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Published Articles

The Volume 19, No 1, March 2014

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Three Dimensional Vibration Analysis of Rectangular Plates with Undamaged and Damaged Boundaries by the Spectral Collocation Method

Ma'en S. Sari and Eric A. Butcher.


The objective of this paper is the development of a new numerical technique for the free vibration analysis of isotropic three dimensional elastic plates with damaged boundaries. In this study it is assumed that the plates have free lateral surfaces and two opposite simply supported edges, while the other edges could be clamped, simply supported or free. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies of three dimensional plates with damaged clamped boundary conditions, where the governing equations and boundary conditions are discretized by the presented method and put into matrix vector form. The damaged boundaries are represented by distributed translational springs. In the present study the boundary conditions are coupled with the governing equation to obtain the eigenvalue problem. Convergence studies are carried out to determine the sufficient number of grid points used. First, the results obtained for the undamaged plates are verified with previous results in the literature. Subsequently, the results obtained for the damaged three dimensional plates indicate the behavior of the natural vibration frequencies with respect to the severity of the damaged boundary. This analysis can lead to an efficient technique for damage detection of structures in which joint or boundary damage plays a significant role in the dynamic characteristics. The results obtained from the Chebyshev collocation solutions are seen to be in excellent agreement with those presented in the literature.

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A Parameterized Model of Bolted Joints in Machine Tools

Hongqi Liu; Bin Li; Kuanmin Mao; Xiaolei Huang; Fangyu Peng


A new dynamic model for bolted joints in heavy machine structures is proposed. The influence of the bolt pre-tightening force, the interface dimensions and the surface roughness on joint dynamics (i.e. the stiffness matrix of finite element) were analysed. Each stiffness coefficient in the matrix can be expressed by an exponential function of preload, and a quadratic polynomial function of geometric dimensions. Sixteen specimens were thoroughly designed and analysed. Then, the resulting stiffness matrices were saved as templates, based on which could establish dynamic models of joints with different influence factor values, using curve-fitting and Response Surface Methodology (RSM). The methodology was validated by experiments with a specimen of the new design and a heavy-duty cutting machine.

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Analysis of the Collapse of Long-Span Reticulated Shell Structures Under Multi-Dimensional Seismic Excitations

Ming-Fei Yang, Zhao-Dong Xu, Xing-Huai Huang and Han-Hu Ye


The collapse processes of three typical long-span reticulated shell structures were simulated using nonlinear dynamic finite element analysis under strong seismic excitations. The plastic kinematic hardening model, which considers failure stain, was adopted for simulating steel. Both geometric and contact nonlinearities were considered in this study. The three failure states- i.e., dynamic local bucking, dynamic overall buckling, and whole collapse- were identified in accordance with the analysis results. Taking the Schwedler reticulated shell structure as an example, seismic waves were applied to the structure in three directions. The critical loads were obtained by the incremental dynamic analysis method (IDAM), and some critical state indices were obtained according to the dynamic responses. The results showed that all the critical indices need to be considered simultaneously in order to judge the dynamic collapse states.

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Free Vibration Analysis of Rotating Functionally-Graded Cantilever Beams

M. N. V. Ramesh and N. Mohan Rao


The increasing needs of the industry involved in development of components for aerospace and power sector demand the engineering community to develop new concepts and strategies to improve the functional requirements of structures and to enhance the strength of materials. This is particularly essential in the cases of rotating beams that are subjected to severe vibration under large pressure loadings, high rotating accelerations, centrifugal forces, geometric stiffening, etc. A theoretical investigation of the free vibration characteristics of rotating cantilever beams, made of a functionally-graded material (FGM) consisting of metal and alumina, is presented in this study. It was assumed that the material properties of the FGM beam were symmetric, but varied continuously in the thickness direction from the core at the mid section to the outer surfaces, according to a power-law relation. Equations of motion were derived from a modelling method, which employed the hybrid deformation variable. The natural frequencies were determined using the Rayleigh-Ritz method. The effect of parameters such as the power law index, the hub radius, and the rotational speed on the natural frequencies of functionally-graded rotating cantilever beams were examined through numerical studies and then compared with the numerical results reported in earlier works.

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Analysis and Optimisation of Wind-Induced Vibration Control for High-Rise Chimney Structures

Zhao-Dong Xu, Jun-Tao Zhu, Deng-Xiang Wang


Wind is a key factor when determining the safety of high-rise structures, such as buildings, chimneys, or towers. Using dampers to control wind-induced vibration is a safe, effective, and economical method for high-rise structures to employ. In this paper, viscoelastic dampers (VEDs) were used to reduce the dynamic responses of a 75-metre-high chimney. First, a simulation method for the stochastic wind field, based on the modified Fourier spectrum, was proposed. The method provided the accurate data of the wind velocity time history, which then simulated wind pressure through the use of a numerical wind tunnel. Then, the finite element model for the Madagascar chimney structure was built, and a wind-induced vibration analysis of the structure with and without VEDs was carried out under the simulated wind excitation. The optimisation -- method, based on the genetic algorithm, was used to optimise the location of the VEDs. It was concluded that the accuracy of the modified Fourier spectrum method (MFSM) was greatly improved, when compared to the spectrum representation method of simulating the stochastic wind field. VEDs can effectively reduce the dynamic responses of chimney towers, especially for the displacement responses. In addition, the proposed optimisation method quickly determined the optimum positions and necessary quantities of VEDs to use, which yielded effective vibration mitigation.

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The Use and Validation of Measured, Theoretical, and Approximate Point-Load Solutions for the Prediction of Train\cbox{-}Induced Vibration in Homogeneous and Inhomogeneous Soils

Lutz Auersch


The layered soil is calculated in the frequency wavenumber domain and the solutions for fixed or moving point or track loads follow as wavenumber integrals. The resulting point load solutions can be approximated by simple formula. Measurements yield the specific soil parameters for the theoretical or approximate solutions, but they can also directly provide the point-load solution (the transfer function of that site). A prediction method for the train-induced ground vibration has been developed, based on one of these site-specific transfer functions. The ground vibrations strongly depend on the regular and irregular inhomogeneity of the soil. The regular layering of the soil yields a cut-on and a resonance phenomenon, while the irregular inhomogeneity seems to be important for high-speed trains. The attenuations with the distance of the ground vibration, due to point-like excitations such as vibrator, hammer, or train-track excitations, were investigated and compared. All theoretical results were compared with measurements at conventional and high-speed railway lines, validating the approximate prediction method.

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