Vibration of strings with nonlinear supports

The dynamic string motion, which displacement is unilaterally constrained by the rigid termination condition of an arbitrary geometry has been simulated and analyzed. The treble strings of a grand piano usually terminate at a capo bar, which is situated above the strings. The apex of a V-shaped section of the capo bar defines the end of the speaking length of the strings. A numerical calculation based on the traveling wave solution is proposed for modeling the nonlinearity inducing interactions between the vibrating string and the contact condition at the point of string termination. It was shown that the lossless string vibrates in two distinct vibration regimes. In the beginning the string starts to interact in a nonlinear fashion with the rigid terminator, and the resulting string motion is aperiodic. Consequently, the spectrum of the string motion depends on the amplitude of string vibrations, and its spectral structure changes continuously with the passage of time. The duration of that vibration regime depends on the geometry of the terminator. After some time of aperiodic vibration, the string vibrations settle in a periodic regime where the resulting spectrum remains constant.     

Application of a hybrid meshless technique for natural frequencies analysis in functionally graded thick hollow cylinder subjected to suddenly thermal loading

A hybrid meshless technique based on composition of meshless local Petrov–Galerkin method (for spatial variables) and Newmark finite difference method (for time domain) is developed for natural frequencies analysis of thick cylinder made of functionally graded materials (FGMs). The FG cylinder is assumed to be under suddenly thermal loading, axisymmetric and plane strain conditions. The dynamic behaviors and time history of displacements are obtained in time domain using Green–Naghdi (GN) theory of coupled thermo-elasticity (without energy dissipation). Using fast Fourier transform (FFT) technique, the displacements are transferred to frequency domain and all natural frequencies are illustrated for various grading patterns of FGMs. The variations of mechanical properties in FG thick hollow cylinder are considered to be in nonlinear volume fraction law through radial direction. The presented hybrid meshless technique furnishes a ground to analyze the effects of various grading patterns of FGMs on natural frequencies, which are obtained employing GN coupled thermo-elasticity governing equations. Also, the frequency history and natural frequencies are illustrated for various grading patterns at several points across thickness of cylinder.     

Exact solutions of functionally graded piezoelectric material sandwich cylinders by a modified Pagano method

The three-dimensional (3D) coupled analysis of simply-supported, functionally graded piezoelectric material (FGPM) circular hollow sandwich cylinders under electro-mechanical loads is presented. The material properties of each FGPM layer are regarded as heterogeneous through the thickness coordinate, and obey an exponent-law dependent on this. The Pagano method is modified to be feasible for the study of FGPM sandwich cylinders. The modifications are as follows: a displacement-based formulation is replaced by a mixed formulation; a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions; a successive approximation method is adopted to approximately transform each FGPM layer into a multilayered piezoelectric one with an equal and small thickness for each layer in comparison with the mid-surface radius, and with the homogeneous material properties determined in an average thickness sense; and a transfer matrix method is developed, so that the general solutions of the system equations can be obtained layer-by-layer, which is significantly less time-consuming than the usual approach. A parametric study is undertaken of the influence of the aspect ratio, open- and closed-circuit surface conditions, and material-property gradient index on the assorted field variables induced in the FGPM sandwich cylinders.     

A class of solvable coupled nonlinear oscillators with amplitude independent frequencies

Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically.     

Self-Reinforced High-Density Polyethylene Prepared by Low Frequency Vibration-Assisted Injection Molding. II: Microstructure Investigation

Scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and wide angle X-ray diffraction (WAXD) were employed to study the microstructure of self-reinforced high-density polyethylene (HDPE) prepared by conventional injection molding (CIM) and a low frequency vibration-assisted injection molding (VAIM). SEM micrographs following permanganic etching showed the self-reinforcement of HDPE is mainly due to the existence of shish-kebab morphology within the core region for VAIM-processed HDPE samples. Pronounced molecular alignment was identified by the WAXD data. An approximate 9% increase in the crystallinity was confirmed by DSC. Both preferred molecular orientation and increased crystallinity serve to yield stronger VAIM-processed injection moldings.     

Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

A novel chaotic image encryption scheme using DNA sequence operations

In this paper, we propose a novel image encryption scheme based on DNA (Deoxyribonucleic acid) sequence operations and chaotic system. Firstly, we perform bitwise exclusive OR operation on the pixels of the plain image using the pseudorandom sequences produced by the spatiotemporal chaos system, i.e., CML (coupled map lattice). Secondly, a DNA matrix is obtained by encoding the confused image using a kind of DNA encoding rule. Then we generate the new initial conditions of the CML according to this DNA matrix and the previous initial conditions, which can make the encryption result closely depend on every pixel of the plain image. Thirdly, the rows and columns of the DNA matrix are permuted. Then, the permuted DNA matrix is confused once again. At last, after decoding the confused DNA matrix using a kind of DNA decoding rule, we obtain the ciphered image. Experimental results and theoretical analysis show that the scheme is able to resist various attacks, so it has extraordinarily high security.     

Prediction of hydrodynamic performance of an FLNG system in side-by-side offloading operation

Floating liquefied natural gas (FLNG) is a type of liquefied natural gas (LNG) production system that shows prospects in exploitation of stranded offshore gas fields. The dynamic performance of an FLNG system in side-by-side configuration with a LNG carrier under the combined actions of wave, current and wind can be quite complex. This paper presents a comprehensive study on the hydrodynamics of an FLNG system with a focus on the nonlinear coupling effects of vessels and connection systems based on the concept FLNG prototype recently designed for South China Sea. In this study, the hydrodynamic characteristics of the two floating vessels connected through hawsers and fenders are investigated using a state-of-the-art time-domain simulation code SIMO, considering their mechanical and hydrodynamic coupling effects. The simulation model consisting of FLNG and LNG carrier is developed and calibrated by a series of model tests including a tuned damping and viscous levels. The hydrodynamic performances of the two floating vessels under an extreme sea state during side-by-side offloading operation are obtained, and their relative motions and the force responses of the connection hawsers and fenders are analyzed. Sensitivity studies are conducted to clarify contributions from the pretension and the stiffness of the connection hawsers. The effects on the hydrodynamic performance of the vessels and on the loads of the connection system are also investigated.     

The resonant secondary emission of the F center in alkali halides

The secondary radiation after resonant excitation of F center and its linear polarization P correlated to the polarization of resonant light have been measured for five alkali halides at low temperatures. In KC1, the spectrum of P over the whole Stokes region is divided into three successive regions, the depolarization range at the one-phonon Raman scattering, the near plateau range, and the depolarization range down to vanishing. The former two have common relevance to resonant energy and symmetries of coupled phonons. These relevances are interpreted adopting a configuration coordinate model for 2s- and 2p-like excited states.