A new simplified method for anti-symmetric mode in-plane vibrations of frame structures with column cracks

This paper is on the natural frequency and mode shape computation of frame structures with column cracks. First, a model of intact frame structures is built to perform vibration analysis. Beam elements are considered as lumped masses and rotational springs at the storey levels of frames. Equivalent model of columns and lumped mass-stiffness effects of beams have been combined to carry out continuous solution for the anti-symmetric mode in-plane vibrations of frames. In addition, frame systems with multiple column cracks are analyzed in terms of anti-symmetric mode vibration characteristics. Cracks are considered as massless rotational springs in compliance with the local flexibility model. Compatibility and continuity conditions are satisfied at crack and storey locations of the equivalent column, modeled using the Euler–Bernoulli beam theory. The proposed method is tested for single-storey single- and multi-bay, H-type and double-storey single-bay frame systems with intact and cracked columns. Results are validated by those given in the current literature and/or obtained by the finite element analyses. © The Author(s) 2016

An optimization study for viscous dampers between adjacent buildings

This paper investigates optimum viscous damper capacity and number for prevention of one-sided structural pounding between two adjacent buildings under earthquake motion. The buildings assumed as shear-type structures are modeled by using lumped mass-stiffness technique. Impact forces due to pounding is simulated by nonlinear elastic spring approximation called Hertz model. A parametric study is conducted by varying storey number and stiffness of buildings in addition to the capacity of the viscous dampers. Pounding force and supplemental damping ratio for each case are presented based upon newly defined nondimensional natural frequency parameter ratio. An optimization procedure for determination of viscous damper capacity is developed based on modified supplemental damping ratio equation. Results are compared with each other to clarify the effect of variation in building parameters on pounding forces and viscous damper capacity. © 2016 Elsevier Lt

A novel methodology using simplified approaches for identification of cracks in beams

In this paper, natural frequency based forward and inverse methods are proposed for identifying multiple cracks in beams. Forward methods include simplified definition of the natural frequency drops caused by the cracks. The ratios between natural frequencies obtained from multi-cracked and un-cracked beams are determined by an approach that uses the local flexibility model of cracks. This approach does not consider nonlinear crack effects that can be easily neglected when the number of cracks is not excessive. In addition, an expression, which removes the necessity of repeating natural frequency analyses, is given for identifying the connection between the crack depths and natural frequency drops. These simplified approaches play crucial role in solving inverse problem using constituted crack detection methodology. Solution needs a number of measured modal frequency knowledge two times more than the number of cracks to be detected. Efficiencies of the methods are verified using the natural frequency ratios obtained by the finite element package. The crack detection methodology is also validated using some experimental natural frequency ratios given in current literature. Results show that the locations and depths ratios of cracks are successfully predicted by using the methods presented. © 2015, Brazilian Association of Computational Mechanics. All rights reserved

Natural frequency analyses of segmented Timoshenko-Euler beams using the Rayleigh-Ritz method

This paper proposes part by part usage of Timoshenko and Euler-Bernoulli beam theories for obtaining natural frequencies of the non-uniform beam that has partially thick and thin beam vibration characteristics. The paper also presents convergence tests to determine proper function among the simple admissible shape functions taken into consideration. By doing so, closer approximation of the Rayleigh-Ritz method is achieved. The method is applied using a simple computation technique. In the analyses of the Timoshenko beams, an additional function is employed to identify shear deformation and rotational inertia effects. Modified angular displacement functions are defined to improve convergence capability of the method. Furthermore, optimal numbers of lateral and angular displacement terms are investigated for suggested function couple of the Timoshenko beams. Efficiencies of part by part modelling and advantages of novel approaches suggested for the Rayleigh-Ritz approximation are introduced by the comparative studies performed on tapered, stepped and continuously segmented beams under some classical end conditions. All of the computational outcomes for the beams with rectangular cross-section are validated by the results given in current literature and also those obtained by the finite element analyses. © The Author(s) 2015

Vibration analysis of non-uniform beams having multiple edge cracks along the beam's height

Bending vibration of non-uniform rectangular beams with multiple edge cracks along the beam's height is investigated. These cracks are called height-edge cracks in this paper. The energy based method is used for defining the vibration of height-edge cracked beams. The opening form of the height-edge crack is determined when the external moment is assumed to be applied for stretching the beam's width. Strain energy increase is obtained by calculating the strain change at the stretched surface by taking into account the effect of angular displacement of the beam due to the bending. The Rayleigh-Ritz approximation method is used in the analysis. The cases of multiple cracks are analysed in the method by using the approach based on the definition of strain disturbance variation along the beam. Examples are presented on a fixed-fixed beam and several cantilever beams having different taper factors. When the results are compared with the results of a commercial finite element program, good agreement is obtained. The effects of taper factors, boundaries and positions of cracks on the natural frequency ratios are presented in graphics. (C) 2009 Elsevier Ltd. All rights reserved

A frequency based algorithm for identification of single and double cracked beams via a statistical approach used in experiment

An algorithm for detecting cracks on the beams and a statistical process for minimising the measurement errors in experiments are presented in this paper. Natural frequencies are determined by using the theoretical model for different depths and locations of single crack. The ratios of cracked and un-cracked beam's natural frequencies constitute the prediction tables scaled in two axes as crack location and crack depth. Frequency contour lines corresponding to measured natural frequency ratios are matched with the interpolated prediction table, called frequency map, and are used for detection of a single crack. However, contour lines do not give any information about the existence of two cracks. The algorithm presented in this paper makes it possible to locate the suitable positions of two cracks searched over the frequency map. The algorithm is tested in the examples employing the frequency map prepared by the theory presented and the input frequency ratios obtained by the commercial finite element program. The algorithm is also verified by using the natural frequencies of cracked and un-cracked cantilever beams employed in several experiments. In measurement, determination of accurate natural frequency ratios is crucial for the success of crack detection. Therefore, this paper also presents a statistical approach called 'recursively scaled zoomed frequencies (RSZF)' for minimising the deviations caused by sensitivity and resolution lack in measured natural frequencies. In this approach, the measured frequencies in spectrum are modified by the mean value of the natural frequencies determined in different frequency scales. Zoomed frequencies are obtained by the cubic spline interpolation method that increases the resolution of frequency spectrum. RSZF comes into further prominence especially when the cracks are needed to be detected by very small sized data. All of the experimental results represent that single crack and double cracks are successfully detected by using the methods presented. © 2012 Elsevier Ltd

Flap-wise and chord-wise vibrations of axially functionally graded tapered beams rotating around a hub

This paper presents flap-wise and chord-wise flexural vibration analyses for centrifugally stiffened tapered beams made of functionally graded material in axial direction. Functions of material properties varying along beam are defined in terms of the power law distribution. Calculations are conducted by simple computation technique of the Rayleigh–Ritz method that uses simple shape functions and energy expressions written for centrifugally stiffened Euler–Bernoulli beams. Effects of taper ratio, hub radius, angular velocity and non-homogeneity are inspected for the thin beams with several classical boundary conditions. Results given as non-dimensional natural frequencies are validated by the results given in existing literature and/or the outputs of finite element analyses performed for axially functionally graded solid beam. Achievements and limitations of the method are discussed and clearly reflected. © 2016 Elsevier Ltd215M756The research topic in this work is supported by “The Scientific and Technological Research Council of Turkey (TUBITAK)” within the framework of national project as “1002 - Short Term R&D Funding Program” (Project no: 215M756 )

Flexural vibration of non-uniform beams having double-edge breathing cracks

Flexural vibration of non-uniform Rayleigh beams having single-edge and double-edge cracks is presented in this paper. Asymmetric double-edge cracks are formed as thin transverse slots with different depths at the same location of opposite surfaces. The cracks are modelled as breathing since the bending of the beam makes the cracks open and close in accordance with the direction of external moments. The presented crack model is used for single-edge cracks and double-edge cracks having different depth combinations. The energy method is used in the vibration analysis of the cracked beams. The consumed energy caused by the cracks opening and closing is obtained along the beam's length together with the contribution of tensile and compressive stress fields that come into existence during the bending. The total energy is evaluated for the Rayleigh-Ritz approximation method in analysing the vibration of the beam. Examples are presented on simply supported beams having uniform width and cantilever beams which are tapered. Good agreements are obtained when the results from the present method are compared with the results of Chondros et al. and the results of the commercial finite element program, Ansys. The effects of breathing in addition to crack depth's asymmetry and crack positions on the natural frequency ratios are presented in graphics. (C) 2010 Elsevier Ltd. All rights reserved