Nonlinear cancellation of the parametric resonance in elastic beams: theory and experiment

A non-linear control strategy is applied to a simply supported uniform elastic beam subjected to an axial end force at the principal-parametric resonance frequency of the first skew-symmetric mode. The control input consists of the bending couples applied by two pairs of piezoceramic actuators attached onto both sides of the beam surfaces and symmetrically with respect to the midspan, driven by the same voltage, thus resulting into symmetric control forces. This control architecture has zero control authority, in a linear sense, onto skew-symmetric vibrations. The non-linear transfer of energy from symmetric motions to skew-symmetric modes, due to non-linear inertia and curvature effects, provides the key physical mechanism for channelling suitable control power from the actuators into the linearly uncontrollable mode. The reduced dynamics of the system, constructed with the method of multiple scales directly applied to the governing PDE’s and boundary conditions, suggest effective forms of the control law as a two-frequency input in sub-combination resonance with the parametrically driven mode. The performances of different control laws are investigated. The relative phase and frequency relationships are designed so as to render the control action the most effective. The control schemes generate non-linear controller forces which increase the threshold for the activation of the parametric resonance thus resulting into its annihilation. The theoretical predictions are compared with experimentally obtained results

Timing jitter characterization of the SFQ coincidence circuit by optically time-controlled signals from SSPDs

We report on the timing jitter characterization of the superconducting single flux quantum (SFQ) coincidence circuit, which is an essential component of the superconducting coincidence photon counter. Two superconducting nanowire single photon detectors (SSPDs), each of which is irradiated with optically time-controlled photons, are connected to the SFQ coincidence circuit, and the timing jitter of the SFQ circuit is evaluated by changing the relative time delay between two input ports for the SFQ comparator unit. We successfully observe the transition curve of the probability of obtaining the signal from the SFQ coincidence circuit by sweeping photon arrival time to each SSPD and confirm that this curve shifts temporally upon changing the bias current to the Josephson transmission line (JTL) in the SFQ circuit. A systematic investigation reveals that the relation between time delay and the bias current to JTL can be estimated. The full width half maximum timing jitter of the SFQ circuit is 1.1 ps, which is sufficiently low so that it does not influence the entire timing jitter of the coincidence photon counter

Barnyard grasses were processed with rice around 10000 years ago

Rice (Oryza sativa) is regarded as the only grass that was selected for cultivation and eventual domestication in the Yangtze basin of China. Although both macro-fossils and micro-fossils of rice have been recovered from the Early Neolithic site of Shangshan, dating to more than 10,000 years before present (BP), we report evidence of phytolith and starch microfossils taken from stone tools, both for grinding and cutting, and cultural layers, that indicating barnyard grass (Echinochloa spp.) was a major subsistence resource, alongside smaller quantities of acorn starches (Lithocarpus/Quercus sensu lato) and water chestnuts (Trapa). This evidence suggests that early managed wetland environments were initially harvested for multiple grain species including barnyard grasses as well as rice, and indicate that the emergence of rice as the favoured cultivated grass and ultimately the key domesticate of the Yangtze basin was a protracted process

Nonlinear dynamics of a spinning shaft with non-constant rotating speed

Research on spinning shafts is mostly restricted to cases of constant rotating speed without examining the dynamics during their spin-up or spin-down operation. In this article, initially the equations of motion for a spinning shaft with non-constant speed are derived, then the system is discretised, and finally a nonlinear dynamic analysis is performed using multiple scales perturbation method. The system in first-order approximation takes the form of two coupled sets of paired equations. The first pair describes the torsional and the rigid body rotation, whilst the second consists of the equations describing the two lateral bending motions. Notably, equations of the lateral bending motions of first-order approximation coincide with the system in case of constant rotating speed, and considering the amplitude modulation equations, as it is shown, there are detuning frequencies from the Campbell diagram. The nonlinear normal modes of the system have been determined analytically up to the second-order approximation. The comparison of the analytical solutions with direct numerical simulations shows good agreement up to the validity of the performed analysis. Finally, it is shown that the Campbell diagram in the case of spin-up or spin-down operation cannot describe the critical situations of the shaft. This work paves the way, for new safe operational ‘modes’ of rotating structures bypassing critical situations, and also it is essential to identify the validity of the tools for defining critical situations in rotating structures with non-constant rotating speeds, which can be applied not only in spinning shafts but in all rotating structures

Ricerca sul tema Tecniche di controllo nonlineare per la stabilizzazione di moti e di stati di equilibrio instabili.

La ricerca sviluppata durante la suddetta visita e durante le visite del Prof. W. Lacarbonara in Giappone ha condotto alle seguenti pubblicazioni. 1) W. Lacarbonara, H. Yabuno (2006) Refined models of elastic beams undergoing large in-plane motions: theory and experiment, International Journal of Solids and Structures 43:5066-5084. 2) W. Lacarbonara, H. Yabuno, K. Hayashi (2007) Nonlinear cancellation of the parametric resonance in elastic beams: theory and experiment, International Journal of Solids and Structures 44:2209-2224. 3) In-Soo Son, Y. Uchiyama, H. Yabuno, W. Lacarbonara (2008) Simply supported elastic beams under parametric excitation, Nonlinear Dynamics 53:129-138

Ricerca sul tema dei modi normali nonlineari di travi rettlinee e curve.

Durante la visita sono state sviluppate le linee teoriche generali di una ricerca sui modi normali nonlineari di travi rettlinee e curve. Si sono messi a punto gli aspetti teorici della modellazione ed i dettagli delle indagini sperimentali correlate. Il Prof. Yabuno ha tenuto attività seminariali tra cui due seminari sui seguenti temi: “Motion Control of an Under-Actuated Manipulator without Feedback Control” e “Stabilization Control Method for Nonlinear Phenomena by Pendulum-Type Vibration Absorbers"

Non-linear control of parametrically excited beams via non-collocated multi-frequency input

A non-linear control strategy is applied to a simply supported uniform beam subjected to an axial end force at the principal-parametric resonance frequency of the first skew-symmetric mode. The control input consists of the bending couples applied by two piezoceramic actuators attached onto the beam surface symmetrically with respect to the midspan and are driven by the same voltage thus generating symmetric control forces. This control architecture has zero control authority, in a linear sense, onto skew-symmetric vibrations. The non-linear transfer of energy from symmetric to skew-symmetric modes, due to non-linear inertia and curvature forces, provides the key physical mechanism for delivering effects from the actuators to the linearly uncontrollable mode. The reduced dynamics of the system, constructed with the method of multiple scales directly applied to the governing PDE's and boundary conditions, suggest effective forms of the control law as a two-frequency input. In particular, the performances of different control laws in sub-combination resonance with the excited mode are investigated. The relative phase and frequency detunings, with respect to the external excitation, are designed so as to render the control action the most effective. The control schemes generate controller forces which increase the threshold for the activation of the parametric resonance thus annihilating the parametric resonance

A theoretical and experimental investigation of nonlinear resonance-cancellation strategies

The proposed research has focused theoretically and experimentally on devising nonlinear strategies to control resonant vibrations in distributed-parameter systems. The specific objective was to design intelligent strategies to control systems when linear theories cannot be applied and recourse to appropriate nonlinear techniques is unavoidable. Emphasis was placed on closed-loop control techniques because these techniques are more robust and are model-independent. The main research objectives can be summarized as follows. (i) Modeling and Analysis Use of reliable and accurate models of shallow arches and shells were made to develop, via nonlinear normal mode approach, first, intuition as to the proper feedback control laws for each system and, then, to construct the steady-state dynamics of the controlled and uncontrolled system. Subsequently, the range of effectiveness for each control law was determined. (ii) Experimental Implementation and Investigation The effectiveness of the nonlinear control strategies numerically and analitically validated were also investigated experimentally. The research objectives have been implemented via a combination of analytical, numerical, and experimental techniques. Namely, (i) application of higher-order direct perturbation techniques (i.e., the method of multiple scales) directly to the governing integral-partial-differential equations of motion and associated boundary conditions (also known as nonlinear normal mode approach); (ii) use of the normal form of the system dynamics for the relevant external/internal resonance conditions as a basis for the design of the control laws; (iii) systematic bifurcation analysis, via path-following techniques, of the modulation equations governing the dominant dynamics of the system (with controls and without controls) and subsequent determination of stable operating regimes for the controlled systems; (iv) use of discretized multiple-degree-of-freedom versions of the systems as set of ordinary-differential equations obtained via Galerkin or rectified Galerkin methods to further corroborate the outcomes of the approximate direct analytical results; (v) design and implementation of an experimental apparatus to validate experimentally the designed nonlinear control strategies

Closed-loop non-linear control of an initially imperfect beam with non-collocated input

A closed-loop non-linear control strategy to reduce the flexural vibrations of a hinged-hinged initially imperfect beam is investigated. The beam is subjected to a harmonic transverse excitation involved in a primary resonance of the first antisymmetric mode. A closed-loop symmetric control action-bending moments imparted by two piezoceramic actuators-although non-collocated, is designed to be non-orthogonal, in a non-linear sense, to the excited mode and be capable of exerting resonant beneficial damping effects onto it. The approximate responses of the controlled and uncontrolled beam are constructed by applying the method of multiple scales directly to the integral-partial differential equations of motion and boundary conditions. The frequency response curve governing the primary resonance of the uncontrolled system is compared with that obtained when the controller is in action. It is shown that, by exerting feasible control efforts, the response of the beam may be reduced by an order of magnitude and is stable in the overall frequency range in contrast with the uncontrolled large-amplitude responses which undergo jumps at the saddle-node bifurcations. © 2003 Elsevier Ltd. All rights reserved