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Subject: search.filters.subject.Calculus of variations

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    Variational approach of Timoshenko beams with internal elastic restraints
    (2013) Raffo, Javier; Grossi, Ricardo
    An exact approach for free transverse vibrations of a Timoshenko beam with ends elastically restrained against rotation and translation and arbitrarily located internal restraints is presented. The calculus of variations is used to obtain the equations of motion, the boundary conditions and the transitions conditions which correspond to the described mechanical system. The derived differential equations are solved individually for each segment of the beam with the corresponding boundary and transitions conditions. The derived mathematical formulation generates as particular cases, and several mathematical models are used to simulate the presence of cracks. Some cases available in the literature and the presence of some errors are discussed. New results are presented for different end conditions and restraint conditions in the intermediate elastic constraints with their corresponding modal shapes.
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    A Study on Mode Shapes of Beams with Internal Hinges and Intermediate Elastic Restraints
    (ASOCIACIÓN ARGENTINA DE MECÁNICA COMPUTACIONAL AMCA, 2012-11) Raffo, Javier Leandro; Grossi, Ricardo
    Dynamic analysis of structural elements becomes an important design procedure. Anadequate understanding of the free vibration is crucial to the design and performance evaluation of a mechanical system. This work deals with the problem of free vibrations of uniform beams with elastically restrained ends and with internal hinges and intermediate translational restraints. The main objective of this work is to obtain the minimum stiffness of a elastic restraint that raises a natural frequency of a beam with an internal hinge, to its upper limit. The minimum stiffness is determined by using the derivative of the function which gives the natural frequencies, with respect tothe support position. Additionally, the effects on natural frequencies of the presence of two internal hinges are analyzed