The dynamic stability of a rotating pre-twisted asymmetric cross-section Timoshenko beam subjected to lateral parametric excitation

A finite element model is presented to study the dynamic stability of a pre-twisted Timoshenko beam having asymmetric aerofoil cross-section subjected to lateral parametric excitation. Solutions referred to as combination resonance are investigated. The effects of shear deformation and rotary inertia are included in the analysis. The effects of coupling due to centre of flexure distance from the centroid and the shear coefficient on the stability are considered. The change in these effects due to pre-twist angle is investigated. It is concluded from the results that the pre-twist angle has an influence on the effects of coupling and the shear coefficient.     

Elastodynamic response of a crack perpendicular to the graded interfacial zone in bonded dissimilar materials under antiplane shear impact

A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of antiplane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.     

Effects of a one-way clutch on the nonlinear dynamic behavior of spur gear pairs under periodic excitation

Nonlinear behavior analysis was used to verify whether a one-way clutch is effective for reducing the torsional vibration of a paired spur gear system under periodic excitation. The dynamic responses were studied over a wide frequency range by speed sweeping to check the nonlinear behavior using numerical integration. The gear system with a one-way clutch showed typical nonlinear behavior. The oscillating component of the dynamic transmission error was reduced over the entire frequency range compared to a system without a one-way clutch. The one-way clutch also eliminated unsteady continuous jump phenomena over multiple solution bands, and prevented double-side contact, even with very small backlash. Installing a one-way clutch on both sides of the gear system was more effective at mitigating the negative effects of external periodic excitation and various parameter changes than a conventional gear system without a one-way clutch.     

On the dynamic performance of roller bearings operating under low rotational speeds with consideration of surface roughness

The dynamic behavior of radially-loaded roller bearings operating at high loads and low speeds with different surface roughness values is investigated. The simulations take into account different lubrication regimes (rigid solid–isoviscous, elastic solid–isoviscous, rigid solid–piezoviscous and elastic solid–piezoviscous) in the loaded and unloaded sections of the bearing. The simulation results provide a detailed understanding of the variation of the film thickness, wear rate and heat generation between the rollers and the raceways as the rollers travel in the orbital direction. Simulation results reveal that an increase in the radial load results in a proportional increase in the wear rate and an exponential increase in the heat generation, although it does not affect the film thickness noticeably.     

On the eigenfrequencies of cantilevered beams carrying a tip mass and spring-mass in-span

The present study is concerned with the derivation of the eigenfrequencies and their sensitivity of a cantilevered Bernoulli-Euler beam carrying a tip mass (primary system) to which a spring-mass (secondary system) is attached in-span. After establishing the exact frequency equation of the combined system, a Dunkerley-based approximate formula is given for the fundamental frequency. Using the normal mode method, a second approximate frequency equation is established which is then used for the derivation of a sensitivity formula for the eigenfrequencies. The frequency equations of some simpler systems are obtained from the general equation as special cases. These frequency equations are then numerically solved for various combinations of physical parameters. The comparison of the numerical results with those from exact frequency equations indicate clearly that the eigenfrequencies of the combined system described above can be accurately determined by the present method.