Free vibration analysis of rotating beams with random properties

S. A. A. Hosseini,S. E. Khadem 국제구조공학회 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.20 No.3

Free vibration analysis of rotating beams with random properties

Hosseini, S.A.A.,Khadem, S.E. Techno-Press 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.20 No.3

In this paper, free vibration of rotating beam with random properties is studied. The cross-sectional area, elasticity modulus, moment of inertia, shear modulus and density are modeled as random fields and the rotational speed as a random variable. To study uncertainty, stochastic finite element method based on second order perturbation method is applied. To discretize random fields, the three methods of midpoint, interpolation and local average are applied and compared. The effects of rotational speed, setting angle, random property variances, discretization scheme, number of elements, correlation of random fields, correlation function form and correlation length on "Coefficient of Variation" (C.O.V.) of first mode eigenvalue are investigated completely. To determine the significant random properties on the variation of first mode eigenvalue the sensitivity analysis is performed. The results are studied for both Timoshenko and Bernoulli-Euler rotating beam. It is shown that the C.O.V. of first mode eigenvalue of Timoshenko and Bernoulli-Euler rotating beams are approximately identical. Also, compared to uncorrelated random fields, the correlated case has larger C.O.V. value. Another important result is, where correlation length is small, the convergence rate is lower and more number of elements are necessary for convergence of final response.

A multiple scales method solution for the free and forced nonlinear transverse vibrations of rectangular plates

Shooshtari, A.,Khadem, S.E. Techno-Press 2006 Structural Engineering and Mechanics, An Int'l Jou Vol.24 No.5

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

Nonlinear response of a resonant viscoelastic microbeam under an electrical actuation

Zamanian, M.,Khadem, S.E.,Mahmoodi, S.N. Techno-Press 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.35 No.4

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.

Nonlinear response of a resonant viscoelastic microbeam under an electrical actuation

M. Zamanian,S.E. Khadem,S.N. Mahmoodi 국제구조공학회 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.35 No.4

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.

An analytical study on the nonlinear vibration of a doublewalled carbon nanotube

Ali Hajnayeb,S.E. Khadem 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.54 No.5

In this paper, free vibrations of a clamped-clamped double-walled carbon nanotube (DWNT) under axial force is studied. By utilizing Euler–Bernoulli beam theory, each layer of DWNT is modeled as a beam. In this analysis, nonlinear form of interlayer van der Waals (vdW) forces and nonlinearities aroused from mid-plane stretching are also considered in the equations of motion. Further, direct application of multiple scales perturbation method is utilized to solve the obtained equations and to analyze free vibrations of the DWNT. Therefore, analytical expressions are found for vibrations of each layer. Linear and nonlinear natural frequencies of the system and vibration amplitude ratios of inner to outer layers are also obtained. Finally, the results are compared with the results obtained by Galerkin method.

Non-linear vibration and stability analysis of a partially supported conveyor belt by a distributed viscoelastic foundation

Ghayesh, M.H.,Khadem, S.E. Techno-Press 2007 Structural Engineering and Mechanics, An Int'l Jou Vol.27 No.1

The main source of transverse vibration of a conveyor belt is frictional contact between pulley and belt. Also, environmental characteristics such as natural dampers and springs affect natural frequencies, stability and bifurcation points of system. These phenomena can be modeled by a small velocity fluctuation about mean velocity. Also, viscoelastic foundation can be modeled as the dampers and springs with continuous characteristics. In this study, non-linear vibration of a conveyor belt supported partially by a distributed viscoelastic foundation is investigated. Perturbation method is applied to obtain a closed form analytic solutions. Finally, numerical simulations are presented to show stiffness, damping coefficient, foundation length, non-linearity and mean velocity effects on location of bifurcation points, natural frequencies and stability of solutions.

A review of recent applications of atmospheric pressure plasma jets for materials processing

Penkov, O. V.,Khadem, M.,Lim, W. S.,Kim, D. E. Springer Science + Business Media 2015 Journal of coatings technology and research Vol.12 No.2

Non-linear vibration and stability analysis of a partially supported conveyor belt by a distributed viscoelastic foundation

M. H. Ghayesh,S. E. Khadem 국제구조공학회 2007 Structural Engineering and Mechanics, An Int'l Jou Vol.27 No.1

The main source of transverse vibration of a conveyor belt is frictional contact between pulley and belt. Also, environmental characteristics such as natural dampers and springs affect natural frequencies, stability and bifurcation points of system. These phenomena can be modeled by a small velocity fluctuation about mean velocity. Also, viscoelastic foundation can be modeled as the dampers and springs with continuous characteristics. In this study, non-linear vibration of a conveyor belt supported partially by a distributed viscoelastic foundation is investigated. Perturbation method is applied to obtain a closed form analytic solutions. Finally, numerical simulations are presented to show stiffness, damping coefficient, foundation length, non-linearity and mean velocity effects on location of bifurcation points, natural frequencies and stability of solutions.

Highly wear-resistant and biocompatible carbon nanocomposite coatings for dental implants

Penkov, O.V.,Pukha, V.E.,Starikova, S.L.,Khadem, M.,Starikov, V.V.,Maleev, M.V.,Kim, D.E. IPC Science and Technology Press 2016 Biomaterials Vol.102 No.-

<P>Diamond-like carbon coatings are increasingly used as wear-protective coatings for dental implants, artificial joints, etc. Despite their advantages, they may have several weak points such as high internal stress, poor adhesive properties or high sensitivity to ambient conditions. These weak points could be overcome in the case of a new carbon nanocomposite coating (CNC) deposited by using a C-60 ion beam on a Co/Cr alloy. The structure of the coatings was investigated by Raman and XPS spectroscopy. The wear resistance was assessed by using a reciprocating tribotester under the loads up to 0.4 N in both dry and wet sliding conditions. Biocompatibility of the dental implants was tested in vivo on rabbits. Biocompatibility, bioactivity and mechanical durability of the CNC deposited on a Co/Cr alloy were investigated and compared with those of bulk Co/Cr and Ti alloys. The wear resistance of the CNC was found to be 250-650 fold higher compared to the Co/Cr and Ti alloys. Also, the CNC demonstrated much better biological properties with respect to formation of new tissues and absence of negative morphological parameters such as necrosis and demineralization. Development of the CNC is expected to aid in significant improvement of lifetime and quality of implants for dental applications. (C) 2016 Elsevier Ltd. All rights reserved.</P>