This contribution investigated repeated elastoplastic pure plane bending/unbending process of beams made of material with an elastic-linear hardening rheological model. The attention is focused on beams with cross sections which have at least one axis of symmetry and are initially straigh orhave constant radius of curvature. Elastoplastic deflection states of beams after repeated bending/unbending process are determined using the large displacement theory. Experiments were conducted to verify the theory for beamsmade of aluminium alloy AA 5050-H38 with rectangular cross sections. It is shown that maximal relative difference between experimental and theoreticalresults in the case of a largely curved beams after repeated bending/unbending process is 1.27%.
COBISS.SI-ID: 11376667
Approximative formulas for post-buckling analysis of non-linearly elastic columns made of Ludwick material are developed for free-clamp, hinge-hinge, and clamp-clamp supports. The columns have a superellipsoidal cross-section. Comparison between analytically obtained and numerical solutions showed good agreement. Additionally, post-buckling configurations for all three types of columns and materials are given in diagrams, from where the influence of material constants on the shape of the deflection curve can be examined.
COBISS.SI-ID: 11694363
In the past decade damping-identification methods based on the continuous wavelet transform (CWT) have been shown to be some of the best methods for analyzing the damping of multi-degree-of-freedom systems. The CWT methods have proven themselves to be resistant to noise and able to identify damping at closely spaced natural frequencies. However, with the CWT-based techniques, the CWT needs to be obtained on a two-dimensional, time-frequency grid, and they are, therefore, computationally demanding. Furthermore, the CWT is susceptible to the edge effect, which causes a non-valid identification at the start and the end of the time-series. This study introduces a new method, called the Morlet-wave method, where a finite integral similar to the CWT is used for the identification of the viscous damping. Instead of obtaining the CWT on a two-dimensional grid, the finite integral needs to be calculated at one time-frequency point, only. Then using two different integration parameters, the damping ratio can be identified. A complete mathematical background of the new, Morlet-wave, damping-identification method is given and this results in a root-finding or a closed-form solution. The presented numerical experiments show that the new method has a similar performance to the CWT-based damping-identification methods, while the method is numerically, significantly less demanding, completely avoids the edge effect, and the procedure is straight forward to use.
COBISS.SI-ID: 11720731