Secondary Resonance Research Articles

Microcantilever dynamics in tapping mode atomic force microscopy via higher eigenmodes analysis

Microcantilever dynamics in tapping mode atomic force microscopy (AFM) is addressed via a multimode approximation, which allows to consider external excitation at primary or secondary resonance and to highlight the effect of higher order eigenmodes. Upon presenting the AFM model and its multimode discretization, the dynamic response is investigated via numerical simulation of single- and three-mode models by considering different bifurcation parameters. Typical features of tapping mode AFM response as nonlinear hysteresis, bistability, higher harmonics contribution, impact velocity, and contact force are addressed. The analysis is conducted by evaluating damping of higher modes according to the Rayleigh criterion, which basically accounts for structural damping representative of the behavior of AFMs in air. Nominal damping situations more typical of AFMs in liquids are also investigated, by considering sets of modal Q-factors with different patterns and ranges of values. Variable attractive-repulsive effects are highlighted, along with the possible presence of a coexisting multi-periodic orbit when the system is excited at second resonance.

Experimental study on moonpool resonance of offshore floating structure

Offshore floating structures have so-called moonpool in the centre area for the purpose of drilling, installation of subsea structures, recovery of Remotely-Operated Vehicle (ROV) and divers. However, this vertical opening has an effect on the operating performance of floating offshore structure in the vicinity of moonpool resonance frequency; piston mode and sloshing mode. Experimental study based on model test was carried out. Moonpool resonance of floating offshore structure on fixed condition and motion free condition were investigated. And, the effect of cofferdam which is representative inner structure inside moonpool was examined. Model test results showed that Molin's theoretical formula can predict moonpool resonance on fixed condition quite accurately. However, motion free condition has higher resonance frequency when it is compared with that of motion fixed. The installation of cofferdam moves resonance frequency to higher region and also generates secondary resonance at lower frequency. Furthermore, it was found that cofferdam was the cause of generating waves in the longitudinal direction when the vessel was in beam sea.

Finite element computation and experimental validation of sloshing in rectangular tanks

Finite element computation and experimental validation of sloshing in rectangular tanks near the primary and secondary resonance modes are presented. In particular, 2D free-surface evolution is studied. The computational analysis is based on solving the Navier-Stokes equations of incompressible flows with a monolithic solver that includes a stabilized formulation and a Lagrangian tracking technique for updating the free surface. The time-dependent behavior of the numerical and experimental wave heights at different control points are compared, where the experimental data is collected using ultrasonic sensors and a shake table that controls the motion of the rectangular container.

Tailoring Dispersion for Broadband Low-loss Optical Metamaterials Using Deep-subwavelength Inclusions

Metamaterials have the potential to create optical devices with new and diverse functionalities based on novel wave phenomena. Most practical optical systems require that the device properties be tightly controlled over a broad wavelength range. However, optical metamaterials are inherently dispersive, which limits operational bandwidths and leads to high absorption losses. Here, we show that deep-subwavelength inclusions can controllably tailor the dispersive properties of an established metamaterial structure thereby producing a broadband low-loss optical device with a desired response. We experimentally verify this by optimizing an array of nano-notch inclusions, which perturb the mode patterns and strength of the primary and secondary fishnet nanostructure resonances and give an optically thin mid-wave-infrared filter with a broad transmissive pass-band and near-constant group delay. This work outlines a powerful new strategy for realizing a wide range of broadband optical devices that exploit the unique properties of metamaterials.

Multimodal analysis of weakly nonlinear sloshing in a spherical tank

AbstractSloshing in a spherical tank due to horizontal excitation is studied by using the nonlinear multimodal method which involves the analytically approximate sloshing modes by Faltinsen & Timokha (J. Fluid Mech., vol. 703, 2012, pp. 391–401). General fully and weakly nonlinear modal equations are derived but an emphasis is on the Moiseev–Narimanov asymptotic modal system which implies that the forcing frequency is close to the lowest natural sloshing frequency and there are no secondary resonances in the forcing frequency range leading to a nonlinear resonant amplification of double and triple harmonics in higher modes. The Moiseev–Narimanov modal system is used to construct an asymptotic time-periodic solution and, thereby, classify the corresponding steady-state wave regimes appearing as stable and unstable planar waves and swirling. The results on the stability boundaries are compared with experiments by Sumner & Stofan (1963,Tech. Rep.TN D-1991, NASA Technical Note) and Sumner (1966,Tech. Rep.TN D-3210, NASA). A good agreement is established for$0. 2\leq h\lesssim 1$. Discrepancy for higher liquid depths$1\lesssim h\lt 2$are explained by secondary resonance.

The “bridging sign”: A MR finding for combined full-thickness tears of the subscapularis tendon and the supraspinatus tendon

In daily practice, we discovered one of the secondary magnetic resonance (MR) findings of the subscapularis (SSC) tendon tear, the "bridging sign", which has not been previously described. To describe the "bridging sign" on shoulder MR imaging and its radiological and clinical significance in patients with SSC tendon tear. Twenty-nine patients who had undergone shoulder arthroscopy and had full-thickness tear of the subscapularis tendon were enrolled. The medical records of the 29 patients were retrospectively reviewed for the duration of shoulder pain, rotator cuff tears, and associated arthroscopic findings: biceps tendon abnormality and superior glenoid labral tear. Then, preoperative shoulder MR images were retrospectively reviewed for the presence or absence of the "bridging sign" and associated MR findings: periarticular fluid and fatty atrophy of the supraspinatus and subscapularis muscles. The type of rotator cuff tear associated with the "bridging sign" was assessed and the sensitivity, specificity, and accuracy of the "bridging sign" for the diagnosis of a certain type of rotator cuff tear were calculated. Associated arthroscopic and MR findings and mean duration of the shoulder pain between the patients with and without the "bridging sign" were compared. The "bridging sign" was seen in 17 of 29 patients and corresponded to a complex of the torn and superomedially retracted subscapularis tendon, coracohumeral ligament, and superior glenohumeral ligament, adhered to the anterior margin of the torn supraspinatus (SSP) tendon on arthroscopy. All patients with the "bridging sign" had combined full-thickness tear (FTT) of the cranial 1/2 portion of the subscapularis tendon and anterior 1/2 portion of the SSP tendon. The sensitivity, specificity, and accuracy of the "bridging sign" for the diagnosis of combined FTTs of the SSC tendon and anterior portion of the SSP tendon were 81.0%, 100%, and 86.2%, respectively. The patients with the "bridging sign" had longer duration of shoulder pain and more frequent associated arthroscopic and MR findings than the patients without the "bridging sign". The "bridging sign" is a highly specific finding for combined full-thickness tears of the subscapularis tendon and anterior portion of the supraspinatus tendon, associated with more chronic shoulder pain and more sever rotator cuff tear.

The acoustic signature of decaying resonant phospholipid microbubbles

Sub-capillary sized microbubbles offer improved techniques for diagnosis and therapy of vascular related disease using ultrasound. Their physical interaction with ultrasound remains an active research field that aims to optimize techniques. The aim of this study is to investigate whether controlled microbubble disruption upon exposure to consecutive ultrasound exposures can be achieved. Single lipid-shelled microbubble scattered echoes have been measured in response to two consecutive imaging pulses, using a calibrated micro-acoustic system. The nonlinear evolution of microbubble echoes provides an exact signature above and below primary and secondary resonance, which has been identified using theoretical results based on the Mooney–Rivlin strain softening shell model. Decaying microbubbles follow an irreversible trajectory through the resonance peak, causing the evolution of specific microbubble spectral signatures. The characteristics of the microbubble motion causes varying amounts of shell material to be lost during microbubble decay. Incident ultrasound field parameters can thus accurately manipulate the regulated shedding of shell material, which has applications for both imaging applications and localized drug delivery strategies.

Investigation of dynamically compacted ground by HVSR-based approach

This paper proposes a HVSR (horizontal to vertical spectral ratio)-based approach to assess a deep and dynamically compacted fill area in Western Sydney. In addition to recognizing that the predominant resonance peak of the HVSR curve is a reflection of the impedance contrast between the surface layers and bedrock, the present paper recognizes that the secondary resonance peaks of the curve at higher frequencies may reflect strong impedance contrast within surface layers. This concept has been applied to develop a methodology of HVSR-based approach relying on the measurement of the HVSR of microtremors at measuring stations, and calibration and verification by independent mechanical and MSOR (multichannel simulation with one receiver) tests. The use of MSOR tests is introduced in this paper to facilitate the calibration of the HVSR forward model, particularly in terms of providing information for the initial guess of the shear wave velocity, Vs, profile in the HVSR forward modelling. The present paper demonstrates the effective use of the HVSR-based approach to assess dynamic compaction in the gaps away from and not covered by the mechanical tests. The mapping between the depth of bedrock and the predominant resonance frequency is also extended to include the mapping of the depths of layers with strong impedance contrasts to the secondary resonance peaks, after the data have been verified by independent mechanical tests.

UNSTEADY POISEUILLE FLOW IN A POROUS ROTATING CHANNEL

Viscous flow in a channel filled with a porous medium is a fundamental problem. The channel may also rotate as in a centrifuge, spacecraft, or under earth's self-rotation. The extended Darcy−Brinkman equations are solved for impulsive and oscillatory pressure gradients. The results show strong interactions among rotation, unsteadiness, and porous permeability. Phenomena such as secondary flow, inertial oscillations and resonances may occur. Increase of the porous parameter (inverse square root of permeability) depresses both the magnitude and (spatial and temporal) oscillations. For a given rotation, the optimum porous medium for maximized steady through flow is found.

Unveiling the Influence of Dark Matter in Axially Symmetric Galaxies

AbstractWe investigate the regular or chaotic nature of orbits of stars moving in the meridional plane (R,z) of an axially symmetric galactic model with a dense, massive spherical nucleus and a dark matter halo component. In particular, we study the influence of the fractional portion of the dark matter, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families. In an attempt to distinguish between regular and chaotic motion, we use the fast Lyapunov indicator method to extensive samples of orbits obtained by integrating numerically the equations of motion as well as the variational equations. Furthermore, a technique which is based mainly on the field of spectral dynamics that utilises the Fourier transform of the time series of each coordinate is used for identifying the various families of regular orbits and also to recognise the secondary resonances that bifurcate from them. Two cases are studied in our work: (i) the case where we have a disk galaxy model and (ii) the case where our model represents an elliptical galaxy. A comparison with early related work is also made.

Stability of the Lagrangian pointL4in the spatial restricted three-body problem – application to exoplanetary systems

This paper is devoted to the study of the stability of the Lagrangian point L4 in the spatial restricted three-body problem and to the possibility of inclined Trojan-like objects in exoplanetary systems (single and binary star systems). The stability is investigated by numerical methods, computing stability maps in different parameter planes. In the case of circular motion of the primary bodies, it is shown that there are stable orbits up to an inclination i = 61° of the test particle. At moderate inclinations (∼10° to ∼50°), we find that the stability limit in the mass ratio of the primaries extends well beyond the linear stability value of 0.0385 – with stable orbits existing even for extreme mass ratios of 0.048. In the case of elliptic motion of the primaries, the stable region in the mass ratio–eccentricity plane shrinks as the inclination increases, with no stable orbits being found for inclinations in excess of i = 61°. Both in the circular and elliptic cases, the structure of the stability regions is closely connected with secondary resonances between the librational frequencies. As an application, the results are applied to 35 known exoplanetary systems showing which of them may possess Trojan-like objects in inclined orbits.

Nonlinear multimode dynamics and internal resonances of the scan process in noncontacting atomic force microscopy

The focus of this paper is on the nonlinear multimode dynamics of a moving microbeam for noncontacting atomic force microscopy (AFM). An initial-boundary-value problem is consistently formulated, which includes both nonlinear dynamics of a microcantilever with a localized atomic interaction force, and a horizontal boundary condition for a constant scan speed and its control. The model considered is obtained using the extended Hamilton's principle, which yields two partial differential equations for the combined horizontal and vertical motions. The model incorporates, for the first time to our knowledge, two independent time-varying terms that depict the vertical base excitation of the AFM and the horizontal forcing term depicts the periodic scanning motion of the cantilever. Manipulation of these equations via a Lagrange multiplier enables construction of a modified equation of motion, which is reduced, via Galerkin's method, to a three-mode dynamical system, corresponding to finite amplitude AFM dynamics. The analysis includes a numerical study of the strongly nonlinear system culminating with a stability map describing an escape bifurcation threshold where the tip, at the free end of the microbeam, “jumps to contact” with the sample. Results include periodic, quasiperiodic, and non-stationary chaotic-like solutions corresponding to primary and secondary internal combination resonances, where the latter corresponds to energy balance between the cantilever modes.

Dual-band terahertz metamaterials based on nested split ring resonators

Two dual-band terahertz metamaterials based on nested split ring resonators (SRRs) were designed and fabricated on a flexible plastic substrate. Each nested SRR structure composed of two electric field coupled resonators exhibited two transmission minimums, which inherently come from the LC resonances of the respective SRRs. The primary and secondary resonance frequencies can be individually fine-tuned by adjusting the geometry of the respective resonator. The fabricated devices exhibited very low insertion loss of 3 dB in the transmission band and the high attenuation of 27 dB in the stop band.

Secondary resonances of a microresonator under AC-DC electrostatic and DC piezoelectric actuations

This article studies the secondary resonances of a clamped-clamped microresonator under combined electrostatic and piezoelectric actuations. The electrostatic actuation is induced by applying the AC-DC voltage between the microbeam and the electrode plate that lies at the opposite side of the microbeam. The piezoelectric actuation is induced by applying the DC voltage between upper and lower sides of piezoelectric layer. It is assumed that the neutral axis of bending is stretched when the microbeam is deflected. The drift effect of piezoelectric layer (the phenomenon where there is a slow increase of the free strain after the application of a DC field) is neglected. The equations of motion are solved by using the multiple scale perturbation method. The system possesses a subharmonic resonance of order one-half and a superharmonic resonance of order two. It is shown that using the DC piezoelectric actuation, the sensitivity of AC-DC electrostatically actuated microresonator under subharmonic and superharmonic resonances may be tuned. In addition, it is shown that the tuning domain of the microbeam under combined electrostatic and piezoelectric actuations at subharmonic and superharmonic conditions is larger than the tuning domain of microbeam under only the electrostatic actuation.

Influence of an electric field on the capillary analogue of the dead-water effect

It is shown that the capillary analogue of the dead-water effect strongly depends on an external electrostatic field: in the presence of the field, the number of nonlinear resonance situations increases sharply. The field increases the wave amplitudes and excites both degenerate and secondary combination resonances, which are not observed without the field.

Parametric noise squeezing and parametric resonance of microcantilevers in air and liquid environments

In this work, parametric noise squeezing and parametric resonance are realized through the use of an electronic feedback circuit to excite a microcantilever with a signal proportional to the product of the microcantilever's displacement and a harmonic signal. The cantilever's displacement is monitored using an optical lever technique. By adjusting the gain of an amplifier in the feedback circuit, regimes of parametric noise squeezing/amplification and the principal and secondary parametric resonances of fundamental and higher order eigenmodes can be easily accessed. The exceptionally symmetric amplitude response of the microcantilever in the narrow frequency bandwidth is traced to a nonlinear parametric excitation term that arises due to the cubic nonlinearity in the output of the position-sensitive photodiode. The feedback circuit, working in both the regimes of parametric resonance and noise squeezing, allows an enhancement of the microcantilever's effective quality-factor (Q-factor) by two orders of magnitude under ambient conditions, extending the mass sensing capabilities of a conventional microcantilever into the sub-picogram regime. Likewise, experiments designed to parametrically oscillate a microcantilever in water using electronic feedback also show an increase in the microcantilever's effective Q-factor by two orders of magnitude, opening the field to high-sensitivity mass sensing in liquid environments.

Nonlinear analysis of the finite-amplitude oscillations of a charged liquid layer on a rigid spherical core for the multimodal initial deformation of the free surface

Within the framework of the analytical asymptotic procedure, in the quadratic approximation in the small dimensionless amplitude of the capillary oscillation of a charged electroconductive fluid layer on the surface of a rigid spherical core, the problem of calculation of the free surface shape at an arbitrary moment is solved for a multimodal initial deformation. The conditions under which the internal nonlinear resonant interaction between the liquid layer oscillation modes and the intermodal energy exchange are realized are analyzed for both the degenerate and the secondary combinational resonances.

Secondary resonance magnetic force microscopy

In this study, we have developed secondary resonance magnetic force microscopy (SR-MFM) for imaging alternating magnetic fields from a sample surface at the secondary resonant frequency of the magnetic cantilever at the same time as the topographic image. SR-MFM images of alternating magnetic fields diverging from the main pole in a driving perpendicular magnetic recording head are presented, and the divergence and convergence of the fields are discussed. The spatial resolution of SR-MFM is estimated to be 18 nm; this is 2.5 times smaller than that of conventional MFM.

Intrinsic Finite Element Modeling of Nonlinear Dynamic Response in Helical Springs

This paper presents an efficient intrinsic finite element approach for modeling and analyzing the forced dynamic response of helical springs. The finite element treatment employs intrinsic curvature (and strain) interpolation and vice rotation (and displacement) interpolation and, thus, can accurately and efficiently represent initially curved and twisted beams with a sparse number of elements. The governing equations of motion contain nonlinearities necessary for large curvatures. In addition, a constitutive model is developed, which captures coupling due to nonzero initial curvature and strain. The method is employed to efficiently study dynamically-loaded helical springs. Convergence studies demonstrate that a sparse number of elements accurately capture spring dynamic response, with more elements required to resolve higher frequency content, as expected. Presented results also document rich, amplitude-dependent frequency response. In particular, moderate loading amplitudes lead to the presence of secondary resonances (not captured by linearized models), while large loading amplitudes lead to complex dynamics and transverse buckling.

Anterior Cruciate Ligament Reconstruction: MR Imaging Signs of Anterior Knee Laxity in the Presence of an Intact Graft

To determine the accuracy of secondary magnetic resonance (MR) imaging signs of anterior cruciate ligament (ACL) insufficiency in predicting clinical anterior translational knee laxity, in the presence of an intact graft, after ACL reconstruction. Institutional review board approval was obtained, and the requirement to obtain informed consent was waived. Fifty-two patients with ACL reconstruction and no injury to the contralateral knee were included. Three patients with visible ACL graft tears at MR imaging were excluded. All patients underwent MR imaging of the affected knee, functional assessment with use of the International Knee Documentation Committee (IKDC) score, and arthrometric testing of both the affected and uninjured knee. A side-to-side difference of more than 3 mm at 133 N was considered to be indicative of knee laxity. Two radiologists independently evaluated all MR images for seven signs of anterior knee laxity. The sensitivity, specificity, negative predictive value (NPV), and positive predictive value (PPV) were calculated for each MR imaging sign. Ten patients demonstrated knee laxity at arthrometric testing. Patients with knee laxity at arthrometric testing had significantly lower IKDC scores (P < .03). Sensitivities for all signs were low (0%-50%). Anterior translation of the tibia of more than 7 mm, a posterior cruciate ligament (PCL) angle of less than 100°, and a PCL curvature ratio of more than 0.39 demonstrated high specificity (range, 82%-90%). Uncovering of the posterior horn of the lateral meniscus and the posterior femoral line had a specificity of 97%-100% and a sensitivity of 0%. All signs had a low PPV and high NPV for laxity. All MR imaging signs demonstrated near-perfect interobserver agreement. Although MR imaging signs of knee laxity in the presence of an intact ACL graft have a high specificity, the low PPV means that MR imaging is of little value in predicting anterior knee laxity as demonstrated with mechanical testing.