Non-classical boundary conditions and DQM for double-beams

The present paper deals with the free vibrations of parallel double-beams joined by a Winkler-type homogeneous elastic foundation. The numerical approach adopted for solving two partial differential equations system is the differential quadrature method (henceforth DQM). A first-rate description of this approach has been furnished by Bert et al. (1996) and Chen et al. [Chen, W., Stritz, A.G., Bert, C.W., 1997. A new approach to the differential quadrature method for fourth-order equations. Int. J. Numer. Meth. Eng. 40, 1941–1956]; a modified version of this method has been proposed by De Rosa and Franciosi (1998). In this paper the differential quadrature method is applied to finding free vibrations of beams system having to the ends translation and rotation elastic constraints. The free vibration frequencies for some classical and non-conventional cases are determined.