Analytical frequency-domain solution for Euler-Bernoulli frames with semi-rigid connections

This paper presents a novel method for analyzing the dynamic response of plane Euler-Bernoulli frames with semi-rigid connections subjected to arbitrary external loads and bending moments. The proposed solution methodology is the Green’s Functions Stiffness Method (GFSM) in the frequency domain. The GFSM is a mesh reduction method closely related with the Finite Element Method (FEM) sharing with it key components such as shape functions, fixed end forces, and stiffness matrices. By capitalizing on the strengths of both FEM and Green’s Functions, the GFSM facilitates the derivation of closed-form solutions for structural analysis. The formulation is initially established in the frequency domain and is later transformed into the time domain using the fast Fourier transform algorithm. To illustrate the applicability of the method, an example involving a one-bay, one-storey plane frame with semi-rigid connections is presented.