Amplitude Frequency Response Curves Research Articles

A non-interference method for measurement of transverse relaxation time of the alkali metal magnetometer in nuclear magnetic resonance oscillator

The transverse relaxation time τ2 of the built-in alkali metal magnetometer is an important parameter to characterize its performance and the working state of the nuclear magnetic resonance (NMR) oscillator system. The method we propose to measure τ2 is to apply the frequency-scanning magnetic fields along the x-axis and obtain τ2 from the 3 dB bandwidth of the measured x-axis amplitude–frequency response curve of the magnetometer. We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method to demonstrate the rationality of this measuring method. Then, both the actual experiment and the simulation experiment results are presented to verify the validity and good accuracy of the method. All the sampled frequencies in the scanning range should be far away from both the 129Xe and 131Xe NMR frequencies, to avoid introducing any influence on the nuclear spins; therefore, this method can provide a non-interference way for measurement of τ2, helping us monitor the NMR oscillator system’s state under normal operating conditions.

An approximate method for solving force and displacement transmissibility of a geometrically nonlinear isolation system

This study presents a modified harmonic balance method, which is used to solve the force and displacement transmissibilities of a vibration isolator with both the quasi-zero-stiffness and geometrically nonlinear damping. The steady-state response of the nonlinear isolation system is obtained by Jacobi elliptic functions, and is used to modify the harmonic components of stiffness and damping force in the harmonic balance method, which can reduce the truncation error produced by the trigonometric Fourier series. When the modified harmonic components are combined based on the orthogonality condition, the elliptic harmonic balance method (EHBM) is obtained. The results show that the amplitude–frequency response curve, and force and displacement transmissibilities obtained by using the EHBM can be compared well with those obtained by using the fourth order Runge–Kutta method. The EHBM can be used to improve the accuracy of the results at the resonance and high frequency regimes. The EHBM is simple and straightforward for the detailed study of the vibration isolation characteristics of the geometrically nonlinear isolator.

Application of nonlocal continuum theory to the primary resonance analysis of an axially loaded nano beam under time delay control

The paper is concerned with the nonlinear primary resonance of nano beams with axial load under the velocity time delay control. In order to have a deep insight into the system, the amplitude frequency response curve of the system is firstly obtained using the multiple scales method. The effects of the control gains and time delays on the system stability are then investigated. The analyses illustrated that both delay feedback gain coefficient and velocity time delay control can mitigate the system vibrations properties (e.g. hardening nonlinearity, resonance amplitude and the corresponding width) to an excellent level. The nonlinear primary resonance of nano beam is also discussed with the influences of small scale effect, axial initial load, wave number, Winkler foundation modulus and the ratio of the length to the diameter. This paper establishes the relationship between the time delay controller and vibration properties of a nano beam system which provides the guidance for applying time delayed active control for different types of nano devices in engineering practices.

Spatiotemporal antiresonance in coupled reaction-diffusion systems.

We present a theoretical study of the spatiotemporal antiresonance in a system of two diffusively coupled chemical reactions, one of which is driven by an external periodic forcing. Although antiresonance is well known in various physical systems, the phenomenon in coupled chemical reactions has largely been overlooked. Based on the linearized dynamics around the steady state of the two-component coupled reaction-diffusion systems we have derived the general analytical expressions for the amplitude-frequency response functions of the driven and undriven components of the system. Our theoretical analysis is well corroborated by detailed numerical simulations on coupled Gray-Scott reaction-diffusion systems exhibiting antiresonance dip in the amplitude-frequency response curve as a result of destructive interference between the coupling and the periodic external forcing imparting differential stability of the two subsystems. This leads to the emergence of spatiotemporal patterns in an undriven subsystem, while the driven one settles down to a homogeneously stable steady state.

Modelling and dynamic analysis of spline-connected multi-span rotor system

Self-excited oscillation induced by the internal frictions of spline joints is a major cause of rotor system instability. In this study, the dynamic equations of spline-connected multi-span rotor systems have been derived by finite element and lumped mass hybrid modelling methods. In this model, the mathematical models of spline joints and rubber sealing rings were deduced in detail. Newmark numerical algorithm was applied to solve differential equations of the coupling system. On this basis, the amplitude–frequency response characteristics of systems without rubber sealing ring as well as the effects of several important parameters, including friction coefficient, transmission torque and unbalance value, on the self-excited vibration of the system were discussed. Then, in the case of rubber sealing ring assembled next to spline joint, the effects of rubber sealing ring on amplitude–frequency response characteristics and self-excited vibrations of the system were analyzed. The obtained results showed that self-excited oscillation occurred in supercritical state when the friction coefficient of spline joint was high enough; however, it merely occurred within a specific speed range. By the increase of friction coefficient or transmission torque, the speed range corresponding to self-excited oscillation became closer to the natural frequency of the system. However, as the unbalance value was increased, the phenomenon of self-excited vibration showed the opposite trend. Rubber sealing ring not only reduced vibration near spline joint, but also suppressed the self-excited vibration of the system induced by internal friction, thus improving system stability. This paper provides a theoretical basis for studying the mechanism and suppression of self-excited oscillation of rotor systems.

Two types of scale effects on the nonlinear forced vibration of axially moving nanobeams

Various non-classical continuum mechanics models appearing in previous studies cannot perfectly explain the mechanical properties of micro- and nanomaterials. Establishing a reasonable continuum mechanics model that comprehensively reflects the scale effect on material deformation is of great practical significance for objectively explaining the variation law of mechanical properties of micro- and nanomaterials under the combined action of different scale effects. Based on nonlocal strain gradient theory, a new scale-dependent model is proposed for axially moving nanobeams. In this study, an asymptotic expansion is performed using the multiscale time method to obtain the amplitude-frequency response curve of the equilibrium solutions for the forced vibration problem. Afterwards, the effects of various system parameters, especially the scale parameters, on the resonance curve are examined. Finally, the effects of nonlocal parameters and material characteristic length parameters on the amplitude-frequency response curves are investigated through typical numerical examples. The numerical results show that the nonlocal parameters promote the emergence of the main resonance, whereas the material characteristic length parameters suppress the emergence of the main resonance. Moreover, these parameters also affect the response amplitude and the skewness and jumping point of the amplitude-frequency characteristic curve.

Leaky integrate-and-fire neurons based on perovskite memristor for spiking neural networks

Artificial neuron is an important part of constructing neuromorphic network in which information can be computed with high parallelism and efficiency like in the human brain. However, owing to the poor biological plausibility, artificial neurons based on traditional complementary metal-oxide-semiconductor (CMOS) platform fail to reveal the rich ion dynamics of the biological counterparts. Organic–inorganic halide perovskites (OHPs) are prospective for imitating the ion dynamics on the membranes of biological neurons because of its intrinsic ion migration. Herein, a diffusive CH 3 NH 3 PbI 3 (MAPbI 3 )-based memristor with superior amplitude-frequency characteristics and highly linear conductivity modulation for more than 1000 states have been fabricated for the construction of a leaky integrate-and-fire (LIF) bio-inspired neuron. The as-designed LIF model can successfully emulate the leakage, spatiotemporal integration and firing functions in a biological neuron. Moreover, by connecting LIF neurons with a 2*2 non-volatile Al 2 O 3 -based synaptic array, a simple spiking neural network (SNN) which is called the 3rd generation of neural network has been implemented at the hardware level to study the cognitive performance of the network. The SNN exhibits outstanding selective sensitivity to particular input sequence, indicating the excellent adaptability and versatility of the network for future applications of neuromorphic computing by utilizing novel ionotropic device. Herein, for the first time, a diffusive CH 3 NH 3 PbI 3 (MAPbI 3 )-based memristor with superior amplitude-frequency characteristics and highly linear conductivity modulation for more than 1000 states have been fabricated for the construction of a leaky integrate-and-fire (LIF) bio-inspired neuron. The as-designed LIF model can successfully emulate the leakage, spatiotemporal integration and firing functions in a biological neuron, indicating the great potential for neuromorphic computing. Furthermore, by connecting LIF neurons with a 2*2 non-volatile Al 2 O 3 -based synaptic array, a simple spiking neural network has been implemented at the hardware level to study the cognitive performance of the network. • The conductance states of MAPbI 3 -based memristor can be modulated linearly and consecutively for more than 1000 states. • The memristor exhibits superior amplitude-frequency response characteristics which may be also suitable for filter. • A leaky integrate-and-fire artificial neuron is implemented, and the leakage, spatiotemporal integration and firing functions are emulated successfully. • By combining the artificial neuron with an synaptic array, a simple spiking neural network has been implemented.

Performance test of an internally modulated He-Ne laser based on optical tunneling effect

To figure out some characteristics of a novel internally modulated He-Ne laser based on optical tunneling effect, especially its modulation characteristics, some experiments are carried out and the measurement results are discussed. By measuring the amplitude-frequency response curve of the laser power, the modulation bandwidth is determined as hundreds of Hz, and an obvious trap band at ~100 Hz was observed. By comparing with the test results of the laser vibrometer, it is found that the modulation characteristics of this kind of laser are mainly determined by the characteristics of the tunneling displacement device and the intra-cavity loss characteristics of the laser.

Double Jump Broadband Energy Harvesting in a Helmholtz–Duffing Oscillator

To improve the ability of energy harvester, a Helmholtz–Duffing oscillator with nonlinear capacitance is considered, which has an asymmetric characteristic. In this paper, we investigates the effect of potential function asymmetries on the dynamic behaviors under harmonic excitation. The electromechanical coupling governing equations of Helmholtz–Duffing energy harvester is established. Then its dynamic response in the region of the primary resonance is sought by the harmonic balance method. The performances of the presented asymmetric nonlinear primary resonance energy harvester and the linear stiffness system are compared. Results clearly demonstrate an improved bandwidth over a case which does not involve an asymmetric potential energy function. It is found that multiple-valued steady-state solutions of frequency-response equation can exist, indicating that the jump phenomenon occurs. Besides, the amplitude–frequency response curves have double-jumping phenomena by the bend, first to the left and then to the right. The influence of the stiffness parameters on the shape of the frequency-response curves is also discussed. It is observed that different shapes of frequency-response curves can exist. The approximate analytical outcomes are in good agreement with the numerical results.

Modeling and Dynamic Characteristics Analysis of Blade-Disk Dual-Rotor System

In this paper, a simplified dynamic model of a dual-rotor system coupled with blade disk is built, and the effects of blade parameters of an aircraft engine on the dynamic characteristics of a dual-rotor system are studied. In the methodology, the blade is simplified as a cantilever structure, and the dynamical equations are obtained by the means of a finite element method. The amplitude-frequency response curves and orbits of shaft centre-vibration shape diagram are used to analyze the effects of blade parameters on dynamic characteristics of a dual-rotor system. The results indicate that the properties of the blades have huge impacts on the critical speed and other dynamic characteristics of the system. With an increase of the length of the blade, the second-order critical speed decreases obviously, but the first-order critical speed is almost invariant; this means that the blades attached on the low-pressure compressor do not affect the first-order critical speed of the dual-rotor system. Meanwhile, note that the high-pressure rotor and low-pressure turbine rotor can excite the first-order resonance of the dual-rotor system, while the low-pressure compressor rotor can only excite the second-order resonance, and then the dynamic model of this six-point support dual-rotor system can further be simplified as a relatively independent single-rotor system with one disk and a four-support dual-rotor system with dual disks.

Characterisation of the internal resonances of a clamped-clamped beam MEMS resonator

Nonlinear coupling between modes through internal resonance has many applications in MEMS resonators. The primary objective of this work is to systematically study all possible internal resonance conditions between the first three modes and the feasibility of mode interaction in an electrostatically excited, straight, clamped-clamped beam. The static displacement and the first three natural frequencies of the beam are obtained for an applied DC voltage by using Galerkin based reduced order model and finite element method. All six possible commensurable relations between the first three frequencies of the beam are obtained by sweeping the non-dimensional parameters ($$\alpha _1$$ and $$\alpha _2 V_\mathrm{dc}^2$$) which depend on beam dimensions, material properties and external forcing. It is also demonstrated by a further examination of the dynamical equations that only one resonance condition is capable of exhibiting modal coupling when externally excited. A detailed analysis is carried out for this feasible resonance condition by altering $$\alpha _1$$ and $$\alpha _2 V_\mathrm{dc}^2$$ and solving the relevant nonlinear coupled equations by using both numerical time integration and the method of multiple scales. From this study, we observe that the lower mode is automatically excited after driving amplitude for the higher mode reaches a critical value—a sign of mode interaction initiation. We also find that amplitude of the higher mode is saturated after interaction with the lower mode for a combination of $$\alpha _1$$ and $$\alpha _2 V_\mathrm{dc}^2$$. Moreover, we see that the frequency bandwidth of modal interaction increases with excitation amplitude for all combinations of $$\alpha _1$$ and $$\alpha _2 V_\mathrm{dc}^2$$. Finally, the role of external damping on the amplitude-frequency response curve of both modes during the mode interaction is also investigated.

Nonlinear vibration absorption of laminated composite beams in complex environment

Nonlinear vibration absorption of a laminated composite beam is investigated with the account of complex environment (moisture and temperature). A passive efficient nonlinear energy sink (NES) vibration absorber is used to control the transverse vibration. The generalized Hamilton principle is applied to derive a dynamic model of the laminated composite beam coupled with the NES. Numerical simulations reveal the effects of temperature, moisture, and laying angle on natural frequencies. It is numerically found that the NES can rapidly reduce the vibration amplitude. Then, approximate analytical solutions are sought via the harmonic balance method. The approximate analytical solutions are confirmed by the numerical solutions. Amplitude–frequency response curves show that the NES can reduce the amplitude to very low values for various temperatures, moisture levels, and laying angles. In a certain ranges of the NES parameters, different control effects are determined via an approximate analysis. It is demonstrated that the NES is a promising approach to control vibration of a laminated composite beam in complex environment.

Periodic response characteristics on a piecewise hysteresis nonlinear system

A piecewise hysteresis nonlinear dynamic model with nonlinear stiffness and damping is established for a system with alternating elastic constraints and hysteresis nonlinearity. First, the amplitude–frequency response equation of the system is solved by using the averaging method under periodic excitation. Two frequency regions with multiple solutions are then identified in the system, and the amplitude–frequency response characteristics under different system parameters are obtained. Thus, the influence law of different piecewise nonlinear factors on system stability is explored. Second, the bifurcation behavior of the system under different external disturbances is analyzed. Given the change of perturbation parameters, the system is found to be a complex dynamic system with alternating periodic, double periodic, and chaotic motions, and many other forms of movement. Moreover, lower buffer damping leads to the complex and unpredictable chaotic state of the system’s dynamic behavior.

Dynamic response characteristics of the protection system for a projectile-borne recorder under high impact loading

To provide an optimal direction for the protection design of a projectile-borne recorder, the dynamic response mechanism of the protection system for the projectile-borne recorder under high impact loading was revealed according to the mechanical vibration theory. On the basis of analysis for the load transfer relation, a simplified dynamic response model based on the two-degree-of-freedom spring-mass-damper system was established. To verify the credibility of the model, numerical simulation was carried out, and the parameters of the response model were identified according to the impulse response analysis and the harmonic analysis. Based on the result that the values of the theoretical calculation agreed well with those of the numerical simulation, it was concluded that the proposed model was more suitable to describe the dynamic response characteristics of the protection system under high impact loading. According to the amplitude-frequency response characteristics, the change of the dynamic response characteristics along various parameters was analyzed, which could be applied to guide the protection design of the projectile-borne recorder.

Resonance and chaos of micro and nano electro mechanical resonators with time delay feedback

The resonance and chaos of micro (nano) electro mechanical resonators with time delay feedback is concerned in the paper. Based on the experimental results, a lumped single degree-of-freedom (1DOF) model is studied and the effects of time delay displacement and velocity feedback on the system are investigated. In order to have a deep insight into the system, the amplitude frequency response curve of the system is firstly obtained using the multiple scales method. The Melnikov function method is then extended to the two time delay systems, and the analytically required condition for chaos was obtained. Finally, the fourth-order Runge–Kutta method, point-mapping method and spectrum diagram are used to simulate the evolution of the dynamic behavior of the time delay control system. Also, the stability of this time delay control system is studied thoroughly. The results show that time delay feedback is a good method for the control system and that reasonable selection of control system parameters can effectively suppress the vibration level for micro/nano-electro-mechanical resonator systems.

Nonlinear transverse vibrations of angle-ply laminated composite piezoelectric cantilever plate with four-modes subjected to in-plane and out-of-plane excitations

In this paper, the nonlinear vibrations of the laminated composite piezoelectric cantilever plate subjected to the transverse and in-plane excitations are investigated. Based on the Reddy’s third-order plate theory and von Karman nonlinear strain-displacement relation, the nonlinear partial differential governing equations of motion are established for the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations by applying Hamilton’s principle. Employing Galerkin’s approach, we discretize the continuous nonlinear dynamic equations of motion into the ordinary differential equations with four modes. Substituting the actual geometric and physical parameters of the laminated composite piezoelectric cantilever plate into the governing equation of motion, we use numerical method to investigate the effects of the lay-up parameters and the geometric parameters on the dimensionless natural frequencies of the cantilever plate. The amplitude-frequency response curves and the basin boundary diagram of two coexisting steady-state solutions are plotted for the laminated composite piezoelectric cantilever plate. The nonlinear dynamic responses of the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations are investigated by changing the lay-up parameters, the transverse excitation, the voltage excitation and the in-plane excitation. The periodic, the quasi-periodic, the chaotic motions and the nonlinear stiffness characteristics can be found. The nonlinear dynamic behaviors help us to optimize the structural and physical parameters of the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations.

Road surface condition detection utilizing resonance frequency and optical technologies

With the booming development of road network and intelligent transportation systems, road surface condition information becomes more and more valuable in traffic accident prevention and route optimization. Although some existing embedded detectors have been providing road condition data in some regions, they are not functional enough in either complex condition recognition or film thickness measurement. This paper introduces a dual-sensor based road condition detector for six surface conditions with ice and water film measurement capability. The reflection type optical sensor and the piezoelectric sensor utilizing resonance technology are integrated in the detector. The finite element analysis was carried out to study the amplitude frequency response characteristics of the piezoelectric sensor and the optical power calculation model based on Fresnel Reflection was built to evaluate the output voltage of the optical sensor in different conditions. Several experiments were done to calibrate the detector and validate its performance. The results indicated that all of the 353 validation data points were correctly sorted and the measurement upper limit of the ice and water film was above 5 mm with accuracy better than 0.5 mm.

Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance

A lumped parameter transverse vibration model of a composite plate harvester is analyzed via harmonic balance approaches. The harvester is mainly composed of a piezoelectric circular composite clamped by two steel rings and a proof mass on the plate. The lumped parameter model is a 1.5 degree-of-freedom strongly nonlinear system with a higher order polynomial stiffness. A harmonic balance approach is developed to analyze the system, and the resulting algebraic equations are numerically solved by adopting an arc-length continuation technique. An incremental harmonic balance approach is also developed for the lumped parameter model. The two approaches yield the same results. The amplitude-frequency responses produced by the harmonic balance approach are validated by the numerical integrations and the experimental data. The investigation reveals that there coexist hardening and softening characteristics in the amplitude-frequency response curves under sufficiently large excitations. The harvester with the coexistence of hardening and softening nonlinearities can outperform not only linear energy harvesters, but also typical hardening nonlinear energy harvesters.

Estimation of dynamic behaviors of hydraulic forging press machine in slow-motion manufacturing process

In this paper, stick–slip phenomenon of hydraulic forging press machine (HFPM), a nonlinear manufacturing system subjected to weak rigidity and negative friction velocity gradient, was investigated in slow-motion process. Dynamic characteristics of non-smooth motion were investigated experimentally under various operating conditions in slow-motion process. Taking into account the quadratic and cubic nonlinearities, the governing equation of the HFPM was derived. The method of multiple scales was employed to obtain approximate solution for velocity oscillation during slow motion. The steady-state responses for each case (i.e., non-resonance, primary, super-harmonic and sub-harmonic oscillation) were examined to investigate the correlation between velocity oscillation and nonlinear vibration in slow motion. The effects of viscous damping coefficient, hydraulic stiffness, friction parameters, excitation amplitude and frequency on the amplitude–frequency response characteristics were studied, and the interaction between system dynamics and tribological effects were presented. The stability of operational conditions and the critical velocity of the forging process were analyzed through the bifurcation techniques. Experimental results conducted on the HFPM verify the effectiveness of the proposed method.

The piezoelectric road status sensor using the frequency scanning method and machine-learning algorithms

This paper introduces a piezoelectric sensor for measuring the thickness of ice and water film on road surfaces, utilizing the frequency scanning method and machine-learning algorithms. With a constant elasticity alloy plate and a three-electrode piezoelectric transducer disc, this sensor detects ice and water by vibrating. During the research, a model of elastic thin plate with small deflections was built to describe the sensor’s vibration characteristics and the sensing unit’s amplitude frequency response curves of different ice and water film thickness were recorded. The curves show a high correlation between the thickness of loads and the curve shapes. In order to expand the measurement range, 425 sets featuring vectors for the machine-learning model were extracted, and some specific features such as median, variance, area, centroid and energy under the curves were utilized. The performance of conventional methods and two regression models based on support vector regression (SVR) and an artificial neural network (ANN) were evaluated with cross-validation results. The measurement range of the sensor turned out to be 0–10 mm. Based on the ANN model, on an average 85.5% and 100% of the neural network outputs had a regression error less than 0.5 mm and 1.0 mm respectively. Finally, the result of an 18-day field test on the roads of the Norwegian University of Science and Technology is presented.