Stability chart of parametric vibrating systems using energy-rate method

2004 ◽  
Vol 39 (8) ◽  
pp. 1319-1331 ◽  
Author(s):  
G.Nakhaie Jazar
Author(s):  
Reza N. Jazar ◽  
M. Mahinfalah ◽  
N. Mahmoudian ◽  
M. A. Rastgaar

2020 ◽  
Vol 14 (8) ◽  
pp. 969-976
Author(s):  
Ahmad Rivai ◽  
Nasrudin Abd Rahim ◽  
Mohamad Fathi Mohamad Elias ◽  
Jafferi Jamaludin

2019 ◽  
Vol 17 (1) ◽  
pp. 1449-1458
Author(s):  
Gao Zhixiang ◽  
Guo Hongyu ◽  
Dong Zhiwei ◽  
Luo Yuan ◽  
Xia Daping

AbstractIn order to analyze the feasibility of chemical softening on low rank coals, bituminous coal was collected from the Qianqiu mine in Henan Province, China, and soaked in water and alkaline solution for different lengths of time. The complete stress-strain and acoustic emission (AE) experiments on the coal samples under uniaxial compression were tested on the RMT-150B Rock Mechanics Testing System and DS2 series AE signal analyzer. The results showed that the coal samples soaked in the water and alkaline solution present different characteristics in the deformation and failure process. As we increase the soaking time, the uniaxial compressive strength and deformation degree of the soaked coal samples in the alkaline solution and water decreased by 42.7% and 94.8% respectively. In the loading test, an AE signal is generated in all coal samples and the maximum ringing count rate and AE energy rate are present near the stress maximum for a short time. Moreover, the ringing count rate and AE energy rate have a good consistency with the stress-strain of the coal samples. The cumulative ringing count of the two groups soaked in water and alkaline solution decreased by 51% and 89% compared to the original coal sample. However, the decreased degree of the samples soaked in the alkaline solution is much higher than that of those soaked in water and the results showed that the alkaline solution has a better softening effect on the coal sample. With the increase of the alkaline solution concentration, the contact angle decreased from 112.5° to 41°. Through microscope and scanning electron microscopy (SEM) analysis of the soaked coal samples, we found that the pores and fissures increased, the structure of coal became loose, and the mechanical strength decreased sharply after soaking in the alkaline solution, thus achieving a chemical softening effect.


1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.


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