STIFFNESS ANALYSIS AND OPTIMIZATION OF STEPPED COLUMNS UNDER COMBINED BENDING AND COMPRESSION

The paper presents the stiffness analysis and optimization of stepped columns constituting the core frame of the industrial building. The two-span cross section of a one- storey industrial building is investigated herein. The quasi-static calculation is performed using the limited load approximation method for the cross-section of the most loaded middle column. The critical Euler characteristic of the compressive longitudinal load is determined by the differential bending equations at the bifurcation instability in the column sections. The parameter optimization of the column cross-section is achieved through the nonlinear mathematical programming. The optimization of medium column cross-section is considered using the proposed calculation when setting a set of constraints for the optimization task.

Control of Period-Doubling and Chaos in Varying Compliance Resonances for a Ball Bearing

Varying compliance (VC) is an inevitable parametrical excitation to rolling bearing systems due to time-varying stiffness from rolling element revolution. Period-doubling instability in the VC primary resonances of ball bearing is presented in many studies. Recently, this instability was demonstrated to be a probable indicator of occurrence of strong one to two internal resonances and chaotic motions, which has potential effects on the stability and safety of the bearing-rotor system. However, few studies have directly attempted to suppress this bifurcation instability. Here, a dynamic stiffness evaluating method is presented for assessing the threshold of the period-doubling and complex motions in VC primary resonances of ball bearings, where the elaborate evolution of the bifurcating process is obtained by harmonic balance and alternating frequency/time domain (HB-AFT) method and using Floquet theory. Our analysis indicates that by introducing certain additional stiffness, the period-doubling and corresponding subharmonic internal resonances can be suppressed. Besides, the evolution and mechanism of type I intermittency chaos in ball bearings will be clarified in depth. It is also shown that extensive chaotic motions for large bearing clearances (e.g., 40 μm) can vanish perfectly by action of additional stiffness.

High-repetition-rate and high-power picosecond regenerative amplifier based on a single bulk Nd:GdVO4 crystal

We report on a high-repetition-rate, high-power continuously pumped Nd:GdVO4 regenerative amplifier. Numerical simulations successfully pinpoint the optimum working point free of bifurcation instability with simultaneous efficient energy extraction. At a repetition rate of 100 kHz, a maximum output power of 23 W was obtained with a pulse duration of 27 ps, corresponding to a pulse energy of $230~\unicode[STIX]{x03BC}\text{J}$ . The system displayed an outstanding stability with a root mean square power noise as low as 0.3%. The geometry of the optical resonator and the pumping scheme enhanced output power in the $\text{TEM}_{00}$ mode with a single bulk crystal. Accordingly, nearly diffraction-limited beam quality was produced with $M^{2}\approx 1.2$ at full pump power.

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

Network response to disturbances in large sand-bed braided rivers

The reach-scale effects of human-induced disturbances on the channel network in large braided rivers are a challenge to understand and to predict. In this study, we simulated different types of disturbances in a large braided river to get insight into the propagation of disturbances through a braided channel network. The results showed that the disturbances initiate an instability that propagates in the downstream direction by means of alteration of water and sediment division at bifurcations. These adjustments of the bifurcations change the migration and shape of bars, with a feedback to the upstream bifurcation and alteration of the approaching flow to the downstream bifurcation. This way, the morphological effect of a disturbance amplifies in the downstream direction. Thus, the interplay of bifurcation instability and asymmetrical reshaping of bars was found to be essential for propagation of the effects of a disturbance. The study also demonstrated that the large-scale bar statistics are hardly affected.

Network response to internal and external perturbations in large sand-bed braided rivers

The intrinsic instability of bars, bifurcations and branches in large braided rivers is a challenge to understand and predict. Even more, the reach-scale effect of human-induced perturbations on the braided channel network is still unresolved. In this study, we used a physics-based model to simulate the hydromorphodynamics in a large braided river and applied different types of perturbations. We analyzed the propagation of the perturbations through the braided channel network. The results showed that the perturbations initiate an instability that propagates in downstream direction by means of bifurcation instability. It alters and rotates the approaching flow of the bifurcations. The propagation celerity is in the same order of magnitude as the theoretical sand wave propagation rate. The adjustments of the bifurcations also change bar migration and reshape, with a feedback to the upstream bifurcation and alteration of the approaching flow to the downstream bifurcation. This way, the morphological effect of a perturbation amplifies in downstream direction. Thus, the interplay of bifurcation instability and asymmetrical reshaping of bars was found to be essential for propagation of the effects of a perturbation. The study also demonstrated that the large-scale bar statistics are hardly affected.