On the flexural vibration of cylinders under axial loads:Numerical and experimental study

The flexural vibration of a homogeneous isotropic linearly elastic cylinder of any aspect ratio is analysed in this paper. Natural frequencies of a cylinder under uniformly distributed axial loads acting on its bases are calculated numerically by the Ritz method with terms of power series in the coordinate directions as approximating functions. The effect of axial loads on the flexural vibration cannot be described by applying infinitesimal strain theory, therefore, geometrically nonlinear strain–displacement relations with second-order terms are considered here. The natural frequencies of free–free, clamped–clamped, and sliding–sliding cylinders subjected to axial loads are calculated using the proposed three-dimensional Ritz approach and are compared with those obtained with the finite element method and the Bernoulli–Euler theory. Different experiments with cylinders axially compressed by a hydraulic press are carried out and the experimental results for the lowest flexural frequency are compared with the numerical results. An approach based on the Ritz formulation is proposed for the flexural vibration of a cylinder between the platens of the press with constraints varying with the intensity of the compression. The results show that for low compressions the cylinder behaves similarly to a sliding–sliding cylinder, whereas for high compressions the cylinder vibrates as a clamped–clamped one.

Measurements and Prediction of Pedestrian Walking Loads on an Aluminium Catwalk

During the last two decades the topic of human induced vibration has attracted a lot of attention among civil engineering practitioners and academics alike. Usually this type of problem may be encountered in pedestrian footbridges or floors of paperless offices. Slender designs are becoming increasingly popular, and as a consequence, the importance of paying attention to vibration serviceability also increases. This paper resumes the results obtained from measurements taken at different points of an aluminium catwalk which is 6 m in length by 0.6 m in width. Measurements were carried out when subjecting the structure to different actions:1)Static test: a steel cylinder of 35 kg was placed in the middle of the catwalk; 2)Dynamic test: this test consists of exciting the structure with singles impulses; 3)Dynamic test: people walking on the catwalk. Identification of the mechanical properties of the structure is an achievement of the paper. Indirect methods were used to estimate properties including the support stiffness, the beam bending stiffness, the mass of the structure (using Rayleigh method and iterative matrix method), the natural frequency (using the time domain and frequency domain analysis) and the damping ratio (by calculating the logarithmic decrement). Experimental results and numerical predictions for the response of an aluminium catwalk subjected to walking loads have been compared. The damping of this light weight structure depends on the amplitude of vibration which complicates the tuning of a structural model. In the light of the results obtained it seems that the used walking load model is not appropriate as the predicted transient vibration values (TTVs) are much higher than the measured ones.