A Simplified Quadrature Element Method to compute the natural frequencies of multispan beams and frame structures

In this paper a new version of the Modified Quadrature Element Method (MQEM) is proposed. Like MQEM, the proposed method overcomes the drawback of the distance δ of the Quadrature Element Method (QEM) without introducing further degrees of freedom at the ends of the element as in the Differential Quadrature Element Method (DQEM), but it makes the computational cost of the stiffness matrix (and the mass matrix) lighter and uses a general procedure to generate the sampling points distribution. The method here presented has been applied to compute the fundamental frequencies of some structures.

► Only one grid point to represent the end point without additional degrees of freedom. ► Stiffness (and mass) matrix computed in a simple way by means of weighting coefficients. ► Grid points generated by means of Gegenbauer polynomials. ► Boundary and slope compatibility conditions handled as multifreedom constraints to give a reduced equations system. ► Good computational cost savings and accuracy, even compared with traditional FEM.