TIME DOMAIN MODELING AND SIMULATION OF NONLINEAR SLENDER VISCOELASTIC BEAMS ASSOCIATING COSSERAT THEORY AND A FRACTIONAL DERIVATIVE MODEL

Abstract

A BROAD CLASS OF ENGINEERING SYSTEMS CAN BE SATISFACTORY MODELED UNDER THE ASSUMPTIONS OF SMALL DEFORMATIONS AND LINEAR MATERIAL PROPERTIES. HOWEVER, MANY MECHANICAL SYSTEMS USED IN MODERN APPLICATIONS, LIKE STRUCTURAL ELEMENTS TYPICAL OF AEROSPACE AND PETROLEUM INDUSTRIES, HAVE BEEN CHARACTERIZED BY INCREASED SLEN-DERNESS AND HIGH STATIC AND DYNAMIC LOADS. IN SUCH SITUATIONS, IT BECOMES INDISPENSABLE TO CONSIDER THE NONLINEAR GEOMETRIC EFFECTS AND/OR MATERIAL NONLINEAR BEHAVIOR. AT THE SAME TIME, IN MANY CASES INVOLVING DYNAMIC LOADS, THERE COMES THE NEED FOR ATTENUA-TION OF VIBRATION LEVELS. IN THIS CONTEXT, THIS PAPER DESCRIBES THE DEVELOPMENT AND VALIDATION OF NUMERICAL MODELS OF VISCOELASTIC SLENDER BEAM-LIKE STRUCTURES UNDERGOING LARGE DISPLACEMENTS. THE NUMERICAL APPROACH IS BASED ON THE COMBINATION OF THE NONLINEAR COSSERAT BEAM THEORY AND A VISCOELASTIC MODEL BASED ON FRACTION-AL DERIVATIVES. SUCH COMBINATION ENABLES TO DERIVE NONLINEAR EQUA-TIONS OF MOTION THAT, UPON FINITE ELEMENT DISCRETIZATION, CAN BE USED FOR PREDICTING THE DYNAMIC BEHAVIOR OF THE STRUCTURE IN THE TIME DOMAIN, ACCOUNTING FOR GEOMETRIC NONLINEARITY AND VISCOELAS-TIC DAMPING. THE MODELING METHODOLOGY IS ILLUSTRATED AND VALIDAT-ED BY NUMERICAL SIMULATIONS, THE RESULTS OF WHICH ARE COMPARED TO OTHERS AVAILABLE IN THE LITERATURE.