Experimental and numerical investigations on wave propagation in planar frames and trusses with shear deformable elements: Introduction of a fast numerical method using degrees of freedom just at joints

In this paper, the formulation of time weighted residual method has been extended to study wave propagation in planar frames and trusses with shear deformable elements. Timoshenko beam theory (TBT) was used to take into account the shear deformations. The salient feature of the method is that, although propagation of waves along the elements, with distributed mass, is fully taken into account, it uses the degrees of freedom (DOFs) defined just at joints of the structures, making the whole analysis simple and efficient compared with finite element method (FEM). To demonstrate the accuracy and efficiency of the proposed method, two experimental setups (i.e., portal frame under moving mass and hammer impact load) were designed and fabricated to measure the frame displacements. The experimental results are presented for the first time in this paper. The digitized results from the experiments and those found from the proposed numerical method, and also those from the FEM, are presented and compared to demonstrate the capabilities of the method. We shall show that, while the FEM needs numerous DOFs to generate acceptable results, the presented method uses just one element for each structural member and still it is capable of generating very accurate results. It may be expected that the Euler-Bernoulli beam theory (EBT) could be suitable for slender beams since the transverse shear strains in this theory remain null. However, we shall show that this is true for relatively low frequencies for which the height of the structural member is significantly less than the wavelength. To demonstrate this, further numerical examples are presented to discuss the suitability of the two theories and also to show the efficacy of the proposed method compared to the FEM. The numerical results show that the proposed method is accurate and efficient in terms of computational cost.