Transversal waves in beams via the network simulation method

Abstract

In this paper the Network Simulation Method (NSM) is proposed as a tool for solving the transverse-motion of thin beams resulting from a bending action. The reliability and robustness of the proposed technique is demonstrated with two examples, in which a pinned–pinned beam and a clamped-mass load beam are, respectively, submitted to different flexural forces. The NSM is a numerical technique for the solution of linear and non-linear problems, which are defined by a mathematical model. Assuming that the electrical variables of voltage and current are equivalent, respectively, to the displacement and the spatial variation of the displacement, a network model for each volume element is designed such that electrical equations are formally equivalent to the spatial discretised equations of the mechanical model. The whole network model, including the devices associated with the boundary conditions, is solved by the numerical computer code PSPICE. The numerical results have been compared with those obtained by the mode-superposition method: the agreement between them is impressive. The temporal behaviour of each quantity involved in the problem is obtained without transform complications, since the whole study has been conducted in the time-domain, with the possibility of obtaining the corresponding spectral content at the end of calculation. The main contribution of the present paper, therefore, is to employ the NSM numerical method in order to arrive at solutions, in the time-domain, of dynamic mechanical problems. One must also emphasize that NSM has not previously been used by other authors to solve physical problems like the ones presented here.