LINEARIZATION OF NONAUTONOMOUS MODELS DESCRIBING FLUID-FILLED ELASTICTUBES 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, i n the theoretical framework of group analysis, we transform to autonom ous form the systems describing fluid filled elastic tubes and nonline ar elastic rods with variable cross-section area. Thus, by means of a hodograph-like transformation or a combination of Backlund-like transf ormations, we reduce the autonomous models in point to linear form. To accomplish such a plan we characterize several model constitutive law s which can be used to approximate in suitable ranges of the concerned variables material laws based on experimental evidence.