Non-linear vibrations of parametrically excited cantilever beams subjected to non-linear delayed-feedback control

Non-linear feedback control provides an effective methodology for vibration mitigation in non-linear dynamic systems. However, within digital circuits, actuation mechanisms, filters, and controller processing time, intrinsic time-delays unavoidably bring an unacceptable and possibly detrimental delay period between the controller input and real-time system actuation. If not well-studied, these inherent and compounding delays may inadvertently channel energy into or out of a system at incorrect time intervals, producing instabilities and rendering controllers’ performance ineffective. In this work, we present a comprehensive investigation of the effect of time delays on the non-linear control of parametrically excited cantilever beams. More specifically, we examine three non-linear cubic delayed-feedback control methodologies: position, velocity, and acceleration delayed feedback. Utilizing the method of multiple scales, we derive the modulation equations that govern the non-linear dynamics of the beam. These equations are then utilized to investigate the effect of time delays on the stability, amplitude, and frequency–response behavior. We show that, when manifested in the feedback, even the minute amount of delays can completely alter the behavior and stability of the parametrically excited beam, leading to unexpected behavior and responses that could puzzle researchers if not well-understood and documented.     

Turbulent natural convection flow in a vertical channel with anti-symmetric heating

This paper presents the fluid flow characteristics of natural convection flow in an anti-symmetrically heated parallel-plate vertical channel using the Particle Image Velocimetry (PIV) system. The channel walls were subjected to uniform temperature conditions, with one wall heated above ambient and the opposing wall maintained below ambient temperature. Velocity measurements were conducted at three different sections on the horizontal plane to validate two-dimensionality of the flow and at three different heights in the vertical plane to establish vertical mean velocity profiles. The results indicate that the flow recirculation in the channel exhibits a similar character to that of a closed cavity and the induced flow rate is much lower than the one for a channel with both walls heated. A correlation for the dimensionless flow rate is developed.     

Two-to-one internal resonance in microscanners

To realize large scanning angles, torsional microscanners are normally excited at their natural frequencies. Usually, a bias DC voltage is also applied to scan around a desired nonzero tilt angle. As a result, a deep understanding of the mirror’s response to a DC-shifted primary resonance excitation is imperative. Along these lines, we use the method of multiple scales to obtain a second-order nonlinear approximate analytical solution of the mirror steady-state response. We show that the response of the mirror exhibits a softening-type behavior that increases as the magnitude of the DC component increases. For a given mirror, we can also identify a DC voltage range wherein the mirror exhibits a two-to-one internal resonance between the first two modes; that is, ω ₂≈2ω ₁. To analyze the mirror behavior within that range, we first treat the case where the excitation frequency is near the first-mode frequency; that is, Ω≈ω ₁. Then we treat the case where the excitation frequency is near the second-mode frequency; that is, Ω≈ω ₂. We analyze the stability of the response and compare the analytical results to numerical solutions obtained via long-time integration of the equations of motion. We show that, due to the internal resonance, the mirror exhibits complex dynamic behavior characterized by aperiodic responses to primary resonance excitations. This behavior results in undesirable oscillations that are detrimental to the mirror performance, namely bringing the target point in and out of focus and resulting in distorted images.

     

Using fractional-order integrator to control chaos in single-input chaotic systems

This paper deals with a fractional calculus based control strategy for chaos suppression in the 3D chaotic systems. It is assumed that the structure of the controlled chaotic system has only one control input. In the proposed strategy, the controller has three tuneable parameters and the control input is constructed as fractional-order integration of a linear combination of linearized model states. The tuning procedure is based on the stability theorems in the incommensurate fractional-order systems. To evaluate the performance of the proposed controller, the design method is applied to suppress chaotic oscillations in a 3D chaotic oscillator and in the Chen chaotic system.     

Convective heat transfer over two blocks arbitrary located in a 2D plane channel using a hybrid lattice Boltzmann-finite difference method

The present paper deals with the numerical investigation of a 2D laminar fluid flow and heat transfer in a plane channel with two square blocks located at arbitrary positions. The numerical model is based on a coupling between the multiple relaxation time-lattice Boltzmann equation and the finite difference method for incompressible flow. Both the horizontal and the vertical separation distances between the two blocks are varied. Particular attention was paid to the distribution patterns of the time averaged local Nusselt number on the top and bottom walls. Results obtained from the present study show a complex flow patterns developed in the channel due to the change of the square blocks positions.     

Experimental Evaluation of a Portable Neutron-Based Gamma-Spectroscopy System for Chloride Measurements in Reinforced Concrete

A portable prompt gamma neutron activation (PGNA) spectroscopy system has been developed to analyze the elemental composition (Ca, Si, Al, etc.) of reinforced concrete and to measure chloride contamination. The portable PGNA system consists of a high purity germanium (HPGe) gamma detector with a 70% relative efficiency, a ²⁵²Cf neutron source and moderator subsystem, and a portable multichannel analyzer system integrated with a laptop computer. Two types of activation experiments were performed to evaluate the device: first, a detector calibration using a Cl gamma standard provided by a PGNA facility; second, an evaluation of the actual performance of the complete system with the ²⁵²Cf source using full scale test slabs containing known amounts of chloride. Both methods indicate that it is feasible to use this device to measure the chloride content of reinforced concrete in the field. The chloride level for the corrosion threshold can be measured with a precision of 10% for a counting time of roughly 6 minutes. This makes the PGNA method competitive with the conventional destructive method.     

10‐Ethyl‐3‐(4‐methoxy­phenyl)‐1,2,4‐triazolo­[4′,3′:2,3]‐1,2,4‐triazino[5,6‐b]­indole

Oxidative cyclization of 5‐ethyl‐3‐(4‐methoxy­benzyl­idene)­hydrazino‐1,2,4‐triazino­[5,6‐b]­indole gave the linearly annel­ated title compound, C₁₉H₁₆N₆O. The skeleton is approx­imately planar, except for the ethyl group.     

Di­thio­cyanatobis­[4,4,5,5‐tetra­methyl‐2‐(4‐pyridyl‐κN)‐1H‐imidazoline‐1‐oxyl]­zinc(II)

In the title compound, [Zn(NCS)₂(C₁₂H₁₆N₃O)₂], the Zn^II ion has a distorted tetrahedral coordination. It is bonded to two thio­cyanate and two pyridyl N atoms. The metal ion and the two thio­cyanate ligands lie on a mirror plane with the Zn—N_py and average Zn—N_NCS bond distances being 2.036 (2) and 1.931 (4) Å, respectively     

On stability analysis of semi-linear fractional differential systems

In this article, new trends of analysis on existence, uniqueness, and stability of solution for semi-linear fractional systems are considered. The results are based on a generalization of Bihari's inequality. Some examples are given to illustrate the results.     

Biosynthesis of TiO2 nanoparticles and their superior antibacterial effect against human nosocomial bacterial pathogens

Research on Chemical Intermediates - Antibacterial titanium dioxide nanoparticles (TiO2NPs) were biologically synthesized by microwave irradiation of Cissus quadrangularis extract followed by...