Effect of Mesh Size and Mode Truncation on Reconstruction of Force Characteristics for Non Punctual Impacts on Composite Elastic Beams

Abstract

dentifying characteristics of a force generated by non punctual impact is performed to better monitor the health of the impacted structure. This can be achieved through using an implemented structural model. For composite beams, the model can be constructed by means of the finite element method. In this work, the impact is assumed to be a uniform distributed pressure and the impact location is known. Reconstructing the force signal is performed by using regularized deconvolution techniques of the Toeplitz like equation giving the answer in terms of strains as function of the input force. Here, the generalized singular value decomposition based method is used in conjunction with truncation filtering. Quality of the reconstructed force is discussed as function of the mesh size and the mode truncation order.

Identification based on a finite element model of an impact force occurring on a composite structure

“…To solve the discrete problem given by Eq. (2.1) results in the following set of algebraic equation [7,20]…”

“…Chinkaa et al [6] used the modal analysis to assess and detect damage to a cantilever beam structure, identifying crack damage using Frequency Based Damage Detection Techniques (FBDDT). El-Bakari et al [7] investigated the identification of a cantilever beam structure's impact force. They presented the deconvolution system problem and used modal analysis and General Singular Value Decomposition to reconstruct the force characteristics (GSVD).…”

Structural deformation reconstruction by the Penrose–Moore pseudo-inverse and singular value decomposition–estimated equivalent force

“…22 Since the load estimation is a typical ill-posed problem, Hasanov and Baysal 23 used SVD to analyze the under-determining degrees of freedom (DOFs) for a cantilever beam to estimate the load distribution. SVD can also process the matrix operators during input estimation such as the Markov state transition matrix 24,25 and the impulse response matrix. 26…”

“…22 Since the load estimation is a typical ill-posed problem, Hasanov and Baysal 23 used SVD to analyze the under-determining degrees of freedom (DOFs) for a cantilever beam to estimate the load distribution. SVD can also process the matrix operators during input estimation such as the Markov state transition matrix 24,25 and the impulse response matrix. 26 In this article, a method is proposed to solve the underdetermined equation using the SVD and Penrose-Moore pseudo-inverse, which explains and emphasizes the physical and mathematical meaning behind the SVD and Penrose-Moore pseudo-inverse.…”