Showing papers on "Nonlinear resonance published in 2018"
TL;DR: The nonlinear supercritical parametric dynamics of a Timoshenko microbeam subject to an axial harmonic excitation force is examined theoretically and theoretically by means of different numerical techniques, and employing a high-dimensional analysis.
88 citations
TL;DR: In this paper, a nonlocal strain gradient elasticity approach is proposed for the mechanical behavior of fluid-conveying nanotubes; a nonlinear analysis, incorporating stretching, is conducted for a model based on both a non-local theory along with a strain gradient one, and the energy minimisation is conducted via Hamilton's method for an oscillating nanotube subject to external forces.
78 citations
TL;DR: Recent research efforts to investigate the nonlinear coupling and energy transfers between multiple modes in micro/nano-mechanical resonators, focusing especially on intermodal coupling, internal resonance and synchronization are reviewed.
Abstract: Extensive development of micro/nano-electromechanical systems (MEMS/NEMS) has resulted in technologies that exhibit excellent performance over a wide range of applications in both applied (e.g. sensing, imaging, timing and signal processing) and fundamental sciences (e.g. quantum-level problems). Many of these outstanding applications benefit from resonance phenomena by employing micro/nanoscale mechanical resonators often fabricated into a beam-, membrane- or plate-type structure. During the early development stage, one of the vibrational modes (typically the fundamental mode) of a resonator is considered in the design and application. In the past decade, however, there has been a growing interest in using more than one vibrational mode for the enhanced functionality of MEMS/NEMS. In this paper, we review recent research efforts to investigate the nonlinear coupling and energy transfers between multiple modes in micro/nano-mechanical resonators, focusing especially on intermodal coupling, internal resonance and synchronization.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.
50 citations
TL;DR: In this article, a small-size numerical model based on the local interaction simulation approach is developed, enabling the efficient analysis of the contact acoustic nonlinearity during the wave crack interactions.
Abstract: This article presents the investigation of nonlinear scattering features of guided waves from rivet hole nucleated fatigue cracks considering the rough contact surface condition. A small-size numerical model based on the local interaction simulation approach is developed, enabling the efficient analysis of the contact acoustic nonlinearity during the wave crack interactions. The study starts with an idealized breathing crack model possessing smooth, perfectly kissing contact surfaces. Then, the nature of rough crack surfaces is considered with randomly distributed initial openings and closures. Several distinctive aspects of the nonlinear scattering phenomenon are discussed: (1) the amplitude effect, which renders significantly different nonlinear response under various levels of excitation wave amplitudes; (2) the directivity and mode conversion features, which addresses the scattering direction dependence of the fundamental and superharmonic wave mode components; (3) the nonlinear resonance phenomenon, which maximizes the nonlinear response during the wave crack interactions at certain excitation frequency ranges. This study demonstrates that these nonlinear features are substantially influenced by the crack surface condition and differ much between an idealized breathing crack and a rough crack in most practical cases. Fatigue tests on a thin aluminum plate with a rivet hole is conducted to induce cracks in the specimen. An active sensor array surrounding the crack zone is implemented to generate and receive ultrasonic guided waves in various directions. Current work emphasizes on using a highly efficient numerical model to explain the nonlinear features of scattered waves from fatigue cracks considering the rough crack surface condition. These special features may provide insights and guidelines for nonlinear guided wave based nondestructive evaluation and structural health monitoring system design. The paper finishes with discussion, concluding remarks, and suggestions for future work.
47 citations
TL;DR: In this article, the authors investigated the nonlinear forced dynamical behavior of a geometrically imperfect viscoelastic shear-deformable microplate and derived five coupled PDEs for the five independent displacements and rotations, which were truncated to a set of nonlinearly coupled ordinary differential equations via application of a two-dimensional modal decomposition based on the Galerkin technique.
45 citations
TL;DR: In this article, the nonlinear resonance of carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load was studied.
Abstract: This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton’s principle. The geometric nonlinearity and shear deformation effects are considered based on the von Karman assumptions and Reddy’s third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.
39 citations
TL;DR: In this paper, the authors developed a method for the synthesis of nonlinear frequency responses near an isolated resonance, based on data that can be easily and automatically obtained experimentally, and applied to a benchmark structure consisting of a cantilevered beam attached to a leaf spring undergoing large deflections.
34 citations
TL;DR: Energetic-particle-driven geodesic acoustic modes observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid and it is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling.
Abstract: Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.
29 citations
TL;DR: In this article, the authors reported the flexural wave propagation in an infinite NAM beam consisting of periodic Duffing resonators by considering the third harmonic generation and found that the NLR bandgap characterizes a distance-amplitude-dependent behavior that leads to a self-adaptive bandwidth in the far field.
Abstract: Nonlinear acoustic metamaterials (NAMs) provide new ways to control elastic waves. In this work, flexural wave propagation in an infinite NAM beam consisting of periodic Duffing resonators is reported by considering the third harmonic generation. Different analytical methods are proposed for the homogenized medium. By combining analytical and numerical approaches, we unveiled extensive physical properties of NAMs, including the nonlinear resonance, the effective density, the nonlinear locally resonant (NLR) bandgap, passbands, and the propagation and coupling of the fundamental and third harmonics. These characteristics are highly interrelated and they feature an identical near-field bifurcation frequency, which facilitates the prediction of functionalities. Moreover, we found that the NLR bandgap characterizes a distance-amplitude-dependent behavior that leads to a self-adaptive bandwidth in the far field. Our work will promote future studies, constructions and applications of NAMs with novel properties.
28 citations
TL;DR: In this paper, a beam-type porous biological implant in a 3D-printed architecture is designed with micron pore size using Scherrer and Williamson-Hall equation to evaluate the surface properties, morphology, and size of the composed powders.
Abstract: Having excellent biocompatibility and apatite mineralization as well as efficient mechanical properties makes bredigite as one of the most attractive bioceramics. A beam-type porous biological implant in a 3D-printed architecture is designed with micron pore size. The surface properties, morphology, and size of the composed powders are evaluated using Scherrer and Williamson-Hall equation. The effect of MNPs deposition into the bredigite bioceramics and correlation with temperature effect on roughness of the prepared bio-nanocomposite are also investigated for hyperthermia application potential. The composed powders are characterized by x-ray diffraction, and then scanning electron microscopy (SEM), differential scanning calorimetry, thermogravimetric analysis (weight change, TGA), and atomic force microscopy are utilized to evaluate the surface topography. The resonance response is the tendency of a bone scaffold to respond at prominent amplitude while the frequency of its oscillations is equal to the structure’s natural frequency of vibration. Therefore, based on the obtained mechanical properties via the experimental approach for the bio-nanocomposite material, an analytical solution based upon the multiple-timescale method is carried out to analyze the nonlinear primary resonance of a 3D-printed porous beam-type biological implant under uniform-distributed load.
According to SEM observations, there are hard agglomerates in the bredigite-magnetite nanoparticles (Br-MNPs) bio-nanocomposite material with low weight fraction of MNPs. However, they are broken down by increasing the amount of MNPs. Also, it is displayed that for lower MNPs weight fraction, the height of jump phenomenon related to the nonlinear resonance response is maximum and minimum for, respectively, irregular and mesoporous shapes of morphology, but their associated forcing amplitudes related to the bifurcation points are minimum and maximum, respectively.
25 citations
TL;DR: In this paper, fundamental issues related to bandwidth and nonlinear resonance in vibrational energy harvesting devices are investigated, and it is shown that using bandwidth as a criterion to measure device performance can be misleading.
TL;DR: In this paper, the authors studied stochastic resonance in an oscillator with nonlinear noise, fractional order external damping, and fractional-order intrinsic damping and derived the exact analytical expression of the output amplitude.
Abstract: We study stochastic resonance (SR) in an oscillator with nonlinear noise, fractional-order external damping, and fractional-order intrinsic damping. Using a moment equation, we derive the exact analytical expression of the output amplitude and find that fluctuations in the output amplitude are non-monotonic. Using numerical simulations we verify the accuracy of this analytical result. We find (i) that nonlinear noise plays a key role in system behavior and that the resonance of the output amplitude is diverse when there is nonlinear noise, (ii) that the order of the fractional-order damping strongly impacts resonant intensity and that the impact on resonant intensity of fractional-order external damping is opposite that of fractional-order intrinsic damping, and (iii) that the evolution of the output amplitude versus the frequency of the external periodic force exhibits three behaviors: a resonance with one peak, a resonance with one peak and one valley, and a resonance with one valley.
TL;DR: In this article, a finite element (FE) modelling framework is presented, validated and extended to multi-storey steel buildings, and the simulation strategies proposed enable an accurate representation of the complex nonlinear dynamics of self-centring structures, over a wide range of excitation frequencies and amplitudes.
TL;DR: In this paper, the impact of initial geometric imperfection on the nonlinear dynamical characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular plates under a harmonic excitation transverse load was examined.
Abstract: The purpose of the present study is to examine the impact of initial geometric imperfection on the nonlinear dynamical characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular plates under a harmonic excitation transverse load. The considered plate is assumed to be made of matrix and single-walled carbon nanotubes (SWCNTs). The rule of mixture is employed to calculate the effective material properties of the plate. Within the framework of the parabolic shear deformation plate theory with taking the influence of transverse shear deformation and rotary inertia into account, Hamilton’s principle is utilized to derive the geometrically nonlinear mathematical formulation including the governing equations and corresponding boundary conditions of initially imperfect FG-CNTRC plates. Afterwards, with the aid of an efficient multistep numerical solution methodology, the frequency-amplitude and forcing-amplitude curves of initially imperfect FG-CNTRC rectangular plates with various edge conditions are provided, demonstrating the influence of initial imperfection, geometrical parameters, and edge conditions. It is displayed that an increase in the initial geometric imperfection intensifies the softening-type behavior of system, while no softening behavior can be found in the frequency-amplitude curve of a perfect plate.
TL;DR: This work experimentally demonstrates the use of a photonic crystal Fano resonance for carving-out short pulses from long-duration input pulses by exploiting an asymmetric Fano Resonance combined with carrier-induced nonlinear effects in a Photonic crystal membrane structure.
Abstract: We experimentally demonstrate the use of a photonic crystal Fano resonance for carving-out short pulses from long-duration input pulses. This is achieved by exploiting an asymmetric Fano resonance combined with carrier-induced nonlinear effects in a photonic crystal membrane structure. The use of a nanocavity concentrates the input field to a very small volume leading to an efficient nonlinear resonance shift that carves a short pulse out of the input pulse. Here, we demonstrate shortening of ∼500 ps and ∼100 ps long pulses to ∼30 ps and ∼20 ps pulses, respectively. Furthermore, we demonstrate error-free low duty cycle return-to-zero signal generation at 2 Gbit/s with energy consumption down to ∼1 pJ/bit and power penalty of ∼2 dB. The device physics and limitations are analyzed using nonlinear coupled-mode theory.
TL;DR: In this paper, a closed-form approximate solution for nonlinear forced vibration of a functionally graded (FG) nanobeam is derived by using multiple time scale method, which shows that decrease of non-homogeneity index and material length scale parameter, or increase of temperature variation and non-local parameter will increase the resonance frequencies of FG nanobeams.
TL;DR: In this article, the response of single and two-degree-of-freedom mechanical systems with elements exhibiting a hysteretic restoring force is studied under harmonic imposed motion to characterize the nonlinear dynamic properties of the system.
Abstract: The response of single and two-degree-of-freedom mechanical systems with elements exhibiting a hysteretic restoring force is studied under harmonic imposed motion to characterize the nonlinear dynamic properties of the system. The hysteretic behavior of the element is described by the Bouc–Wen model, which is simple but able to represent different hysteretic behaviors. Since for a given restoring force the nonlinear response is affected by the oscillation amplitude, frequency-response curves for various excitation levels are constructed. The curve of periodic solutions for increasing excitation amplitude has been investigated analyzing the evolution of the resonance frequencies. Furthermore, in addition to known behaviors, to some extent already observed for single-degree-of-freedom hysteretic oscillators, a richer class of solutions and bifurcations is found for a 2-DOF system. New branches of stable periodic oscillations are bifurcated where conditions of internal resonance are encountered by varying the excitation amplitude; these are characterized by the onset of novel modes with an oscillation shape significantly different than that of modes on the fundamental branch. Finally, comparison between systems close to and far from internal resonance allowed to enlighten the role of the nonlinear coupling in the vibration mitigation.
TL;DR: The interactions between two nonlinear normal modes are shown to be responsible for the creation of the isolas in the case of a nonlinear set-up consisting of two masses sliding on a horizontal guide.
Abstract: The objective of the present paper is to provide experimental evidence of isolated resonances in the frequency response of nonlinear mechanical systems. More specifically, this work explores the presence of isolas, which are periodic solutions detached from the main frequency response, in the case of a nonlinear set-up consisting of two masses sliding on a horizontal guide. A careful experimental investigation of isolas is carried out using responses to swept-sine and stepped-sine excitations. The experimental findings are validated with advanced numerical simulations combining nonlinear modal analysis and bifurcation monitoring. In particular, the interactions between two nonlinear normal modes are shown to be responsible for the creation of the isolas.
TL;DR: In this paper, the nonlinear dynamics of a rigid-flexible space antenna under the conditions of two-toone or three-to-one internal resonance analytically and experimentally are derived via the assumed modes method.
Abstract: During the on-orbit service of an deployable antenna, the resonance of the antenna will affect the accuracy of direction. The nonlinear dynamics of a rigid-flexible space antenna is studied under the conditions of two-to-one or three-to-one internal resonance analytically and experimentally. The nonlinear dynamic equations for the planar vibration of the antenna structure with two degrees of freedom are derived via the assumed modes method. Then, the resonance parameter planes are obtained according to the length ratio, the mass ratio and the stiffness of the torsional spring in the antenna system. Afterwards, the method of multiple scales is utilized to obtain the approximate solutions under two-to-one or three-to-one internal resonance. Furthermore, the bifurcation characteristics of the nonlinear normal modes of the antenna system are investigated as well. The results show that more than one nonlinear normal mode exist over a wide range of the detuning parameter. To validate the accuracy of the approximate solution, a numerical solution and an experimental investigation are presented, respectively. The results show that both the numerical and the experimental results agree well with the analytical one.
TL;DR: The results show that nonlinear mode-coupled solutions exist over a wide range of the detuning parameter, both the numerical and the experimental results agree well with the analytical one.
TL;DR: In this paper, the control of nonlinear oscillations and resonance in a thin rectangular clamped plate representative of an aircraft panel with forcing frequency near to that of the aircraft panel was studied.
Abstract: This work is concerned with the control of nonlinear oscillations and resonance in a thin rectangular clamped plate representative of an aircraft panel with forcing frequency near to that of the fi...
TL;DR: In this paper, the authors proposed a mathematical model that considers the nonlinear effects of heave motion on pitch restoring coefficient, pitch motion on buoyancy, and bracings on the buoyancy.
TL;DR: In this article, the effect of offset displacement mainly caused by overloading on the primary resonance and displacement transmissibility is investigated, and the results indicate that the system exhibits a softening characteristic under certain conditions.
Abstract: The primary resonance and 1/3 subharmonic resonance of a quasi-zero stiffness (QZS) vibration system under base excitation with load mismatch are studied in this research. The incremental harmonic balance (IHB) method is applied to obtain highly accurate solutions involving more dynamic behaviors. The effect of the offset displacement mainly caused by overloading on the primary resonance and displacement transmissibility is investigated. The results indicate that the system exhibits a softening characteristic under certain conditions. Although the isolation performance of the QZS system deteriorates, it still outperforms the equivalent linear system for excitation amplitudes that are not too large. The parametric analysis of the 1/3 subharmonic resonance shows that the response is unbounded, and interesting dynamic behaviors can be observed, such as the jump phenomenon. Moreover, the 1/3 subharmonic resonance can be avoided by applying a larger damping or reducing the excitation amplitude to a lower level.
TL;DR: In this article, the linear and nonlinear resonance experiments are performed on composite laminate beam with cyclic loading damage, and the effect of different cyclic load damage on the linear response is analyzed.
Abstract: In the present work, the linear and nonlinear resonance experiments are performed on composite laminate beam with cyclic loading damage. The effect of different cyclic loading damage on the linear and nonlinear resonance response is analyzed. The nonlinear resonance studies the amplitude dependence of different modes. The frequency and the loss factor as function of the amplitude are determined for each cyclic loading damage. For the linear resonance, the specimens are tested at low amplitude excitation. The frequency and loss factor are evaluated for each cyclic damage. The nonlinear parameters are quantified as function of the damage. The linear parameters are compared with the nonlinear parameters.
TL;DR: In this paper, the origin of nonlinearity was investigated on MEMS pVEHs using a 3-µm-thick Pb(Zr,Ti)O3 film.
Abstract: Nonlinear resonance in piezoelectric vibration energy harvesters (pVEHs) has a large effect on the characteristics of power generation In this study, the origin of nonlinearity was investigated on MEMS pVEHs using a 3-µm-thick-Pb(Zr,Ti)O3 film The resonant frequency and mass of the pVEHs were 1806 Hz and 363 mg, respectively From the resonance curves of the output voltage and tip displacement measured at a low acceleration, where linear resonance was obtained, the electromechanical coupling and mechanical quality factors of the pVEHs were determined to be 03% and 430, respectively Although the high output power density of 41 µWmg−1G−2 was obtained at the acceleration of 0024 G, the effect of nonlinear resonance appeared and suppressed the output power density at the acceleration of 007 G and more (G is the gravitational acceleration) The comparison between the results of experiment and numerical analysis using an equivalent circuit model revealed that the nonlinear damping effect has a larger contribution than a nonlinear spring on the suppression of the output power density at a high acceleration
TL;DR: Vibrations of thin stretched strings carrying an alternating electric current in a non-uniform magnetic field are described by nonlinear equations to study the combined effect of geometric nonlinearity and Joule heating acting opposite to each other.
TL;DR: In this paper, the resonant interaction of the nonlinear normal modes which belong to different vibration branches of the carbon nanotubes (CNTs) is studied by the efficient semi-inverse asymptotic method.
Abstract: The resonant interaction of the nonlinear normal modes which belong to different vibration branches of the carbon nanotubes (CNTs) is studied by the efficient semi-inverse asymptotic method. Under the condition of the 1:1 resonance of the beam-like and circumferential flexure modes we obtain the dynamical equations, the solutions of which describe the coupled stationary states. They are characterized by the non-uniform distribution of the energy along the circumferential coordinate. The non-stationary solutions for the obtained equations correspond to the slow change of the energy distribution. It is shown that adequate description of considered resonance processes can be achieved in terms of new variables, which correspond to the coordinates of some domains of the CNT. These variables are the linear combinations of the shell- and beam-like normal modes. Using such variables we have analysed not only nonlinear normal modes, but also the limiting phase trajectories describing the strongly non-stationary dynamics. The evolution of the considered resonance processes with the oscillation amplitude growth is analysed by the phase portrait method and verified by the numerical integration of the respective dynamical equations.
TL;DR: In this paper, the nonlinear resonance of a cavity filled with a nonlinear biphasic medium made of a liquid and gas bubbles at a frequency generated by nonlinear frequency mixing was analyzed through numerical simulations by mixing two source signals of frequencies well below the bubble resonance.
Abstract: This paper studies the nonlinear resonance of a cavity filled with a nonlinear biphasic medium made of a liquid and gas bubbles at a frequency generated by nonlinear frequency mixing. The analysis is performed through numerical simulations by mixing two source signals of frequencies well below the bubble resonance. The finite-volume and finite-difference based model developed in the time domain simulates the nonlinear interaction of ultrasound and bubble dynamics via the resolution of a differential system formed by the wave and Rayleigh–Plesset equations. Some numerical results, consistent with the literature, validate our procedure. Other results reveal the existence of a frequency shift of the cavity resonance at the difference-frequency component, which rises with pressure amplitude and evidences the global changes undergone by the bubbly medium under finite amplitudes. Finally, this work shows the enhancement of the amplitude of the difference-frequency component generated by parametric excitation using the nonlinear resonance shift, which is more pronounced when the second primary frequency is constant, the first one is varied to match the nonlinear resonance, and both have the same amplitude.