Energy analysis of multiple-cracked Euler-Bernoulli beam

This paper presents energy analysis of multiple-cracked beams. The study deals with crack energy reduction functions for consuming strain energy due to crack growth and the degree of conformity between these functions and experimental results. Three different reduction functions are employed in this research work. A comprehensive analysis is performed providing a comparison of the functions for a beam with one and two cracks. In order to elucidate advantages and disadvantages of each function, we employ them in different crack detection problems. For different cases of crack localization and quantification in a crack detection problem, the best function that fits the experimental results more accurately is highlighted

Spectrally formulated finite element for vibration analysis of an Euler-Bernoulli beam on Pasternak foundation

In this article, vibration analysis of an Euler-Bernoulli beam resting on a Pasternak-type foundation is studied. The governing equation is solved by using a spectral finite element model (SFEM). The solution involves calculating wave and time responses of the beam. The Fast Fourier Transform function is used for temporal discretization of the governing partial differential equation into a set of ordinary differential equations. Then, the interpolating function for an element is derived from the exact solution of governing differential equation in the frequency domain. Inverse Fourier Transform is performed to rebuild the solution in the time domain. The foremost advantages of the SFEM are enormous high accuracy, smallness of the problem size and the degrees of freedom, low computational cost and high efficiency to deal with dynamic problems and digitized data. Moreover, it is very easy to execute the inverse problems by using this method. The influences of foundation stiffness, shear layer stiffness and axial tensile (or compressive) forces on the dynamic characteristic and divergence instability of the beam are investigated. The accuracy of the present SFEM is validated by comparing its results with those of classical finite element method (FEM). The results show the ascendency of SFEM with respect to FEM in reducing elements and computational effort, concurrently increasing the numerical accuracy

A finite element model for extension and shear modes of piezo-laminated beams based on von Karman's nonlinear displacement-strain relation

Piezoelectric actuators and sensors have been broadly used for design of smart structures over the last two decades. Different theoretical assumptions have been considered in order to model these structures by the researchers. In this paper, an enhanced piezolaminated sandwich beam finite element model is presented. The facing layers follow the Euler-Bernoulli assumption while the core layers are modeled with the third-order shear deformation theory (TSDT). To refine the model, the displacement-strain relationships are developed by using von Karman's nonlinear displacement-strain relation. It will be shown that this assumption generates some additional terms on the electric fields and also introduces some electromechanical potential and non-conservative work terms for the extension piezoelectric sub-layers. A variational formulation of the problem is presented. In order to develop an electromechanically coupled finite element model of the extension/shear piezolaminated beam, the electric DoFs as well as the mechanical DoFs are considered. For computing the natural frequencies, the governing equation is linearized around a static equilibrium position. Comparing natural frequencies, the effect of nonlinear terms is studied for some example

Damage Identification in Collocated Structural Systems Using Structural Markov Parameters

This paper presents a novel approach to damage identification in a class of collocated multi-input multi-output structural systems. In the proposed approach, damage is identified via the structural Markov parameters obtained from a system identification procedure, which is in turn exploited to localize and quantify damage by evaluating relative changes occurring in the mass and stiffness matrices associated with the structural system. To this aim, an explicit relationship between structural Markov parameters versus mass and stiffness matrices is developed. The main strengths of the proposed approach are that it is capable of quantitatively identifying the occurrence of multiple damages associated with both mass and stiffness characteristics in the structural system, and it is computationally efficient in that it is solely based on the structural Markov parameters but does not necessitate costly calculations related to natural frequencies and mode shapes, making it highly attractive for structural damage detection and health monitoring applications. Numerical examples are provided to demonstrate the validity and effectiveness of the proposed approach