Static and dynamic analysis of multi-cracked beams with local and non-local elasticity

The thesis presents a novel computational method for analysing the static and dynamic behaviour of a multi-damaged beam using local and non-local elasticity theories. Most of the lumped damage beam models proposed to date are based on slender beam theory in classical (local) elasticity and are limited by inaccuracies caused by the implicit assumption of the Euler-Bernoulli beam model and by the spring model itself, which simplifies the real beam behaviour around the crack. In addition, size effects and material heterogeneity cannot be taken into account using the classical elasticity theory due to the absence of any microstructural parameter. The proposed work is based on the inhomogeneous Euler-Bernoulli beam theory in which a Dirac's delta function is added to the bending flexibility at the position of each crack: that is, the severer the damage, the larger is the resulting impulsive term. The crack is assumed to be always open, resulting in a linear system (i.e. nonlinear phenomena associated with breathing cracks are not considered). In order to provide an accurate representation of the structure's behaviour, a new multi-cracked beam element including shear effects and rotatory inertia is developed using the flexibility approach for the concentrated damage. The resulting stiffness matrix and load vector terms are evaluated by the unit-displacement method, employing the closed-form solutions for the multi-cracked beam problem. The same deformed shapes are used to derive the consistent mass matrix, also including the rotatory inertia terms. The two-node multi-damaged beam model has been validated through comparison of the results of static and dynamic analyses for two numerical examples against those provided by a commercial finite element code. The proposed model is shown to improve the computational efficiency as well as the accuracy, thanks to the inclusion of both shear deformations and rotatory inertia. The inaccuracy of the spring model, where for example for a rotational spring a finite jump appears on the rotations' profile, has been tackled by the enrichment of the elastic constitutive law with higher order stress and strain gradients. In particular, a new phenomenological approach based upon a convenient form of non-local elasticity beam theory has been presented. This hybrid non-local beam model is able to take into account the distortion on the stress/strain field around the crack as well as to include the microstructure of the material, without introducing any additional crack related parameters. The Laplace's transform method applied to the differential equation of the problem allowed deriving the static closed-form solution for the multi-cracked Euler-Bernoulli beams with hybrid non-local elasticity. The dynamic analysis has been performed using a new computational meshless method, where the equation of motions are discretised by a Galerkin-type approximation, with convenient shape functions able to ensure the same grade of approximation as the beam element for the classical elasticity. The importance of the inclusion of microstructural parameters is addressed and their effects are quantified also in comparison with those obtained using the classical elasticity theory

Free Flexural Vibration of Multiple Stepped Beams by Spectral Element Method

The free vibration analyses of multiple-stepped Bernoulli-Euler beam with various boundary conditions have been studied by many researchers using different methods of analysis such as Differential Quadrature Element Method (DQEM), Composite Element Method (CEM), Admonian Decomposition Method (ADM), Differential Quadrature Method (DQM), Local adaptive Differential Quadrature Method (LaDQM), Discrete Singular Convolution (DSC) algorithm etc., besides the conventional analytical methods and finite element methods. In this work the Spectral Element Method (SEM) for analysis of stepped-beams has been used. The second part of the work is concerned with the free flexural vibration of multiple-stepped Timoshenko beam with various boundary conditions using the Spectral Element Method (SEM). Accurate computation of even the higher modes of vibration frequencies with consideration of least number of degrees of freedom is possible using SEM thus promising very high computational efficiency. Validation of this method is performed with various numerical solutions. A comparison between application of both Euler-Bernoulli and Timoshenko beam theory to the same beam is carried out and various important physical parameters are also investigate

Vibration Analysis of a Fan/Compressor Blade

The vibration of blades in gas turbine engines has become an important issue during the last decade because of its significant impact on high cycle fatigue failure due to resonant vibrations. The main objective of this thesis is the vibration analysis of compressor/fan blade using three-dimensional finite element analysis together with various analytical approaches. First, the analytical solutions were established using various analytical methods, Bernoulli-Euler, Rayleigh, Rayleigh-Ritz, two-dimensional plate, and Timoshenko beam methods. Then, the vibration behaviors of the blade are analyzed in full extent using commercially available finite element solver, MSC.NASTRAN, and correlated with the analytical solutions. The finite element analysis was performed in three different models, straight plate, tapered solid, and blade models. Finally, the recommendations are made for more accurate finite element modeling and analysis procedures

Free vibration of a cracked double-beam carrying a concentrated mass

This paper presents the free vibration of a cracked double-beam carrying a concentrated mass located at an arbitrary position. The double-beam consisting of two different simply supported beams connected by an elastic medium is modelled by using finite element method. The influence of the concentrated mass on the frequencies and mode shapes is investigated. The relationship between the natural frequency and the location of concentrated mass is established and related to the mode shapes. The numerical simulations show that when there is a crack, the frequency of the double-beam changes sharply when the concentrated mass is located close to the crack position. This sharp change can be amplified by wavelet transform and this is useful for crack detection. The crack location can be determined by the location of peaks in the wavelet transform of the relationship between frequency and mass location

Harmonic Response of the Offshore Crane Boom Structure

Pedestal crane is one of the offshore oil and gas production facilities. It is used as a lifting machine to transfer offshore personnel, load equipments, tools and food stuff from the supply boat to the fixed platform or vice versa. The pedestal crane components basically consist of the operator cabin which is mounted on a pedestal, the crane boom structure and the lifting block. In the crane operation, the hoisting speed for picking up or lowering down the payload provides sustained cyclic or dynamic loads to the crane system. The purpose of this project is to study the dynamic characteristic of the offshore crane boom structure due to excitation by the payload

Free vibrations of simply-supported beam bridges under moving loads: Maximum resonance, cancellation and resonant vertical acceleration

The advent of high-speed railways has raised many concerns regarding the behaviour of bridges. Particularly, the analysis of the free vibrations generated by each load is of great interest because they can possibly accumulate and create resonance phenomena. Regarding simply supported beams, earlier contributions showed that the free vibrations created by a single moving force are of maximum or zero amplitude (cancellation) for certain speeds. In the present paper new closed-form expressions are given for the cancellation speeds of a generic mode, as well as for the most representative points of maximum amplitude. Similar new results are provided for elastically supported beams as well. A simpler, closed-form approximate expression of the cancellation condition for an elastically supported beam is also derived from the analysis of a single passing load; this approximate formula is in good agreement with the exact results. Knowing a priori the speeds of maximum free vibrations or cancellation is of great interest for experimental tests on bridges, particularly as regards the evaluation of amplitude-dependent magnitudes such as structural damping. Regarding the resonance phenomena, if the resonance speeds coincide with either a maximum free vibration or a cancellation speed, then a maximum resonance or a cancellation of resonance will occur. The most relevant cases thereof have been investigated, and new expressions which allow predicting them for a generic mode are given. Finally, a new approximate formula is proposed for estimating the maximum acceleration of simply supported bridges caused by resonances of the fundamental mode. After extensive numerical testing, the formula has proved to be a useful tool for a first assessment of simply supported bridges according to building codes such as Eurocodes. (C) 2012 Elsevier Ltd. All rights reserved.The authors acknowledge the financial support of the State Secretariat for Research of the Spanish Ministry of Science and Innovation (Secretaria de Estado de Investigacion, Ministerio de Ciencia e Innovacion, MICINN) in the framework of the Research Project BIA2008-04111.Museros Romero, P.; Moliner, E.; Martinez-Rodrigo, M. (2013). Free vibrations of simply-supported beam bridges under moving loads: Maximum resonance, cancellation and resonant vertical acceleration. Journal of Sound and Vibration. 332(2):326-345. https://doi.org/10.1016/j.jsv.2012.08.008326345332

Dynamic Behavior of Sandwich Beams With Internal Resonators

Dynamic behavior of sandwich beams with internal resonators was investigated. The effect of inserting spring-mass resonators into the sandwich core was theoretically analyzed and it was shown that a wave attenuation bandgap exists due to local resonance. Steady state experiments were used to demonstrate such an attenuation bandgap. Frequency response functions were obtained for a beam with resonators and without resonators. It was shown that insertion of resonators into the core causes a wave attenuation bandgap to open up. The experimental results were verified using finite element simulations. Further experiments were carried out by tuning the resonators at 12 Hz and it was demonstrated that a wave attenuation bandgap can be created at low frequencies which would help attenuate low frequency periodic loads such as those associated with hull slamming. The antiresonance phenomenon was experimentally demonstrated. By inserting local resonators tuned at the first flexural resonance frequency of the beam, it was shown that the excessive vibrations associated with resonance modes can be attenuated by inserting local resonators tuned at the global beam resonance frequency. The behavior of such sandwich beams under impact loads was also considered. Using finite element simulations, the effect of a chosen local resonance frequency on attenuating impact loads was analyzed. The behavior of a chosen internal resonator under different impact loads was also considered. By performing transverse impact experiments, the finite element models were verified and the advantage of using internal resonators in impact loading conditions was demonstrated. The effect of resonator periodicity was analyzed using a phased array method. The propagation constant for a sandwich beam with internal resonators was obtained by treating the resonators as an array of phase shifted forces. It was shown that the resonator periodicity causes Bragg gaps in addition to the local resonance gaps. The effect of resonator parameters on these bandgaps was analyzed and the relationship between the bounding frequencies and the unit cell mode shapes was obtained. The interaction between the local resonance bandgap and the periodicity induced bandgaps was studied. It was shown that a wider combined gap, with a very narrow passband in between, can be obtained by tuning the local resonators at the Bragg gap cut-on frequency