibrations as solutions of a second﹐rder matrix differential equation. These solutions are given in terms of...
newconsistentstiffness,geometricstiffnessandmassmatrixfor;mulationsforTimo- shenkobeamelementwithacubicdisplacementfunction.Ithasincludedthefotaryinertia correctionforthemassmatrix.Theelementisassessedbystatic,dynamicandStability testproblems. K吖wordsTimoshenkobeam,finiteelement.formulations 责任编辑:一土 相关...
consistentstiffness,andmassmatrixformulationsforMTBelement.Ithasincluded the rotary inertiacorrectioncaused by thesheardeformationofthebeamforthe massmatrix.Anumerical examplepresentedbyN.G.Stephen is re—examined using bothTBTandMTB theory respectively
Furthermore, geometric stiffness matrix and mass matrix of the proposed element are calculated by writing governing equation on stability and beam free vibration. At last, accuracy and efficiency of proposed element are evaluated through numerical tests. These tests show high accuracy of the element ...
Vertical displacement and bending rotation of the beam were interpolated by Lagrange polynomials supported on the Gauss-Lobatto-Legendre (GLL) points. By using GLL integration rule, the mass matrix was diagonal and the dynamic responses can be obtained efficiently and accurately. The results were ...
In addition, no further physical subdivision of the beam is necessary to obtain higher accuracy, thereby simplifying the grid layout. Element mass and stiffness matrices are developed using several different types of interface restrained assumed modes. Finally, numerical examples are included, ...
First, based on the Timoshenko beam theory, a basic four-spring beam model is used with all the soil resistance components considered and simulated by a series of distributed and concentrated springs. From: Computers and Geotechnics, 2023
Iis the moment of inertia of the beam's rectangular cross section in theyz-plane, in m⁴. Here, assume you scale the model to represent a uniform mass distribution across the beam, where the mass per area equals 1 and the moment of inertia isI=bt3/12. ...
The beam matrix is taken as poly methyl methacrylate. The nanotubes have different layouts in the matrix (aligned and randomly oriented) and are also distributed through the beam thickness as one uniform and three different functionally graded distributions. A micromechanical model is applied to ...
The beam matrix is taken as poly methyl methacrylate. The nanotubes have different layouts in the matrix (aligned and randomly oriented) and are also distributed through the beam thickness as one uniform and three different functionally graded distributions. A micromechanical model is applied to ...