Dynamic Flexibility Matrix Analysis of Frames

The dynamic flexibility matrix is developed for uniform members in bending including translation of joints. A force method approach for the dynamic response of continuous beams and frames with translation of joints is then developed following ideas originally indicated by Hohenemser and Prager. All of the equations necessary for the determination of natural frequencies and/or dynamic response are developed in matrix form and programmed for automatic computation on the IBM 709 digital computer. Application is made to the determination of the natural frequencies and the dynamic response of two frames: a three-member, one-bay, one-story rigid frame and a six-member, one-bay, two-story rigid frame. The numerical results are compared to results obtained by other methods. Up to six mode shapes and frequencies were obtained in these examples. The number of matrix manipulations in this method was found to exceed the number in the deformation method but the computer times were comparable. In certain cases this procedure could be advantageous.