Instability Attenuation And Bifurcation Studies of A Non-Ideal Rotor Involving Time Delayed Feedback

In non-ideal vibratory system, the excitation is a nonlinear function of system response. The dynamic behavior of such system is often characterized by an energy source with limited power. The study of instability phenomena in non-ideal rotor driven through a non-ideal energy source is of considerable current interest. The non-ideal rotor system often gets destabilized on exceeding a critical input power near the resonance. This kind of instability is termed as Sommerfeld effect marked with nonlinear jump phenomena. This paper investigates the attenuation of nonlinear jump phenomena and numerical study of bifurcations of a non-ideal unbalanced rotor system with internal damping using time delayed feedback via active magnetic bearings. The results show that the time delay indeed plays a critical role on the suppression of the jump phenomena. Following, some new insights are also revealed through a numerical study of saddle node, Hopf and trans-critical bifurcations with time delay as a bifurcation parameter. The transient analysis confirms the results obtained analytically through the steady-state consideration.

Modelling and Simulation of Nonlinear Jump Phenomena of a Non-ideal Rotor Involving Fractional Order PD Controller

Rotating machinery with high speed powered by industrial motors frequently suffers from instability by exhibiting non-linear jump phenomena, formally known as Sommerfeld effect. The drives whose excitation is a function of the system responses, referred to as non-ideal. The system dynamics of such systems exhibit a couple of complex and interesting features when the input power exceeds a critical value. The present research suggests a novel approach to study the efficacy of active magnetic bearing with fractional PD controller to suppress the instability caused by the Sommerfeld effect. The steady-state results obtained by solving the system characteristic equation numerically is compared with the transient analysis. Finally, root locus method is introduced to obtain the bifurcation points at which this kind of instability completely disappears.

Algebraic aspects of hypergeometric differential equations

We review some classical and modern aspects of hypergeometric differential equations, including A-hypergeometric systems of Gel$$'$$ ′ fand, Graev, Kapranov and Zelevinsky. Some recent advances in this theory, such as Euler–Koszul homology, rank jump phenomena, irregularity questions and Hodge theoretic aspects are discussed with more details. We also give some applications of the theory of hypergeometric systems to toric mirror symmetry.

Parameter Identification of a Strongly Nonlinear Rotor-Bearing System Based on Reconstructed Constant Response Tests

A strongly nonlinear rotor-bearing system often has multiple solutions under harmonic excitations and jump phenomena. For example, a hardening nonlinearity may include a jump-down in the acceleration process and jump-up in the deceleration process. It is challenging to measure all of these multiple responses and establish an accurate dynamic model from experimental data to predict these phenomena. This paper used a fixed frequency test method to measure all of these multiple responses under harmonic excitations and developed a novel strategy to characterize and identify nonlinearities in a strongly nonlinear rotor-bearing system based on reconstructing constant response tests from fixed frequency test data. The fixed frequency tests are achieved by monotonically increasing the voltage applied to the exciter at a fixed frequency and using the force drop-out phenomenon through the resonance to control the force applied to the structure. This test method could measure multivalued response curves of a strongly nonlinear rotor-bearing system in a nonrotating state. The constant response tests could be reconstructed from these multivalued response curves. The relationship of equivalent stiffness versus displacement can be established, and hence, the nonlinear stiffness is characterized and identified from constant response tests. A rotor-bearing system with a strongly nonlinear support is used to demonstrate the method, and the nonlinear support stiffness parameters are identified and validated in a nonrotating state. The identified nonlinear rotor-bearing model also could predict the jump phenomena in the acceleration or deceleration process. The results demonstrate the feasibility and effectiveness of the approach, and also show the potential for practical applications in engineering.

Lidar Observations of Mountain Waves During Bora Episodes

Airflows over mountain barriers in the Alpine region may give rise to strong, gusty downslope winds, called Bora. Oscillations, caused by the flow over an orographic barrier, lead to formation of mountain waves. These waves can only rarely be observed visually and can, in general, not be reliably reproduced by numerical models. Using aerosols as tracers for airmass motion, mountain waves were experimentally observed during Bora outbreak in the Vipava valley, Slovenia, on 24-25 January 2019 by two lidar systems: a vertical scanning lidar positioned just below the peak of the lee side of the mountain range and a fixed direction lidar at valley floor, which were set up to retrieve two-dimensional structure of the airflow over the orographic barrier into the valley. Based on the lidar data, we determined the thickness of airmass layer exhibiting downslope motion, observed hydraulic jump phenomena that gave rise to mountain waves and characterized their properties.

Sommerfeld Effect and Passive Energy Reallocation in a Self-Synchronizing System

Two eccentric rotors are mounted rigidly on a common vibrating base structure. Each of these rotors are separately driven by two motors, which are by nature non-ideal. Although power input for both rotors are different, the two rotors acquire the same speed via communication through the energized vibrating base. The phenomena is known as ‘self-synchronization’. Additionally, the presence of two non-ideal drives within the vibrating system also lead to the onset of the nonlinear jump phenomena (formally known as the Sommerfeld effect). Numerical simulations are carried out on a model developed on MSC Adams. From the generated responses, an overview of ‘self-synchronization’ as well as the various modes of synchronization are studied adjacent to the nature of Sommerfeld effect inherent within this system. The aim is to reduce the structural vibrations, mainly by virtue of self-synchronization. Henceforth, the behavior of the synchronized system is also examined in the presence of two secondary vibration reducing devices — a tuned Dynamic Vibration Absorber (DVA) and a Nonlinear Energy Sink (NES). Both are designed to passively absorb the excess vibrating energy from the synchronized system, at the onset of resonance.

Nonlinear Vibrations of Buried Rectangular Plate

We perform an investigation on the vibration response of a simply supported plate buried in glass particles, focusing on the nonlinear dynamic behaviors of the plate. Various excitation strategies, including constant-amplitude variable-frequency sweep and constant-frequency variable-amplitude sweep are used during the testing process. We employ the analysis methods of power spectroscopy, phase diagramming, and Poincare mapping, which reveal many complicated nonlinear behaviors in the dynamic strain responses of an elastic plate in granular media, such as the jump phenomena, period-doubling bifurcation, and chaos. The results indicate that the added mass, damping, and stiffness effects of the granular medium on the plate are the source of the nonlinear dynamic behaviors in the oscillating plate. These nonlinear behaviors are related to the burial depth of the plate (the thickness of the granular layer above plate), force amplitude, and particle size. Smaller particles and a suitable burial depth cause more obvious jump and period-doubling bifurcation phenomena to occur. Jump phenomena show both soft and hard properties near various resonant frequencies. With an increase in the excitation frequency, the nonlinear added stiffness effect of the granular layer makes a transition from strong negative stiffness to weak positive stiffness.