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, D. C ., NGUYEN , H. H ., RAPOSO , C. A ., and MARANHAO , C. H. M . On the solutions for an extensible beam equation with internal damping and source terms . Differ. Equ. Appl . 11 ( 2019 ), 367 – 377 . [16] SIMON , J . Compact sets in
Forrai L. Dynamic stability of internally damped multibearing rotors using finite elements, IFTOMM, Proc. 7th Int. Conf. on Rotordynamics , Wien, Austria, 2006, Paper-ID 63 on CD-ROM Lalanne M., Ferraris G. Rotordynamics
displacement form the characteristics of MR fluid. The studies done over the years on each model showed highlighted their limitation from not considering the hysteresis behavior of damper [ 8 ], [ 9 ], stiffness [ 10 ] and internal damping of MR damper (MR