A numerical solution is presented to investigate the influence of the geometry and the amplitude of the transverse ridge on the characteristics of elastohydrodynamic lubrication for point contact problem under steady state condition. Several shapes of ridges with different amplitudes are used in the stationary case, such as flattop ridge, cosine wave ridge and sharp ridge of triangular shape. Results of film thickness and pressure distributions of the aforementioned ridge feature are presented at different locations through an elastohydrodynamically lubricated contact zone for different amplitude of the ridge. Simulations were performed using the Newton-Raphson iteration technique to solve the Reynolds equation. The numerical results reveal that, to predict optimum solution for lubricated contact problem with artificial surface roughness, the geometrical characteristics of the ridge should have profiles with smooth transitions such as those of a cosine wave shape with relatively low amplitude to reduce pressure spike and therefore cause the reduction in the film thickness. The position of the location of the ridge across the contact zone and the amplitude of the ridge play an important role in the formation of lubricant film thickness and therefore determine the pressure distribution through the contact zone.

For a deeper understanding of the inner ear dynamics, a Finite-Element model of the human cochlea is developed. To describe the unsteady, viscous creeping flow of the liquid, a pressure-displacement-based Finite-Element formulation is used. This allows one to efficiently compute the basilar membrane vibrations resulting from the fluid-structure interaction leading to hearing nerve stimulation. The results show the formation of a travelingwave on the basilar membrane propagating with decreasing velocity towards the peaking at a frequency dependent position. This tonotopic behavior allows the brain to distinguish between sounds of different frequencies. Additionally, not only the middle ear, but also the transfer behavior of the cochlea contributes to the frequency dependence of the auditory threshold. Furthermore, the fluid velocity and pressure fields show the effect of viscous damping forces and allow us to deeper understand the formation of the pressure difference, responsible to excite the basilar membrane.

In this paper, a comprehensive study is carried out on the dynamic behaviour of Euler–Bernoulli and Timoshenko beams resting on Winkler type variable elastic foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying along the length direction. The free vibration problem is formulated using Rayleigh-Ritz method and Hamilton’s principle is applied to generate the governing equations. The results are presented as non-dimensional natural frequencies for different material gradation models and different foundation stiffness variation models. Two distinct boundary conditions viz., clamped-clamped and simply supported-simply supported are considered in the analysis. The results are validated with existing literature and excellent agreement is observed between the results.

A compliant beam subjected to large deformation is governed by a multifaceted nonlinear differential equation. In the context of theoretical mechanics, solution for such equations plays an important role. Since it is hard to find closed-form solutions for this nonlinear problem and attempt at direct solution results in linearising the model. This paper investigates the aforementioned problem via the multi-step differential transformation method (MsDTM), which is well-known approximate analytical solutions. The nonlinear governing equation is established based on a large radius of curvature that gives rise to curvature-moment nonlinearity. Based on established boundary conditions, solutions are sort to address the free vibration and static response of the deforming flexible beam. The geometrically linear and nonlinear theory approaches are related. The efficacy of the MsDTM is verified by a couple of physically related parameters for this investigation. The findings demonstrate that this approach is highly efficient and easy to determine the solution of such problems. In new engineering subjects, it is forecast that MsDTM will find wide use.

The paper presents the methodology that makes it possible to evaluate computational model and introduce current corrections to it. The methodology ensures proper interpretation of nonlinear results of numerical analyses of thin-walled structures. The suggested methodology is based on carrying out, in parallel to nonlinear numerical analysis, experimental research on some selected crucial zones of loadcarrying structures. Attention is drawn to the determinants concerning the performance of an adequate experiment. The author points out on indicating the role of model tests as a fast and economically justified research instruments practicable when designing thin-walled load-carrying structures.

The presented considerations are illustrated by an example of a structure whose geometrical complexity and ranges of deformation are characteristic for modern solutions applied in the load-carrying structures of airframes. As the representative example, one selected the area of the load-carrying structure that contains an extensive cut-out, in which the highest levels and stress gradients occur in the conditions of torsion evoking the post-buckling states within the permissible loads. The stress distributions within these ranges of deformations were used as the basis for determining the fatigue life of the structure.

The paper presents experimental investigations of pressure fluctuations near the tip clearance region of the rotor blades of the axial-flow low-speed compressor stage in stable and unstable parts of the overall performance characteristic. In this investigation, unsteady pressure was measured with the use of high frequency pressure transducers mounted on the casing wall of rotor passage. The pressure signals and their frequency characteristics were analyzed during the steady-state processes, before the rotating stall, during the transition from the steady-state process to the rotating stall, and during a stabilized phenomenon of low-frequency rotating stall. As the operating point moves to the unstable region of flow characteristic, an inception of the rotating stall can be observed, which rotates with a speed of about 41.4% of the rotor speed. The results of this study confirm that in the low-speed axial compressor stage operating in a rotating stall regime there appears one stall cell that spreads over to adjacent rotor blade channels. As the flow rate is reduced further, the frequency of the rotating stall decreased to 34.8% of the rotor speed and the number of blade channels with the stall cell increases.

For riveted joints with eccentricities of the load path, bending moments referred to as secondary bending are induced under nominally tensile loading conditions. Two simple theoretical models proposed in the literature to estimate the associated bending stresses are evaluated in the paper. Both approaches have been implemented in computer programs and applied to estimate the effect of several variables on the calculated bending stresses in the lap joint. Possibilities of the experimental and numerical verification of the models are also considered. Finally, a correlation between the secondary bending computed by one of the simple models and the observed fatigue properties of riveted specimens, as reported in the literature, is investigated. It is shown that deviations of the experimental results from the theoretical expectations stem from additional to secondary bending factors, like the inhomogeneous load transmission through the joint and the residual stresses induced by riveting process. These phenomena are known to be relevant to the fatigue behaviour of riveted joints, but they are not accounted for by the simple models. A conclusion from the present study is that despite the limitations and approximations inherent in the simple models, they provide reliable estimates of nominal bending stresses at the critical rivet rows and can be utilized in currently used semi-empirical concepts for predictions on the fatigue life of riveted joints.