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1

Static analysis of functionally graded plate using nonlinear classical plate theory with von-Karman strains

Singh S. J., Harsha S. P.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 3

707--726

EN

The present study is based on the nonlinear bending analysis of an FGM plate with Von-Karman strain based on the non-linear classical plate theory (NLCPT) with in-plane displacement and moderate rotation. Non-linear bending analysis based on stresses and transverse deflections is then carried out for the plate for the complex solution obtained using an analytical method viz. Navier’s method. The equations of motion and boundary conditions are obtained using the Principle of Minimum Potential Energy (PMPE) method and material property is graded in thickness direction according to simple power-law distribution in terms of volume fractions of the constituents. The effect of the span-to-thickness ratio and FGM exponent on the maximum central deflection and stresses are studied. The results show that the response is transitional with respect to ceramic and metal and the complex solution predicts the real behavior of stresses and deflections in the functionally graded plate. The functionally graded plate is found to be more effective for moderately thick and thick plates, which is inferred by a complex nature of the solution. For FGM plates, the transverse deflection is in-between to that of metal and ceramic rich plates. The complex nature of the solution also gives information about the stress distribution in the thickness direction.

2

Nonlinear dynamic analysis of a rotor bearing system due to distributed defects using factorial design of experiments

Harsha S. P., Nataraj C.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 2

379-399

EN

This paper focuses on accurate performance prediction which is essential to the design of high performance rotor bearing system. It considers distributed defects such as internal radial clearance and surface waviness of the bearing components. In the analytical formulation the contacts between the rolling elements and the races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The governing differenlial equations of motion are obtained by using Lagrange's equations. In terms of the feature that the nonlinear bearing forces act on the system, a reduction method and corresponding integration technique is used to increase the numerical stability and decrease computer time for system analysis. Poincare maps are used to elucidate and to iIIustrate the diversity of the system behavior. For investigating the nonlinear behavior of a rotor bearing system, effects of distributed defects are considered simultaneously. lt is shown that the system dynamic behavior is sensitive to small variations of distributed defects.

3

Nonlinear dynamic dnalysis of high speed rolling element bearings due to cage run-out

Harsha S. P., Kankar P. K., Purohit R. K.

Computer Assisted Mechanics and Engineering Sciences

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2005

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Vol. 12, No. 1

31-48

EN

The paper presents an analytical model to investigate the nonlinear dynamic behavior of rotor bearing system due to cage run-out. Due to run-out of the cage, the rolling elements no longer stay equally spaced. The mathematical model takes into account the sources of nonlinearity such as Hertzian contact force and cage run-out, resulting transition from no contact-to-contact state between rolling elements and races. The contact between the rolling elements and races is treated as nonlinear springs. The nonlinear stiffness is obtained by application of Hertzian contact deformation theory. The implicit type numerical integration technique Newmark-j3 with Newton Raphson method is used to solve the nonlinear differential equations iteratively. The results are presented in the form of Fast Fourier Transformations (FFT) and contact force-time responses. It is implied from the obtained FFT that due to the cage run-out, the ball passage frequency is modulated with the cage frequency.

4

Nonlinear dynamic behaviors of high speed rotor supported by rolling element bearings

Harsha S. P., Prakash R., Sandeep K.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 4

705-720

EN

The paper presents a model for investigating structural vibrations in rolling element bearings. The mathematical formulation accounted for tangential motions of rolling elements as well as inner and outer races with the sources of nonlinearity such as the Hertzian contact force, surface waviness and internal radial clearance transition resulting from no contact to contact state between rolling elements and the races. The contacts between the rollers and races are treated as nonlinear springs and the springs act only in compression to simulate the contact deformation and resulting force. The nonlinear stiffness is obtained by using the equations for the Hertzian elastic contact deformation theory. As the nonlinear bearing forces act on the system, a new reduction method and corresponding integration technique is proposed to increase the numerical stability and decrease computer time for system analysis. The effects of various defects of a rotor bearing system in which the rolling element bearings show the periodic, quasi-periodic and chaotic behavior are analyzed. Poincare maps and Fourier spectra are used to elucidate and to illustrate the diversity of the system behavior. It is shown that due to defects such as surface waviness and internal radial clearance the system exhibits an undesirable jump phenomenon with quasi-periodic, subharmonic and chaotic motions.