Effect of Mass Models in the Dynamic Analysis of Structures

Abstract

In this research the utilization of distributed, lumped, and consistent mass models in the dynamic analysis of structures is studied, and the results obtained by these models for example problems are compared. In distributed mass model, the dynamic stiffness matrix for a planar beam element is derived by integrating the differential equations of motion. In lumped mass model, the mass of the structure is lumped at the nodal points where translational displacements are defined. However, in the consistent mass model the mass characteristics corresponding to the nodal coordinates of beam element are evaluated by a procedure similar to the determination of the element stiffness coefficients. These mass models are executed for three numerical examples. Results of two examples are compared with analytical solutions. The last example analysis of planar frames with distributed mass model is calculated with using a developed computer program by using two comparison results of other examples. The Fourier series approach is used for the solution of dynamic equations. Numerical results have shown the effectiveness of the dynamic stiffness approach with the distributed mass model. The distributed mass model gives the exact values of the natural frequencies with the exception of numerical errors in computer calculations. This research is different from the other studies that demonstrate the application of the modeling and calculation of the natural frequency values’ accuracy regarding to choose mass model. It is also shows the method to deal with the external excitation.