On a hybrid analytical–experimental technique to assess the storage modulus of resilient materials using symbolic computation

This paper presents details of symbolic computation used to develop hybrid analytical–experimental methods. These methods are considered rigorous since they are based on the exact analytical solution and not in an approximate discrete approach solution. This is illustrated through a simple example of solid mechanics, involving a boundary value problem with hyperbolic differential equation and Neumann boundary condition from the classical theory of longitudinal vibration of rods, in which the authors recur to symbolic computation (as revealed to be essential) to obtain a novel analytical expression and its solution. Then, by comparing the analytical and experimental responses, the unknown material parameters of the specimen are assessed through an inverse problem. The main idea may be used in different types of experiments. Here, a simple application from the longitudinal vibration of an elastic bar is presented for illustration purposes. It consists of a simple technique that has been developed by the authors to assess the storage modulus of resilient materials, as for e.g. composition cork-like materials. Compared to alternative procedures that use a numerical finite element method, the proposed method is much simpler; and while compared to the discrete two degrees-of-freedom model currently used in many laboratories it shows better accuracy.