LINEARIZATION OF NONAUTONOMOUS MODELS DESCRIBING FLUID-FILLED ELASTIC TUBES AND NONLINEAR ELASTIC RODS WITH VARIABLE CROSS-SECTION

The problem of reducing nonautonomous and nonlinear models of physical interest to canonical integrable forms is considered herein. First, in the theoretical framework of group analysis, we transform to autonomous form the systems describing fluid filled elastic tubes and nonlinear elastic rods with variable cross-section area. Thus, by means of a hodograph-like transformation or a combination of Backlund-like transformations, we reduce the autonomous models in point to linear form. To accomplish such a plan we characterize several model constitutive laws which can be used to approximate in suitable ranges of the concerned variables material laws based on experimental evidence.