Super Harmonic Research Articles

Subharmonic and superharmonic resonances of five-layered porous functionally graded sandwich cylindrical shells with two-layered viscoelastic cores

In this research, the subharmonic (SUBH) and superharmonic (SUPH) resonances of five-layered porous functionally graded sandwich (PFGS) cylindrical shells with two-layered viscoelastic cores (VECs) are investigated. The sandwich cylindrical shell is composed of three porous functionally graded (PFG) face layers and two VECs. The VECs are made of Kelvin–Voigt type material. The material properties of the PFG face layers are considered as continuous through the thickness of each face regarding a porosity coefficient and a volume fraction index. Two types of five-layered PFGS cylindrical shells with two-layered VESs, including porosity evenly distributed (Type 1) and porosity unevenly distributed (Type 2) along the thickness direction, are considered in this research. Based on the Donnell shell theory, von-Kármán equation, and Hooke’s law, the stress-strain relations are developed for the five-layered PFGS cylindrical shells. The discretized governing equation via Galerkin’s method is also derived. With the governing equations proposed and the method of multiple scales, the SUBH and SUPH resonances of the shells are investigated systematically. The influences of geometrical, and material parameters on the SUBH and SUPH resonances of the system are studied and presented. New results for SUBH and SUPH resonances of the five-layered PFGS cylindrical shells with two-layered VECs are provided for the first time and can be utilized as a benchmark for researchers and engineers in this area.

Classification of the major nonlinear regimes of oscillations, oscillation properties, and mechanisms of wave energy dissipation in the nonlinear oscillations of coated and uncoated bubbles

Acoustic waves are dissipated when they pass through bubbly media. Dissipation by bubbles takes place through thermal damping (Td), radiation damping (Rd), and damping due to the friction of the liquid (Ld) and friction of the coating (Cd). Knowledge of the contributions of Td, Rd, Ld, and Cd during nonlinear bubble oscillations will help in optimizing bubble and ultrasound exposure parameters for the relevant applications by maximizing a desirable outcome or oscillation pattern. In this work, we investigate the mechanisms of dissipation in bubble oscillations and their contribution to the total damping (Wtotal) in various nonlinear regimes. By using a bifurcation analysis, we have classified nonlinear dynamics of bubbles that are sonicated with their third superharmonic (SuH) and second SuH resonance frequency (fr), pressure dependent resonance frequency (PDfr), fr, subharmonic (SH) resonance (fsh = 2fr), pressure dependent SH resonance (PDfsh), and 1/3 order SH resonance, which are important exposure ranges for various applications. The corresponding Td, Rd, Ld, Cd, Wtotal, scattering to dissipation ratio, maximum wall velocity, and maximum backscattered pressure from non-destructive oscillations of bubbles were calculated and analyzed using the bifurcation diagrams. Universal ultrasound exposure parameter ranges are revealed in which a particular non-destructive bubble related phenomenon (e.g., wall velocity) is enhanced. The enhanced bubble activity is then linked to relevant ultrasound applications. This paper represents the first comprehensive analysis of the nonlinear oscillations regimes, the corresponding damping mechanisms, and the bubble related phenomena.

The Relationship between Sea-Swell Bound Wave Height and Wave Shape

The nonlinear wave shape, expressed by skewness and asymmetry, can be calculated from surface elevation or pressure time series using bispectral analysis. Here, it is shown that the same analysis technique can be used to calculate the bound superharmonic wave height. Using measured near-bed pressures from three different field experiments, it is demonstrated that there is a clear relationship between this bound wave height and the nonlinear wave shape, independent of the measurement time and location. This implies that knowledge on the spatially varying bound wave height can be used to improve wave shape-induced sediment transport predictions. Given the frequency-directional sea-swell wave spectrum, the bound wave height can be predicted using second order wave theory. This paper shows that in relatively deep water, where conditions are not too nonlinear, this theory can accurately predict the bispectrally estimated bound superharmonic wave height. However, in relatively shallow water, the mismatch between observed and predicted bound wave height increases significantly due to wave breaking, strong currents, and increased wave nonlinearity. These processes are often included in phase-averaged wind-wave models that predict the evolution of the frequency-directional spectrum over variable bathymetry through source terms in a wave action balance, including the transfer of energy to bound super harmonics. The possibility to calculate and compare with the observed bound super harmonic wave height opens the door to improved model predictions of the bound wave height, nonlinear wave shape and associated sediment transport in large-scale morphodynamic models at low additional computational cost.

Detection algorithm of ultra-high harmonics in distribution networks

Power quality of distribution network is an emerging issue due to rapid increase in usage of non-linear loads on the one hand and utilization of sensitive devices on the other hand. Especially, harmonic emission is an important concern in both electric utilities and end users of electric power. Therefore, an accurate and rapid harmonic analysis method is of interest. New technologies have enabled the investigation of electricity consumption mode at an unprecedented scale and in multiple dimensions. However, an effective method that can capture the complexity of all the factors relevant to understanding a phenomenon such as ultrahigh harmonics (2–15 kHz). How to detect the super high order harmonic accurately has become the premise and foundation of the study of super high order harmonic. The key challenge in developing such approaches is the identification of effective models to provide a comprehensive and relevant systems view. An ideal method can identify super high harmonics and predict outcomes, by measured data across several dimensions variation. In this paper, the data integration, current methods and available implementation is discussed. Finally, the current challenges in integrative methods is discussed.

A simple method to analyze the super-harmonic and ultra-harmonic behavior of the acoustically excited bubble oscillator

The bubble oscillator is a highly nonlinear system, which makes it difficult to generate a comprehensive understanding of its oscillatory behavior. One method used to investigate such complex dynamical systems is the bifurcation analysis. Numerous investigations have employed the method of bifurcation diagrams to study the effect of different control parameters on the bubble behavior. These studies, however, focused mainly on investigating the subharmonic (SH) and chaotic oscillations of the bubbles. Super-harmonic (SuH) and ultra-harmonic (UH) bubble oscillations remain under-investigated. One reason is that the conventional method used for generating bifurcation diagrams cannot reliably identify features that are responsible for the identification of SuH and UH oscillations. Additionally, the conventional method cannot distinguish between the UHs and SHs. We introduce a simple procedure to address this shortcoming. In this method, the maxima of the bubble oscillatory response were selected and plotted alongside the traditional bifurcation points for the corresponding control parameter. Results show that depending on the control parameters the conventional method or the method of maxima may miss intricate details of the oscillations. In order to have a comprehensive knowledge on the rich dynamics of the system, the two methods should be employed side by side. Through plotting the two bifurcation structures in tandem, the oscillatory behavior of the bubble was analyzed with more detail, and stable SuH and UH bubble oscillations were investigated. Based on this new analysis, the conditions for the generation and amplification of UH and SuH regimes are discussed.

K–Super Harmonic Mean Labeling of Certain Snake Graphs

k–Super Harmonic Mean Labeling of Certain Snake Graphs

English

English

A new upper bound 2.5545 on 2D Online Bin Packing

The 2D Online Bin Packing is a fundamental problem in Computer Science and the determination of its asymptotic competitive ratio has research attention. In a long series of papers, the lower bound of this ratio has been improved from 1.808, 1.856 to 1.907 and its upper bound reduced from 3.25, 3.0625, 2.8596, 2.7834 to 2.66013. In this article, we rewrite the upper bound record to 2.5545. Our idea for the improvement is as follows. In 2002, Seiden and van Stee [Seiden and van Stee 2003] proposed an elegant algorithm called H ⊗ C , comprised of the Harmonic algorithm H and the Improved Harmonic algorithm C , for the two-dimensional online bin packing problem and proved that the algorithm has an asymptotic competitive ratio of at most 2.66013. Since the best known online algorithm for one-dimensional bin packing is the Super Harmonic algorithm [Seiden 2002], a natural question to ask is: could a better upper bound be achieved by using the Super Harmonic algorithm instead of the Improved Harmonic algorithm? However, as mentioned in Seiden and van Stee [2003], the previous analysis framework does not work. In this article, we give a positive answer for this question. A new upper bound of 2.5545 is obtained for 2-dimensional online bin packing. The main idea is to develop new weighting functions for the Super Harmonic algorithm and propose new techniques to bound the total weight in a rectangular bin.

A note on online hypercube packing

In this paper, we study an online multi-dimensional bin packing problem where all items are hypercubes. Hypercubes of different size arrive one by one, and we are asked to pack each of them without knowledge of the next pieces so that the number of bins used is minimized. Based on the techniques from one dimensional bin packing and specifically the algorithm Super Harmonic by Seiden (J ACM 49:640–671, 2002), we extend the framework for online bin packing problems developed by Seiden to the hypercube packing problem. To the best of our knowledge, this is the first paper to apply a version of Super Harmonic (and not of the Improved Harmonic algorithm) for online square packing, although the Super Harmonic has been already known before. Note that the best previous result was obtained by Epstein and van Stee (Acta Inform 41(9):595–606, 2005b) using an instance of Improved Harmonic. In this paper we show that Super Harmonic is more powerful than Improve Harmonic for online hypercube packing, and then we obtain better upper bounds on asymptotic competitive ratios. More precisely, we get an upper bound of 2.1187 for square packing and an upper bound of 2.6161 for cube packing, which improve upon the previous upper bounds 2.24437 and 2.9421 (Epstein and van Stee in Acta Inform 41(9):595–606, 2005b) for the two problems, respectively.

A note on the nonlinear modeling of piezoelectric rods

AbstractPiezoceramic materials are usually calculated using linear constitutive equations if the exciting electric field is small. If the structure is excited near a resonance frequency the assumption of a linear material becomes invalid. Therefore nonlinear constitutive equations have to be used if the super harmonics in the measured velocity signals should be modeled. In this paper nonlinear constitutive equations are derived from the electric enthalpy density to describe the longitudinal oscillations of a piezoceramic rod. The kinetic energy considers the inertia effects in transversal direction so the model is not limited to the slender rod theory. With Hamilton's principle a variational principle is derived which is approximated using a Rayleigh Ritz ansatz with the first eigenfunction of the linearized system. The resulting nonlinear ODE is solved by application of the harmonic balance method. The amplitudes of displacement of the fundamental, the second and the third super harmonic oscillations are solved numerically. In a first step the results of the theoretical model are compared with measurements. The material parameters of the nonlinear constitutive equations are calculated using a parametric identification method. As a result it is shown that the theoretical model can describe the Duffing type nonlinearities found in measurements.

Contrast superharmonic imaging: A feasibility study

Harmonic imaging provided significant improvement in image quality by taking advantage of the scattered second harmonic (2H) component from contrast bubbles. However, differentiation between contrast and tissue (usually termed contrast-to-tissue ratio, CTR) is sometimes cumbersome and this is mainly due to tissue contamination. We have previously demonstrated, using simulations and in vitro measurements, that CTR increases as a function of the order of the harmonic number. A new contrast imaging method based on the detection of the higher harmonics was developed and termed superharmonic (SH). This technique has been shown to be more sensitive to contrast by increasing the signal from contrast and suppressing that from tissue (high CTR). The purpose of this study was to determine the clinical feasibility and usefulness of SH in patients using a commercially available contrast agent (SonoVue®) for quantification of myocardial perfusion. A total of 10 patients with various cardiac diseases were assessed. Apical four-chamber views were acquired using SH in triggered mode before and after contrast injection. The superharmonic was performed with a newly developed probe transmitting at 0.8 MHz with a mechanical index of 0.2. Myocardial perfusion was determined visually and analyzed quantitatively using radiofrequency (RF) processing from different regions of interest. The results showed that, before contrast injection, SH was totally blinded to tissue and no superharmonic components were generated in the image view. After administration of SonoVue®, myocardial opacification was visualized by SH after contrast entered the myocardium. An increase of more than 15 dB in the myocardial bubbles echo compared to tissue echo was measured. In addition, the technique was used to visualize myocardial perfusion after myocardial septal ablation for hypertrophic cardiomyopathy. The clinical results showed the ability of contrast SH imaging in differentiating low and normal perfusion areas, demonstrating the high sensitivity and specificity of the technique. (E-mail: a.bouakaz@erasmusmc.nl)

Improved contrast to tissue ratio at higher harmonics

The challenge in ultrasound contrast imaging is a better discrimination between the perfused tissue and the contrast bubbles, which is usually expressed by contrast to tissue ratio (CTR). Imaging based on the second harmonic frequency showed a higher CTR than imaging at the fundamental frequency. However, because of nonlinear propagation of ultrasound waves, harmonic frequencies are generated. These harmonic frequencies will be linearly reflected by the tissue and therefore limit the CTR at the second harmonic frequency. In order to reduce the scattering of tissue at harmonic frequencies and by that increase the CTR, nonlinear distortion has to be reduced. We demonstrate in this study that the CTR increases with the harmonic number. The increase is substantial when transmitting at lower frequencies. To take advantage of the higher harmonics (third, fourth, fifth and the ultraharmonics and termed here super harmonics), we have developed a new phased array transducer with a wide frequency band. In-vitro measurements using the new probe show an increase of 40 dB of the CTR for super harmonic components over the conventional second harmonic system. The increase in CTR is in agreement with the calculations using existing models for the response of encapsulated bubbles and known theory of nonlinear propagation.

Super harmonic imaging: a new imaging technique for improved contrast detection

For ultrasound contrast agents (UCA), nonlinear imaging now has become fundamental. All of the current contrast-imaging methods are dominantly based on the nonlinear response of UCA bubbles. The discrimination between the perfused tissue and the UCA is the challenge in the field of UCA-imaging. This differentiation is usually associated or expressed by the ratio of the scattered power from the contrast agent to the scattered power from the tissue and is termed “contrast-to-tissue ratio” (CTR). Second harmonic imaging showed a better discrimination between tissue and UCA than fundamental imaging because of a higher CTR. We demonstrate, in this study, that the CTR increases as a function of the order of the harmonic frequency. Currently, due to the limited bandwidth of the transducers, only the second harmonic is selectively imaged, resulting in images with a superior quality to fundamental images, but still degraded and not optimal because of the harmonic generation in the underlying tissue (due to nonlinear propagation) and hence giving a limited CTR. To increase the CTR and to take advantage of the higher harmonics (third, fourth, fifth and the ultraharmonics and termed here super harmonics), we have developed a new phased array transducer. The array transducer contains two different types of elements arranged in an interleaved pattern (odd and even elements). The total number of elements is 96. The elements can operate separately and at a distinct frequency, enabling separate transmission and reception modes. The odd elements (48) operate at typically 2.8 MHz center frequency and 80% bandwidth. The even elements (48) have a center frequency of 900 kHz with a bandwidth of 50%. In vitro measurements using the dual frequency probe show an increase of 40 dB in the CTR for super harmonic components over the conventional second harmonic system. The increase in CTR is in agreement with the calculations using existing models for the response of encapsulated bubbles and known theory of nonlinear propagation. Animal experiments have demonstrated the feasibility of this approach using commercially available UCA and showed a similar increase of the CTR (E-mail: bouakaz@tch.fgg.eur.nl).