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Abstract The control and dynamic stability analysis of roll oscillation of the strongly nonlinear semisubmersible system are not widely investigated in the frequency domain. In particular, the suppression of undesirable nonlinear responses like period doubling route to chaos, subharmonic oscillation etc. of such a system under harmonic excitation has not been attempted so far. The nonlinear semisubmersible system is characterized by a fairly strong quintic nonlinearity arising out of the restoring action. In the present study, the incremental harmonic balance method along with arc-length continuation technique (IHBC) is employed to identify the primary and higher order subharmonic responses of the system. Stability of the responses is checked by the Floquet's theory. A reformulation of the IHBC is then presented to control the responses of the semisubmersible system with quintic nonlinearity under state feedback control with time delay. The stability of the controlled responses is examined by applying the semi-discretization method for delay differential equation. It is shown that by considering appropriate feedback gains and time delay, (i) appreciable reduction of the amplitudes of primary responses, (ii) exclusion of all higher order subharmonics 2T, 3T, 4T, 8T, and (iii) the reduction of the extent of domain of various types of instability phenomena like, bifurcation of solutions, jump phenomena, chaotic responses etc. are possible. Further, it is found that the negative velocity feedback gain is much more effective than the full state feedback gains or varying the time delay parameter for better control of the roll oscillation of the system. Highlights • Studied roll oscillation of nonlinear semisubmersible under state feedback control with time-delay. • Employed IHB method with continuation technique. • Applied Floquet theory and semi discretization technique for the stability of periodic motions. • Investigated the effects of control parameters on the suppression of responses. • Validated results with numerical integration. [ABSTRACT FROM AUTHOR]

We investigate the nonlinear responses of graphene-matrix composite to harmonic and subharmonic resonances. Assuming anisotropic mechanical properties of graphene, we derive size-dependent governing equations of motion for graphene resting on a matrix based on the von Karman hypotheses and nonlocal elasticity theory. Response of graphene oscillation under a uniform pressure is obtained using the averaging method. We study the effects of length scale as well as the presence of the elastic matrix on harmonic and subharmonic oscillations of graphene. Our results reveal that subharmonic oscillation of order 1/3 can occur when the ratio of excitation to natural frequencies exceeds three. Also, the subharmonic oscillation of the system is triggered in an appropriate initial condition. [ABSTRACT FROM AUTHOR]

Highlights: [•] The dynamics and stability of DC–DC converters fed from voltage source is wellknown. [•] We have investigated the nonlinear phenomena of a boost converter fed from PV panel. [•] Four different types of controllers (e.g., peak current mode) have been used. [•] For all the cases the range of stability in the parameter space have been obtained. [•] The results have been validated through experimental observation. [ABSTRACT FROM AUTHOR]

Abstract: The present paper describes an improved version of the elliptic averaging method that provides a highly accurate periodic solution of a non-linear system based on the single-degree-of-freedom Duffing oscillator with a snap-through spring. In the proposed method, the sum of the Jacobian elliptic delta and zeta functions is used as the generating solution of the averaging method. The proposed method can be used to obtain the non-odd-order solution, which includes both even- and odd-order harmonic components. The stability analysis for the approximate solution obtained by the present method is also discussed. The stability of the solution is determined from the characteristic multiplier based on Floquet’s theorem. The proposed method is applied to a fundamental oscillator in a non-linear system. The numerical results demonstrate that the proposed method is very effective for analyzing the periodic solution of half-swing mode for systems based on Duffing oscillators with a snap-through spring. [ABSTRACT FROM AUTHOR]

[Display omitted] • The buoyant DME and LPG jet diffusion flames are studied for Re = 250–2000. • Fuel jet interacts with outer vortices at subharmonic frequencies. • The vortex merging leads to alternating flame bulge upstream of the tube exit. • DMD captures the spatial characteristics of the flame vortex dynamics. An experimental study is conducted on the buoyant jet diffusion flames to explore the interaction between the fuel jet and the outer vortex and their impact on the flame structure. Dimethyl ether (DME) and liquefied petroleum gas (LPG) diffusion flames are investigated. A laminar diffusion burner setup is used to study the flame dynamics of three different tube diameters (6, 8, and 10 mm) over a wide range of Reynolds numbers (250–2000). Flame flicker frequencies are analyzed using chemiluminescence signals and image processing techniques, and high-speed Schlieren images visualized flame dynamics and structure. The spatiotemporal structure of jet diffusion flames is analyzed using the dynamic mode decomposition (DMD) tool. Analysis of the Schlieren images revealed that the outer vortex structure interacts with the fuel jet, which eventually leads to convective feeding to the outer vortical structure. The outcome is the radial expansion of the leading vortex, which allows the trailing vortex to merge and produce a subharmonic frequency. However, all test conditions, regardless of the presence of subharmonic frequency in the buoyant diffusion flame, follow the established relationship between Strouhal-Froude numbers. The dominant mode of DMD captured the spatial features of the outer vortex at associated temporal frequencies. The large-scale coherent structure is observed in the region of subharmonic oscillation due to the merging of successive vortices. This process occurs at the alternate flame bulge formed near the tube exit. [ABSTRACT FROM AUTHOR]

In a current-mode switching DC-DC converter, the amount of deliverable energy to the load depends on the inductor current limit for the safety of the power components and the slope compensation current which is determined by the slope of the inductor current and the switching duty cycle. However, excess or insufficient slope compensation current may reduce the available load current or cause subharmonic oscillations, respectively. This paper presents an input-to-output conversion ratio sensing circuit which sets a proper slope-compensation (SC) current to avoid both excess slope compensation current and subharmonic oscillations. Both the slope and the duty-cycle of the proposed slope-compensation current are automatically adjusted based on the sensed input-to-output conversion ratio. As a result, the maximum available output current and the main-loop bandwidth of the converter are improved by the proposed structure. The compensation current is generated based on a fast (<0.5 μ s settling time) sensing circuit to track the input voltage or the load current changes. The proposed slope-compensation circuit was integrated into a boost topology with 0.038 mm2 extra silicon area and 190 μ A current consumption. [ABSTRACT FROM AUTHOR]