Internal Resonance Frequency Research Articles

Interplay between internal resonance and nonlinear magnetic interaction for multi-directional energy harvesting

To investigate the coupling effects between the internal resonance and nonlinear magnetic interaction for multi-directional energy harvesting, this study proposed a single piezoelectric cantilever–nonlinear magnetic pendulum structure. The proposed structure was mainly composed of a piezoelectric cantilever beam, a magnetic pendulum fixed at the free end of the beam, and a base permanent magnet below the pendulum. Internal resonance was induced by the nonlinear coupling between the pendulum motion in the two-dimensional space and the beam bending vibration at resonance. The magnetic interactions between the magnetic pendulum and the base magnet introduced nonlinearity. The proposed structure was theoretically modeled and experimentally realized to demonstrate its energy harvesting capabilities. Owing to the positive coupling effects between the internal resonance and nonlinearity in the proposed structure under the properly chosen parameters, the experimental results showed that the internal resonance bandwidth of the proposed structure for the x-direction energy harvesting was three times wider than that of the traditional piezoelectric cantilever-pendulum system. Meanwhile, the proposed structure also achieved an additional internal resonant frequency range (3.4 Hz–4.3 Hz) for improving the z-direction energy harvesting performance. The experimental maximum power output of the proposed structure achieved 0.64 mW at 7.5 Hz in the investigated frequency domain.

Identification by means of a genetic algorithm of nonlinear damping and stiffness of continuous structures subjected to large-amplitude vibrations. Part II: one-to-one internal resonances

A procedure is presented to identify the nonlinear damping and stiffness parameters of harmonically forced continuous systems showing nonlinear vibrations with a one-to-one internal resonance. The identification is obtained by using a two-degree-of-freedom (2DOF) model. Cubic nonlinear damping is introduced in the 2DOF model in addition to the classical viscous one. Different damping coefficients are considered within or outside the internal resonance frequency range. The parameter estimation relies on the harmonic balance method. It is shown that a three-harmonic expansion is needed to obtain a converged solution, although often only the first harmonic, without mean component, is experimentally measured with accuracy. The proposed novel cascade procedure consists in (i) a single-term harmonic balance parameter estimation used as initiation of (ii) a minimization of the distance between data and a three-term harmonic balance model by means of a genetic algorithm. These procedures are validated by parameter identification on synthetic (numerically generated) and experimentally measured frequency–responses. The nonlinear damping model is validated by comparison with level-adjusted linear damping model estimated at each level of harmonic force, demonstrating its ability to account for the evolution of damping with the vibration amplitude for different branches of solutions.

A Time-Shifting Algorithm for Alleviating Convergence Difficulties at Interior Acoustic Resonance Frequencies

This paper proposes a time-shifting boundary element method in the time domain to calculate the radiating pressures of an arbitrary object pulsating at eigenfrequencies of the interior (i.e., interior resonance frequencies). In this paper, the frequency shifting is time-step-dependent and could be viewed as an iterative, or relaxation, technique for the solution of the problem. The proposed method avoids numerical problems due to the internal resonance frequency by initializing the iteration with each scaled frequency. The scaled frequency is approximately equal to the true frequency at the last iterating time step. A sphere pulsating at the eigenfrequency in an infinite acoustic domain was calculated first; the result was compared with the analytical solution, and they were in good agreement. Moreover, two arbitrary-shaped radiators were taken as study cases to predict the radiating pressures at the interior resonance frequencies, and robustly convergent results were obtained. Finally, the accuracy of the proposed method was tested using a problem with a known solution. A point source was placed inside the object to compute the surface velocities; the computed surface pressures were identical to the pressures computed using the point source.

Design and manufacturing of an electrostatic MEMS relay for high power applications

This paper addresses the design and manufacturing of a crab-leg based MEMS relay for a high power application. Thanks to a contact resistance lower than 100 mΩ, the relay can hold a current in the order of magnitude of an Ampere without further thermal limitation for the final application. First, an analytical model of the relay, considering its geometry and the contact resistance, is presented. The model is developed in order to focus on the contact deformation. It ensures a low bending moment due to the target contact deformation below 1 nm reducing thus the contact resistance. The design has also been done to overcome the internal resonance frequencies of the future application, i.e. electrical motor. Then, a novel manufacturing process for thicker MEMS is proposed based on micro-fabrication techniques. Finally, the performances of the relay are evaluated and a contact resistance as low as 65 mΩ (comparable to the state-of-the-art) for an applied force of 5 mN, much lower than values reported in the literature is presented.

Exploiting double jumping phenomenon for broadening bandwidth of an energy harvesting device

The steady state response of a particular harvesting system is investigated under the condition of external and internal resonance, with emphasis on the double jump phenomenon. Following the trend of recent researches on exploring nonlinearity aspects for broadening the frequency resonance bandwidth, the problem of effective energy harvesting from a broadband source is dealt with. The proposed harvester can be embedded within vibrational structures and can dually act as a vibration absorber. The governing non-linear partial differential equations are truncated into a set of perturbed equations via Galerkin method. The method of multiple scales is applied to derive the modulated amplitude versus frequency at the vicinity of flapwise and chordwise primary resonances, as well as around other internal resonance frequencies. The amplitude-frequency response plot reveals resonance peaks bending to the left and right, i.e., splitting into two different tongues in contrast to conventional jumps which lean only toward higher or lower frequency directions. Numerical results demonstrate that this internal resonance-based harvesting design can produce sufficient power for the consumption of typical MEMS devices.

A mechanism for overcoming the effects of the internal resonances of coil springs on vibration transmissibility

Internal resonances in suspension springs can result in significantly increased vibration transmission at the corresponding natural frequencies. Particularly for the case of metal coil springs used in vehicle suspensions, these internal resonances can be as low as 50 Hz and can lead to increased structure-borne noise in certain frequency bands. Although, in practice, this can be mitigated to some extent by using rubber pads in series with the coil springs, high vibration transmission in the vicinity of the internal resonance frequencies remains an important issue. In this paper, a mechanism is identified that can overcome the increased vibration transmission due to the internal resonances. This involves the use of a pivoted arm with a pivot bushing that is relatively stiff for translational motion. The quasi-static load is primarily carried by the suspension spring but the dynamic load at higher frequencies is also transmitted through the pivot bushing. By appropriate selection of parameters, in particular the moment of inertia of the pivoted arm and the stiffness of the pivot bushing, it can be arranged that the dynamic loads acting through the spring and the bushing largely cancel each other out at the spring natural frequency. It is shown that this mechanism is contained within common designs of railway vehicle primary suspension. Nevertheless, their design is largely based on their quasi-static behaviour and this principle of dynamic load cancellation has not previously been explained. The dynamic behaviour of different suspension arrangements is compared and the selection of suitable parameter values that can achieve this dynamic load cancellation is explained. Field measurements are also presented which confirm this behaviour.

Eliminating the fictitious frequency problem in BEM solutions of the external Helmholtz equation

The problem of the fictitious frequency spectrum resulting from numerical implementations of the boundary element method for the exterior Helmholtz problem is revisited. When the ordinary 3D free space Green’s function is replaced by a modified Green’s function, it is shown that these fictitious frequencies do not necessarily have to correspond to the internal resonance frequency of the object. Together with a recently developed fully desingularized boundary element method that confers superior numerical accuracy, a simple and practical way is proposed for detecting and avoiding these fictitious solutions. The concepts are illustrated with examples of a scattering wave on a rigid sphere.

Combined Source Integral Equation-Based Theory of Characteristic Modes for Impenetrable Bodies

The theory of characteristic modes (TCM) based on the combined source integral operator (CSIO) is developed for perfect electric conductors and for impedance boundary condition. This formulation is similar to the one based on the combined field integral operator (CFIO), circumvents the interior resonance problem appearing in the electric field integral operator-based TCM. The eigenvalues obtained by the CSIO-based formulation agree well with the analytical and numerical CFIO-based solutions. However, the eigenvectors of the resonating modes computed with the CSIO-based approach are found to be corrupted at the internal resonance frequencies.

Analysis of Characteristics of Al MKID Resonators

We have prepared two kinds of Al resonators using thin films made by evaporation or sputtering and studied temperature behavior of their quality factors and resonance frequencies with the help of the extended Mattis-Bardeen (M-B) equations and its approximated analytical expressions. We have found that temperature behavior of both the internal quality factor and resonance frequency shift measured in evaporated Al thin-film resonators are well agreed with those calculated by the analytical expressions of the complex conductivity given by the M-B theory. In the Al thin film resonators made by sputtering, the internal quality factor and resonance frequency shift show a peak and a bump near 0.17 K in the respective temperature dependence. It is found that inverse of the internal quality factor is well approximated by a-b*log(T) below 0.15 K, where T is the temperature. This type of temperature dependence strongly indicates the existence of the magnetic impurity scattering of residual quasiparticles due to the Kondo effect. It is shown that temperature dependence of the internal quality factor and resonance frequency shift observed in the sputtered Al resonators can be well fitted by the theory taking the Kondo effect and kinetic inductance of the residual quasiparticles into account.

Analytical Modeling and Experimental Verification of Nonlinear Mode Coupling in a Decoupled Tuning Fork Microresonator

This paper provides the analytical and experimental studies into the nonlinear mode coupling in a tuning fork microresonator, with electrostatic actuation at forced and internal resonance frequencies. The analytical investigation leads to modal equations that take into account kinematic and electrostatic nonlinearities. The equations of motion are derived using Lagrange’s energy method. The theoretical resonance curves are determined by using the two-variable expansion perturbation technique near simultaneous subharmonic and internal resonances. The two desired mode shapes of the device are tailored to establish an approximate two-to-one frequency ratio between their natural frequencies. A sample device design is fabricated in a commercial foundry process. The influence of AC driving levels and a detuning parameter, due to inevitable fabrication imperfections, on the system dynamics are investigated theoretically and experimentally. It is shown that the deviation from ideal internal resonance condition separates the region of the nonlinear vibration into two distinct excitation frequencies. The model and simulated results obtained by the perturbation analysis are validated by comparing them with the experimental results. [2017–0297]

Characteristic Mode Equations for Impedance Surfaces

Characteristic mode formalism is presented for closed surfaces modeled with the impedance boundary condition. The characteristic equations are expressed in terms of the electric, magnetic, and combined field integral operators (EFIO, MFIO, and CFIO). Similarly as for perfectly conducting (PEC) surfaces, the modal solutions based on EFIO (MFIO) are corrupted by spurious solutions, as the frequency coincides with the internal resonance frequency of a cavity with PEC (perfect magnetic conductor) walls, whereas the CFIO-based approach gives physically correct modal solutions.

Micromechanical and surface adhesive properties of single saccharomyces cerevisiae cells

The adhesion and mechanical properties of a biological cell (e.g. cell membrane elasticity and adhesiveness) are often strong indicators for the state of its health. Many existing techniques for determining mechanical properties of cells require direct physical contact with a single cell or a group of cells. Physical contact with the cell can trigger complex mechanotransduction mechanisms, leading to cellular responses, and consequently interfering with measurement accuracy. In the current work, based on ultrasonic excitation and interferometric (optical) motion detection, a non-contact method for characterizing the adhesion and mechanical properties of single cells is presented. It is experimentally demonstrated that the rocking (rigid body) motion and internal vibrational resonance frequencies of a single saccharomyces cerevisiae (SC) (baker’s yeast) cell can be acquired with the current approach, and the Young’s modulus and surface tension of the cell membrane as well as surface adhesion energy can be extracted from the values of these acquired resonance frequencies. The detected resonance frequency ranges for single SC cells include a rocking (rigid body) frequency of 330 ± 70 kHz and two breathing resonance frequencies of 1.53 ± 0.12 and 2.02 ± 0.31 MHz. Based on these values, the average work-of-adhesion of SC cells on a silicon substrate in aqueous medium is extracted, for the first time, as . Similarly, the surface tension and the Young’s modulus of the SC cell wall are predicted as and 9.20 ± 2.80 MPa, respectively. These results are compared to those reported in the literature by utilizing various methods, and good agreements are found. The current approach eliminates the measurement inaccuracies associated with the physical contact. Exciting and detecting cell dynamics at micro-second time-scales is significantly faster than the currently known metabolistic response times of cells (milliseconds to seconds), thus, it has the potential to decouple metabolistic and mechanotransduction effects from external stimuli and to operate at high throughput rates.

Internal resonance and low frequency vibration energy harvesting

A nonlinear vibration energy harvester with internal resonance is presented. The proposed harvester consists of two cantilevers, each with a permanent magnet on its tip. One cantilever has a piezoelectric layer at its base. When magnetic force is applied this two degrees-of-freedom nonlinear vibration system shows the internal resonance phenomenon that broadens the frequency bandwidth compared to a linear system. Three coupled partial differential equations are obtained to predict the dynamic behavior of the nonlinear energy harvester. The perturbation method of multiple scales is used to solve equations. Results from experiments done at different vibration levels with varying distances between the magnets validate the mathematical model. Experiments and simulations show the design outperforms the linear system by doubling the frequency bandwidth. Output voltage for frequency response is studied for different system parameters. The optimal load resistance is obtained for the maximum power in the internal resonance case. The results demonstrate that a design combining internal resonance and magnetic nonlinearity improves the efficiency of energy harvesting.

Analysis of Parameters Assessment on Laminated Rubber-Metal Spring for Structural Vibration

This paper presents the analysis of parameter assessment on laminated rubber-metal spring (LR-MS) for vibrating structure. Three parameters were selected for the assessment which are mass, Young's modulus and radius. Natural rubber materials has been used to develop the LR-MS model. Three analyses were later conducted based on the selected parameters to the LR-MS performance which are natural frequency, location of the internal resonance frequency and transmissibility of internal resonance. Results of the analysis performed were plotted in frequency domain function graph. Transmissibility of laminated rubber-metal spring (LR-MS) is changed by changing the value of the parameter. This occurrence was referred to the theory from open literature then final conclusion has been make which are these parameters have a potential to give an effects and trends for LR-MS transmissibility.

Wave Algorithm Analysis of Damping Energy Transfer between Two Globally Coupled Vibro-Impact Oscillators with Proportional Viscous Damping (In Case of Perfect Elastic Collision at Balanced Position)

In this paper, we study periodic energy transfer in multiple vibro-impact oscillators under proportional viscous damping by using wave algorithm. Internal resonance frequency is obtained by the condition that some off-diagonal elements become to 0 in state transition matrix. Under equivalent modal damping rate, we derive the condition of periodic damped and periodic energy transfer that contains sub-harmonic resonance which depends on mass ratio between the impact and non-impact small oscillators. Under non-equivalent modal damping rate, modulation of the frequency in imperfect damped energy transfer is observed. We obtain a state transition matrix of non-equivalent modal damping rate as the perturbation of that in equivalent. The modulation of periodic damped energy transfer depends on the decay of the modal damping rate in the small impact oscillator.

Fatigue damage identification by means of modal parameters

Object of the present paper is an experimental investigation about high cycles fatigue damage and corresponding variation of modal parameters (internal damping and resonance frequency) in steel specimens. On the basis of a modal approach, a mixed technique has been developed in order to relate fatigue damage and intrinsic properties of the material. The experimental procedure consists of the modal parameters assessment on steel specimens, once before fatigue test beginning, and thus repeatedafter every 105 cycles, both with constant and increasing loading levels. Infrared thermography has been used to emphasize the specimen thermal emission and the related damage phenomena.

Dynamic Analysis of a Si/SiGe-Based Impact Ionization Avalanche Transit Time Photodiode With an Ultrahigh Gain-Bandwidth Product

We investigate the dynamic performance of a Si/SiGe-based impact ionization avalanche transit time photodiode (PD) fabricated on a standard Si substrate that operates at the 830-nm wavelength. The bandwidth-enhancement effect under negative-photoconductance (NPC) operation can greatly relax the internal transit time as well as the tradeoff between the gain and bandwidth performance that characterizes the traditional avalanche PD. Our modeling and measurement results show that the extracted internal resonant frequency increases significantly with the reverse leakage current. By choosing the proper bias voltage in the NPC region, we can simultaneously achieve a wide 3-dB bandwidth (30 GHz), ultrahigh gain-bandwidth product (690 GHz) with a 53.2% external efficiency at unit gain, and clear eye opening at 10 Gb/s.

Optical nanoswitch: an engineered plasmonic nanoparticle with extreme parameters and giant anisotropy

Naturally available optical materials are known to provide a wide variety of electric responses, spanning from positive to negative permittivity values. In contrast, owing to drastically modified conduction properties at the microscopic level, at such high frequencies magnetism and conductivity are very challenging to realize. This implies that extreme (high or low) values of permittivity, although highly desirable for a wide range of optical applications, are difficult to realize in practice. Here, we suggest the design of an engineered resonant nanoparticle composed of two conjoined hemispheres, whose optical response may be changed at will from an ideal electric conductor to an ideal magnetic conductor. Near the nanoparticle internal resonant frequency, we derive a closed-form solution that describes the electromagnetic response of this nanoparticle, showing how its light interaction may become dramatically dependent on the local field polarization, passing through all possible impedance values (from zero to infinity) by a simple mechanical or polarization rotation. Considering realistic frequency dispersion and loss in optical materials, we further show that these concepts may be applied to different geometries, with possibility for future experimental feasibility. We forecast various applications of this geometry as an optical nanoswitch, a novel nanocircuit element and as a building block for novel optical metamaterials.

A sodium ordering transition above room temperature in Na xCoO 2 deduced by mechanical spectrum

The mechanical spectrum of Na 0.66CoO 2 above room temperature was measurement using the vibrating reed method at kilohertz frequency. A novel transition was observed around 427 K as indicated by temperature-dependent internal friction and resonance frequency. The characteristic transition temperature is defined as the start of a step increase of resonance frequency with the decrease of temperature, which is concurrent with the decrease of internal friction below a plateau. At the same time, this characteristic transition temperature shifts towards lower temperatures at a lower cooling rate, or higher heating rate during its respective thermodynamic processes. This unconventional behavior seems to be explained by critical slowing down at a second-order phase transition. Furthermore, sodium ordering is expected for this phase transition.

Chaotic motions and fractal basin boundaries in spring-pendulum system

This study investigates the chaotic response of the spring-pendulum system. In this system besides of strange attractors, multiple regular attractors may co-exist for some values of system parameters, and it is important to study the global behavior of the system using the basin boundaries of the attractors. Here multiple scales method is used to distinguish the regions of stable and unstable attractors. Early studies show that there are unstable regions for the spring-pendulum system. In this study using bifurcation diagrams and Poincaré maps, it is shown that in some cases the response becomes quasi-periodic or chaotic for some deviations from external and internal resonance frequencies. Also it will be shown that the response is sensitive to the value of damping parameters, which may result in chaotic response. Results show that the jumping phenomena may occur when multiple regular attractors exist. Using basin boundaries of attractors it is also shown that in some regions these boundaries are fractal.