Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.

Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.

Geometric Programming for Nonlinear Satellite Buffer Networks With Time Delays under L_(1)-Gain Performance

Dear Editor,This letter concerns the parameter tuning problem for nonlinear satellite buffer networks with communication delays, aiming to optimize their stability properties under L_(1)-gain. We first model the satellite buffer networks by a nonlinear time-delay positive system and propose a novel characterization under which the nonlinear system is asymptotically stable with a prescribed L_(1)-induced performance.

Output Feedback Stabilization of High-Order Nonlinear Time-Delay Systems With Low-Order and High-Order Nonlinearities

Dear Editor,to This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities.By constructing reduced-order observer,based on homogeneous domination theory together with the adding a power integrator method,an output feedback controller is developed guarantee the equilibrium of the closed system globally uniformly asymptotically stable.

Modeling Geometrically Nonlinear FG Plates: A Fast and Accurate Alternative to IGA Method Based on Deep Learning

Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.

Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink

Inspired by the demand of improving the riding comfort and meeting the lightweight design of the vehicle, an inerter-based X-structure nonlinear energy sink(IXNES) is proposed and applied in the half-vehicle system to enhance the dynamic performance. The X-structure is used as a mechanism to realize the nonlinear stiffness characteristic of the NES, which can realize the flexibility, adjustability, high efficiency, and easy operation of nonlinear stiffness, and is convenient to apply in the vehicle suspension, and the inerter is applied to replacing the mass of the NES based on the mass amplification characteristic. The dynamic model of the half-vehicle system coupled with the IX-NES is established with the Lagrange theory, and the harmonic balance method(HBM) and the pseudo-arc-length method(PALM) are used to obtain the dynamic response under road harmonic excitation. The corresponding dynamic performance under road harmonic and random excitation is evaluated by six performance indices, and compared with that of the original half-vehicle system to show the benefits of the IX-NES. Furthermore, the structural parameters of the IX-NES are optimized with the genetic algorithm. The results show that for road harmonic and random excitation, using the IX-NES can greatly reduce the resonance peaks and root mean square(RMS) values of the front and rear suspension deflections and the front and rear dynamic tire loads, while the resonance peaks and RMS values of the vehicle body vertical and pitching accelerations are slightly larger.When the structural parameters of the IX-NES are optimized, the vehicle body vertical and pitching accelerations of the half-vehicle system could reduce by 2.41% and 1.16%,respectively, and the other dynamic performance indices are within the reasonable ranges.Thus, the IX-NES combines the advantages of the inerter, X-structure, and NES, which improves the dynamic performance of the half-vehicle system and provides an effective option for vibration attenuation in the vehicle engineering.

Effect of Wave Nonlinearity on the Instantaneous Seabed Liquefaction

The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.

MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

Using harmonic beam combining to generate pulse-burst in nonlinear optical laser

The ultrashort lasers working in pulse-burst mode reveal great machining performance in recent years. The number of pulses in bursts effects greatly on the removal rate and roughness. To generate a more equal amplitude of pulses in burst with linear polarization output and time gap adjustable, we propose a new method by the harmonic beam combining(HBC).The beam combining is commonly used in adding pulses into the output beam while maintaining the pulse waveform and beam quality. In the HBC, dichroic mirrors are used to combine laser pulses of fundamental wave(FW) into harmonic wave(HW), and nonlinear crystals are used to convert the FW into HW. Therefore, HBC can add arbitrarily more HW pulses to generate pulse-burst in linear polarization with simple structure. The amplitude of each pulse in bursts can be adjusted the same to increase the stability of the burst, the time gap of each pulse can be adjusted precisely by proper time delay. Because HBC adds pulses sequentially, the peak power density of the burst is the same as each pulse, pulses can be combined without concern of back-conversion which often occurs in high peak power density. In the demonstration, the extendibility of HBC was verified by combining two beams with a third beam. The combined efficiency rates were larger than 99%, and the beam quality of each beam was maintained at M^(2)≈1.4.

Probability Distribution Characteristics of Strong Nonlinear Waves Under Typhoon Conditions in the Northern South China Sea

The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area.In this study,the third-generation wave model WAVEWATCH III is employed to simulate wave fields under extreme sea states.The model,integrating the ST6 source term,is validated against observed data,demonstrating its credibility.The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown,and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics.The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas.The waves during the typhoon exhibit strong nonlinear characteristics,and freak waves exist.The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series.The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed.The results show that with an increase in the platform area,the probability of a strong nonlinear wave beneath the platform increases.

Dirac method for nonlinear and non-homogenous boundary value problems of plates

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

Ultrahigh-brightness 50 MeV electron beam generation from laser wakefield acceleration in a weakly nonlinear regime

We propose an efficient scheme to produce ultrahigh-brightness tens of MeV electron beams by designing a density-tailored plasma to induce a wakefield in the weakly nonlinear regime with a moderate laser energy of 120 mJ.In this scheme,the second bucket of the wakefield can have a much lower phase velocity at the steep plasma density down-ramp than the first bucket and can be exploited to implement longitudinal electron injection at a lower laser intensity,leading to the generation of bright electron beams with ultralow emittance together with low energy spread.Three-dimensional particle-in-cell simulations are carried out and demonstrate that high-quality electron beams with a peak energy of 50 MeV,ultralow emittance of28 nm rad,energy spread of 1%,charge of 4.4 pC,and short duration less than 5 fs can be obtained within a 1-mm-long tailored plasma density,resulting in an ultrahigh six-dimensional brightness B6D,n of2×1017 A/m2/0.1%.By changing the density parameters,tunable bright electron beams with peak energies ranging from 5 to 70 MeV,a small emittance of B0.1 mm mrad,and a low energy spread at a few-percent level can be obtained.These bright MeV-class electron beams have a variety of potential applications,for example,as ultrafast electron probes for diffraction and imaging,in laboratory astrophysics,in coherent radiation source generation,and as injectors for GeV particle accelerators.

Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of attention.In this paper,an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks(NESs)for the first time.The proposed asymmetric tristable NES(ATNES)is composed of a pair of oblique springs and a vertical spring.Then,the three stable states,symmetric and asymmetric,can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs.The governing equations of a linear oscillator(LO)coupled with the ATNES are derived.The approximate analytical solution to the coupled system is obtained by the harmonic balance method(HBM)and verified numerically.The vibration suppression efficiency of three types of ATNES is compared.The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states.In addition,compared with the symmetrical tristable NES(TNES),the ATNES can effectively control smaller structural vibrations.In other words,the ATNES can effectively solve the threshold problem of TNES failure to weak excitation.Therefore,this paper reveals the vibration reduction mechanism of the ATNES,and provides a pathway to expand the effective excitation amplitude range of the NES.

THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS

We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.

Compression and stretching of ring vortex in a bulk nonlinear medium

We explore the nonlinear gain coupled Schrödinger system through the utilization of the variables separation method and ansatz technique.By employing these approaches,we generate hierarchies of explicit dissipative vector vortices(DVVs)that possess diverse vorticity values.Numerous fundamental characteristics of the DVVs are examined,encompassing amplitude profiles,energy fluxes,parameter effects,as well as linear and dynamic stability.

Differences between two methods to derive a nonlinear Schrödinger equation and their application scopes

The present paper chooses a dusty plasma as an example to numerically and analytically study the differences between two different methods of obtaining nonlinear Schrödinger equation(NLSE).The first method is to derive a Korteweg–de Vries(KdV)-type equation and then derive the NLSE from the KdV-type equation,while the second one is to directly derive the NLSE from the original equation.It is found that the envelope waves from the two methods have different dispersion relations,different group velocities.The results indicate that two envelope wave solutions from two different methods are completely different.The results also show that the application scope of the envelope wave obtained from the second method is wider than that of the first one,though both methods are valuable in the range of their corresponding application scopes.It is suggested that,for other systems,both methods to derive NLSE may be correct,but their nonlinear wave solutions are different and their application scopes are also different.

THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

MetaPINNs:Predicting soliton and rogue wave of nonlinear PDEs via the improved physics-informed neural networks based on meta-learned optimization

Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.

Comparison of nonlinear modeling methods for the composite rubber clamp

The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.