Exact Frequencies Research Articles

Free vibration analysis of nonsymmetrically laminated cross-ply L-shaped frames

Fiber-reinforced composite laminates can be tailored to produce structural elastic couplings that optimize their response in dynamic environments. It is therefore essential that the free vibration characteristics of structural elements fabricated from fiber-reinforced composites be accurately modeled and investigated. In this work, an analytical wave-based approach is extended to study the in-plane vibrations of nonsymmetrically laminated cross-ply L-shaped frames. The proposed theory accounts for the effects of shear deformation, rotary inertia, and the elastic coupling between in-plane bending and longitudinal deformations. The reflection matrices at the boundaries, together with the reflection and transmission matrices at the corner joint of the L-shaped frame are derived. A traveling wave approach is then used to systematically assemble the small-order matrices into a single expression that can be used to efficiently calculate the exact natural frequencies. An expression for evaluating the mode shapes of the frame for general boundary conditions is also given. The application of the wave-based method is illustrated through several numerical examples and the results are validated using independent finite element models. As part of the numerical analysis, the influence of the number of cross-ply layers on the natural frequencies is investigated.

Determination of the exact mode frequencies of multi-storey structures by state-space method and a comparison with mode superposition method

A comparative research has been carried out for obtaining the time-consuming exact solution (state-space) and approximate solution (mode superposition) of transient and steady-state vibrations of linearly damped linear frame buildings. In the mode superposition method, the proportional damping matrix has been constructed by different approaches such as modal combination of mass and stiffness matrixes (Rayleigh) and disregarding the off-diagonal elements of the non-classical damping matrix, while in the state-space method the non-proportional damping matrix is constructed in exact situation. These observations are individually investigated, which the most suitable parameter to render the approximate results as close as possible to the exact results. Harmonic forces are applied on the different storeys of three and five storey frame buildings, and the responses are displayed in comparative tables and figures. The maximum responses are calculated by square root of sum of the squares (SRSS) method. A MATLAB code is generated and the equations of exact and approximate methods are solved.

Quasinormal modes of charged fermions in linear dilaton black hole spacetime: exact frequencies

We study charged massless fermionic perturbations in the background of $4$-dimensional linear dilaton black holes in Einstein-Maxwell-dilaton theory with double Liouville-type potentials. We present the analytical fermionic quasinormal modes, whose Dirac equations are solved in terms of hypergeometric functions. We also discuss the stability of these black holes under the charged fermionic perturbations.

Interpolation method for wideband signal reconstruction based on blade tip timing measurement

Blade tip timing (BTT) technique has become a promising way of online damage diagnosis for compressor and turbine blades by monitoring their vibrations. However, there are some disadvantages in previous algorithms for BTT signals, including not high precision, strict sensor layout, signal bandwidth limit, and weak anti-noise ability. To solve these problems, a novel interpolation method for wideband signal reconstruction (IWSR) is presented. Simulations are conducted using a lumped parameter model, which shows that IWSR reconstructs noiseless signals with overall errors mainly below 1%, and identifies the exact frequencies of 5 dB noise signals. In addition, the results validate its signal separation function and verify that its sensor layout is almost arbitrary, and its maximum allowable bandwidth is half the product of sensor number and rotational frequency. Experimental results demonstrate its effectiveness in frequency identification. In conclusion, IWSR provides precise information for real-time blade damage diagnosis, which benefits turbomachinery safety.

Chemical Identification in the Specular and Off-Specular Rough-Surface Scattered Terahertz Spectra Using Wavelet Shrinkage.

We present the development and implementation of a novel wavelet shrinkage technique for the retrieval of obscured characteristic resonant signatures in the scattered terahertz (THz) reflectivity of molecular crystals. In this implementation, the wavelet basis functions associated with the absorption features were identified using the second-order total variation of the wavelet coefficients. Additionally, wavelet coefficients at certain scales were modified using the phase function corrections and wavelet hard thresholding. Reconstruction of the original spectra using these modified wavelet coefficients yielded the exact resonant frequencies of the chemicals, which were otherwise unrecognizable in the spectral artifacts of the rough surface scattering. We examined the robustness of this method over controlled levels of rough surface scattering, validated using the Kirchhoff approximation, in spectroscopic targets made from α-lactose monohydrate and 4-aminobenzoic acid (PABA), which have close spectral lines. We successfully retrieved the spectral absorption fingerprints in both specular and off-specular reflection geometries. This technique can be utilized for stand-off material characterization using the THz reflection spectroscopy in uncontrolled environments and potentially can be adopted for other broadband spectroscopic modalities.

Effect of spring mid-support condition on the vibrations of the axially moving string

In this study, the axially moving string with spring-loaded middle support is discussed. The supports assumed as simple support on the string both ends. The intermediate support shows the characteristics of the spring. The string velocity is accepted as harmonically varying around a mean value. The Hamiltonian principle is used to find the equations of motion. The equations of motion become nonlinear, considering the nonlinear effects caused by string extensions. The equations of motion and boundary conditions are become dimensionless by nondimensionalization. Approximate solutions were found by using multiple time scales which is one of the perturbation methods. By solving the linear problem that is obtained by the first terms of the perturbation series, the exact natural frequencies were calculated for the different locations of the mid-support, various spring coefficients, and various axial velocity values. The second-order nonlinear terms reveal the correction terms for the linear problem. Stability analysis is carried out for cases where the velocity change frequency is away from zero and two times the natural frequency. Stability boundaries are determined for the principal parametric resonance case.

Vibration of a Segmented Rod

This paper presents the governing equation of motion, boundary conditions and exact vibration frequencies of a segmented rod where the segments are connected by hinges with elastic rotational springs of constant stiffness. The mass of each segment is assumed to be evenly distributed along the length of the rod. Another discrete model called Hencky bar-chain model (short for HBM; which is equivalent to the finite difference model for discretizing continuous rod) assumes the rod mass to be lumped at the ends instead and a different set of boundary conditions are adopted clamped end. The vibration results of a clamped–clamped segment rod are compared with those of the HBM. It is shown that the HBM underestimates the vibration frequencies when compared to the segmented rod model for a finite number of segments while both models furnish vibration solutions that converge to the solutions of Euler beam for infinitely large number of segments.

Path integral Liouville dynamics simulations of vibrational spectra of formaldehyde and hydrogen peroxide

Formaldehyde and hydrogen peroxide are two important realistic molecules in atmospheric chemistry. We implement path integral Liouville dynamics (PILD) to calculate the dipole-derivative autocorrelation function for obtaining the infrared spectrum. In comparison to exact vibrational frequencies, PILD faithfully captures most nuclear quantum effects in vibrational dynamics as temperature changes and as the isotopic substitution occurs.

On the free vibrations of locally-resonant structures

This paper addresses the free-vibration response of structures coupled with periodically-distributed resonators, generally referred to as locally-resonant structures. The first step is to show that all exact natural frequencies can be calculated by a proper formulation of the Wittrick-Williams algorithm, involving a condensed dynamic stiffness matrix whose size depends only on the number of degrees of freedom of the structure and is independent of the number of degrees of freedom within every resonator. Indeed, the presence of resonators is accounted for in the condensed dynamic stiffness matrix via a pertinent frequency-dependent stiffness, readily obtainable from the resonator motion equations. Within this framework, a novel procedure is proposed to construct the condensed dynamic stiffness matrix of locally-resonant plates, applicable for any number of resonators. Numerical applications show the exactness of the proposed formulation.

Abstract LB-314: Development of reference material guaranteed copy number of DNA for liquid biopsy

Abstract cfDNA (cell free DNA) analysis using liquid biopsy plays an important role in cancer research. In particular NGS (next-generation sequencer)-based assay has attracted wide interests, because it can not only screen many cancer genes but also can detect ultra-low-concentration mutations at the same time. However, there is no reference material to evaluate correctly its performance. Currently, most researchers use diluted human genomic DNA that is commercially available as reference, but adjusting its concentration is difficult because of the Poisson distribution. Herein, we have developed a method to dispense cells with counting a cell one by one using inkjet technology (Manabu Seo, et. Al., 2019, Anal. Chem.). By lysing cells after dispensing, the defined copy number of DNA is prepared with a single molecule level. In this study, we assessed the feasibility of our reference material prepared by inkjet as a control for rare mutation detection (e.g. minimal sampling bias and high reproducibility). Spike-in control samples with exact allele frequencies with 0.07%, 0.53%, 0.64%, and 1.0%, were prepared by accurately dispensing with inkjet the cells that contain a sequence of exons 18, 19, 20, and 21 of EGFR. The EGFR sequence has G719A, E746_A750del, T790M, C797S, L858R, and L861Q mutations. For comparison, a few samples were also prepared by manual dilution process. The EGFR mutations were analyzed by the method of high-sensitivity procedure using NGS (Yoji Kukita, et. Al., 2013, PLoS ONE.). Result of the inkjet method had less variation than the manual dilution method, and high repeatability was obtained. Especially in E746_A750del (0.53%) the inkjet samples were tested three times (n = 24 each), and their CVs (coefficient of variation) were 17%, 17%, and 12%. In contrast, the manual sample's one was 33%. In addition, linearity of T790M and L858R were R2 = 0.98 and R2 = 0.96, respectively. The reference material produced by inkjet method can be provided under the same conditions at each facility and make it possible to improve the reliability of liquid biopsy. Therefore, the reference material could be appropriate standard for external quality control for EGFR mutant detection of liquid biopsy. Citation Format: Yusuke Osaki, Yoshiharu Sato, Miho Ishii, Yuki Yonekawa, Ryo Matoba. Development of reference material guaranteed copy number of DNA for liquid biopsy [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr LB-314.

Light dressing of a diatomic superconducting artificial molecule

In this work, we irradiate a superconducting artificial molecule composed of two coupled tunable transmons with microwave light while monitoring its state via joint dispersive readout. Performing high-power spectroscopy, we observe and identify a variety of single- and multiphoton transitions. We also find that at certain fluxes, the measured spectrum of the system deviates significantly from the solution of the stationary Schr\"odinger equation with no driving. We reproduce these unusual spectral features by solving numerically the full master equation for a steady-state and attribute them to an Autler-Townes-like effect in which a single tone is simultaneously dressing the system and probing the transitions between new eigenstates. We show that it is possible to find analytically the exact frequencies at which the satellite spectral lines appear by solving self-consistent equations in the rotating frame. Our approach agrees well with both the experiment and the numerical simulation.

Dry Panels Supporting External Quality Assessment Programs for Next Generation Sequencing-Based HIV Drug Resistance Testing.

External quality assessment (EQA) is a keystone element in the validation and implementation of next generation sequencing (NGS)-based HIV drug resistance testing (DRT). Software validation and evaluation is a critical element in NGS EQA programs. While the development, sharing, and adoption of wet lab protocols is coupled with the increasing access to NGS technology worldwide, rendering it easy to produce NGS data for HIV-DRT, bioinformatic data analysis remains a bottleneck for most of the diagnostic laboratories. Several computational tools have been made available, via free or commercial sources, to automate the conversion of raw NGS data into an actionable clinical report. Although different software platforms yield equivalent results when identical raw NGS datasets are analyzed for variations at higher abundance, discrepancies arise when variations at lower frequencies are considered. This implies that validation and performance assessment of the bioinformatics tools applied in NGS HIV-DRT is critical, and the origins of the observed discrepancies should be determined. Well-characterized reference NGS datasets with ground truth on the genotype composition at all examined loci and the exact frequencies of HIV variations they may harbor, so-called dry panels, would be essential in such cases. The strategic design and construction of such panels are challenging but imperative tasks in support of EQA programs for NGS-based HIV-DRT and the validation of relevant bioinformatics tools. Here, we present criteria that can guide the design of such dry panels, which were discussed in the Second International Winnipeg Symposium themed for EQA strategies for NGS HIVDR assays.

Vibration of two-phase local/nonlocal Timoshenko nanobeams with an efficient shear-locking-free finite-element model and exact solution

According to paradoxical behaviors of common differential nonlocal elasticity, employing the two-phase local/nonlocal elasticity, to consider the size effects of nanostructures, has recently attracted the attentions of nano-mechanics researchers. Now, due to more complexity of the two-phase elasticity problems than the differential nonlocal ones, it is essential to achieve efficient methods for studying the mechanical characteristics of two-phase nanostructures. Therefore, in this work, the exact solution corresponding to the vibrations of two-phase Timoshenko nanobeams is provided for the first time. Furthermore, the shear-locking problem is investigated in the case of two-phase finite-element method (FEM), and since the FE model of local/nonlocal nanobeam is more complex than the classic one, due to coupling of all elements together, one of the main aims of the present work is to create an efficient locking-free local/nonlocal FEM with a simple and efficient beam element. To extract the exact natural frequencies, the basic form of two-phase elasticity is replaced with the equal differential equation and the obtained higher-order governing equations are solved by satisfying additional constitutive boundary conditions. To construct the two-phase FE model, an efficient and simple shear-locking-free Timoshenko beam element is introduced, and next, basic form of two-phase elasticity including local and integral form of nonlocal elasticity is utilized. No need for satisfying higher-order boundary conditions, shear-locking-free, simple shape functions and well convergence are advantages of the present two-phase finite element model. Several convergence and comparison studies are conducted, and the reliability and locking-free properties of the present two-phase finite element model are confirmed. Also, the influences of two-phase elasticity on the natural frequencies of Timoshenko nanobeams with different thickness ratios are studied.

Accurate frequency estimation for removal of orbital fringes in SAR interferograms

ABSTRACT Differential interferogram of space-borne SAR data may be affected by residual orbital fringes resulting from errors in the orbit (i.e. baseline) determination that hinder subsequent InSAR applications (deformation or elevation measurements). In this paper, an easy-to-use method was developed to remove the orbit errors in complex SAR interferogram in the radar coordinate system by accurately estimating the frequencies of the orbital ramp phase. The method first finds an approximate integer frequency by searching for the peak of the sum of the Fourier spectra of all the rows of the interferogram. It then uses the 100-order Burg spectral estimation algorithm to estimate the power spectrum for each row of the interferogram, and calculates the high-resolution power spectrum over the frequency range Hz. Finally, the method obtains the exact frequency of the orbital ramp phase in the row direction by searching for the peak of the sum of the high-resolution power spectra of all rows. By performing the same operations on all columns of the interferogram, the exact frequency in the column direction can be obtained. The orbital ramp phase can be calculated using these exact frequencies and be removed from the interferogram. Validation tests demonstrate that our method can accurately estimate the frequencies of the orbital ramp phase in the row and column directions, and eliminate the orbital ramp fringes from the simulated and actual interferograms. The proposed method only needs to calculate the high-resolution spectrum in a small frequency range, so the burden of calculation is light. The proposed method is easy to use since phase unwrapping or a priori satellite orbit information is not required.

Exact Nonlinear Dynamic Analysis of a Beam With a Nonlinear Vibration Absorber and With Various Boundary Conditions

AbstractWe study the nonlinear vibration of a beam with an attached grounded and ungrounded nonlinear vibration absorber (NVA) using the exact natural frequencies and mode shapes of the loaded beam. The nonlinearity in the beam is due to midplane stretching and that in the NVA is of cubic stiffness nonlinearity. We consider various boundary conditions and derive their closed-form characteristic equations and mode shapes. The method of multiple scales (MMS) is directly applied to the nonlinear partial differential equations of motion to obtain explicit expressions of the nonlinear frequency, modulation, and loci of the saddle-node bifurcation equations. Our analytical approach is validated using direct numerical simulation. Parametric studies demonstrate that the performance of the NVA does not only depend on its key design variables and location, but also on the boundary conditions, midplane stretching of the beam, and type of configuration (i.e., grounded NVA versus ungrounded NVA). Our analysis also indicates that the use of common approach such as employing approximate modes in estimating the nonlinear response of a loaded beam produces significant error (i.e., up to 1200% in some case). These observations suggest that the exact modes shape and natural frequencies are required for a precise investigation of the nonlinear dynamic of loaded beams. These findings could contribute to the design improvement of NVAs, microelectromechanical systems (MEMS), energy harvesters, and metastructures.

Free vibration and stability of an axially moving thin circular cylindrical shell using multiple scales method

This paper investigates the linear free vibration of axially moving simply supported thin circular cylindrical shells with constant and time-dependent velocity considering the effect of viscous structure damping. Classical shell theory is employed to express strain-displacement relation. Linear elasticity theory is used to write stress–strain relation considering Hook’s Law. Governing equations in cylindrical coordinates are derived using the Hamilton principle. Equilibrium equations are rewritten with the help of Donnell–Mushtari shell theory simplification assumptions. Motion equations for displacements in axial and circumferential directions are solved analytically concerning to displacement in the radial direction. As the displacement in the radial direction is the combination of driven and companion modes, the third motion equation is discretized using the Galerkin method. The set of ordinary differential equation obtained from the Galerkin method is solved using the steady-state method, which in practice leads to the prediction of the exact frequencies of vibration. By employing multiple scale method the critical speed values of a circular cylindrical shell and several types of instabilities are discussed. The numerical results show that by increasing the mean velocity, the system always loses stability by the divergence instability in different modes, and the critical speed values of lower modes are higher than those of higher modes. As well as the unstable regions for the resonances between velocity function fluctuation frequencies and the linear combination of natural frequencies is gained from the solvability condition of second order multiple scale method. The accuracy of the method is checked against the available data.

An investigation of airfoil dual acoustic feedback mechanisms at low-to-moderate Reynolds number

An experimental investigation was performed in an anechoic wind tunnel involving acoustic measurements, hot-wire anemometry and surface flow visualisation techniques to investigate airfoil tonal noise generating mechanisms. Tests were conducted using a NACA 0012 airfoil at corrected angles of attack of 0° and 1.58° and Reynolds numbers of 50,000 to 150,000. A dual acoustic feedback model is presented, where feedback processes act independently on the airfoil pressure and suction surfaces between the point of boundary layer separation and the trailing edge. It is proposed that the tones generated on both airfoil surfaces, with the same or similar frequencies on each surface, interfere constructively. The primary tone possesses near exact frequencies on both surfaces, whereas the secondary tones have larger differences in frequencies between both surfaces, thus explaining their relative magnitudes based on acoustic superposition. This model provides a better comparison with the experimentally obtained tonal frequencies than the existing feedback models. Despite this agreement, the feedback model cannot perfectly predict the acoustic tones as the tones are not perfectly equispaced. An empirical feedback length is calculated by reverse engineering an acoustic feedback length scale by using the recorded primary tone as an input that also minimises the secondary tone prediction errors. This empirical length closely matches the dual acoustic feedback model presented in this paper.

Multiple Output Inductive Charger for Electric Vehicles

Multiple output chargers have widely been adopted in various electronic devices due to their benefit concerning cost, power density, and space for installation. On the contrary, inductive power transfer (IPT) has been applied increasingly in electric vehicles (EVs) since it is safer and more convenient as compared to conductive chargers. However, research works on multiple output chargers using an IPT system for EV charging applications are rarely presented. This paper proposes a new concept of a multiple output IPT charger, which can charge several output batteries independently and simultaneously by adopting only one full bridge inverter at the primary side combining with multiple transmitters. A total of two possible IPT-coil structures are analyzed, and the minimum distance between each channel's coils is determined to neglect the cross-coupling between them. A total of two options are proposed to attain a zero phase angle (ZPA) condition for the primary inverter of the proposed system. First option is to operate the compensation tanks of every output channel at exact ZPA frequencies. The other option is to let one channel work in the inductive region of its input impedance and other channel work in the capacitive region. By adopting an appropriate design, the reactive powers of these tanks can be nearly canceled by each other and the phase of inverter current can be nearly in-phase with the input voltage as a result. A total of two proposed options are compared to give recommendation whether option 1 or 2 should be selected according to various applications’ requirements. To simplify control complexity, IPT output current sources topologies are selected, compared, and analyzed to construct the proposed multiple output system in both above-mentioned options. Double-sided LCC and series–parallel topologies are adopted to demonstrate the proposed idea for options 1 and 2, respectively. In order to verify feasibility and validity of the proposed method, experimental results of two output channels with the total output power of 1.5 kW are provided. Experimental results indicate that the ZPA is achieved for the primary inverter with both of the above-mentioned options even under different load conditions. Some comparisons between the conventional and the proposed IPT charging structure in terms of cost, reliability, and complexity are included in the discussion section.

The evolution of lying in well-mixed populations.

Lies can have profoundly negative consequences for individuals, groups and even for societies. Understanding how lying evolves and when it proliferates is therefore of significant importance for our personal and societal well-being. To that effect, we here study the sender-receiver game in well-mixed populations with methods of statistical physics. We use the Monte Carlo method to determine the stationary frequencies of liars and believers for four different lie types. We consider altruistic white lies that favour the receiver at a cost to the sender, black lies that favour the sender at a cost to the receiver, spiteful lies that harm both the sender and the receiver, and Pareto white lies that favour both the sender and the receiver. We find that spiteful lies give rise to trivial behaviour, where senders quickly learn that their best strategy is to send a truthful message, while receivers likewise quickly learn that their best strategy is to believe the sender's message. For altruistic white lies and black lies, we find that most senders lie while most receivers do not believe the sender's message, but the exact frequencies of liars and non-believers depend significantly on the payoffs, and they also evolve non-monotonically before reaching the stationary state. Lastly, for Pareto white lies we observe the most complex dynamics, with the possibility of both lying and believing evolving with all frequencies between 0 and 1 in dependence on the payoffs. We discuss the implications of these results for moral behaviour in human experiments.

Reply to “Comment on ‘Some exact quasinormal frequencies of a massless scalar field in Schwarzschild spacetime’”

We address the concerns raised by the author of "Comment: Some exact quasinormal frequencies of a massless scalar field in Schwarzschild spacetime" appeared in arXiv:1807.05940. In particular, we explain why the analysis in our paper [Phys. Rev. D{\bf{98}}, 024017 (2018)] is relevant and correct.