Simple Harmonic Excitation Research Articles

Dynamical characterisation of fractional-order Duffing-Holmes systems containing nonlinear damping under constant simple harmonic excitation

The dynamics of a fractional-order Duffing-Holmes system with a nonlinear damping term is investigated under a combined constant-simple harmonic excitation. The harmonic balance method is used to derive the approximate analytical solution of the system, focusing on the effects of constant excitation, simple harmonic excitation, and fractional-order coefficients and orders on the dynamical properties of the system; the analytical necessary conditions for chaotic motion are obtained by applying Melnikov theory, and the effects of various parameters of the system on chaotic motion are further analysed; the bifurcation diagrams and the maximum Lyapunov Exponential maps are calculated for different simple harmonic excitation amplitudes; the dynamics of the system under specific excitation frequencies and amplitudes are investigated by using time-domain maps, spectrograms, phase-plane maps, and Poincare cross sections; the static bifurcation of the system is investigated by applying the singularity theory; and global bifurcation characteristics are calculated by using the cellular mapping algorithm. It is shown that the amplitude-frequency curves of the system can be transformed from purely stiff to coexisting soft and stiff characteristics, or even purely soft, with the increase of the constant excitation for a certain amplitude of the simple harmonic excitation; the coefficients and orders of the fractional-order differential terms in the approximate solution affect the amplitude, resonance frequency, and stability of the system in the form of the equivalent linear damping and linear stiffness. The bifurcation topology shows that the system has a jumping phenomenon; with the increase of the amplitude of the constant excitation, the stability of the system in the stable state with small amplitude becomes stronger gradually until it reaches the strongest.

Structure-preserving analysis on chaotic characteristics of transverse vibration for embedded double-walled carbon nanotube

Abstract Analysing the ultra-high frequency vibrational characteristics of carbon nanotubes, especially on the chaotic characteristics, is a key scientific problem in the dynamic design of the carbon nanotube devices. Considering the van der Waals force between the inner layer and the outer layer of the embedded double-walled carbon nanotube, and the effects of the elastic medium as well as the effects of the simple harmonic external excitation, the coupling dybamic model describing the transverse vibration of the embedded double-walled carbon nanotube is presented. The generalized multi-symplectic formulations with an explicit multi-symplectic structure residual are deduced by introducing the dual momenta. The Preissmann approach, which has been proved to be a structure-preserving method that can be used to reproduce the chaotic characteristics of carbon nanotubes, is employed to discrete the generalized multi-symplectic formulations. The numerical results imply that, the transverse vibration of the embedded double-walled carbon nanotube subjected to the external excitation larger than the critical external excitation will enter the chaotic state through a period-doubling bifurcation path. In addition, the critical external excitation for the chaos of the inner layer carbon nanotube’s transverse vibration is larger than that of the outer layer carbon nanotube’s transverse vibration. The above findings reported in this paper provide some guidance for the dynamic design of the carbon nanotube devices directly.

Validation of a scaled dynamic test system for simulating a high‐speed train passing bridges under seismic excitation

AbstractThis study presents the validation of a dynamic test system to simulate a high‐speed train passing bridges under seismic excitation. The system comprises scaled models of a CRH380A high‐speed train and an 11‐span simply supported bridge on a shake table array. This innovative apparatus combines seismic loading with the moving train load to replicate train‐track‐bridge interaction (TTBI) during earthquakes. It allows investigation of various train speeds and seismic excitations, providing invaluable insights into TTBI. First, the detailed similarity design principle based on the equations of motion was discussed, and its applicability to the wheel‐rail contact relationship was verified. Then, the dynamic characteristics of the scaled model were identified, and the impact of the error between the scaled model and the theoretical model on the TTBI response was assessed. Furthermore, the comparison of the dynamic test model and the numerical simulation in acceleration responses validated the accuracy of the rigid‐flexible coupling model method for the actual TTBI system. Test cases without external excitation, with simple harmonic excitation and with seismic excitation were conducted on the dynamic test system. Results showed that the influence of track irregularity and running speed on train response aligns with the classical train‐bridge interaction theory. The successful implementation of this test system marks a significant advance in understanding TTBI mechanics and has significant implications for seismic safety enhancement of railway infrastructure.

Joint Resonance Analysis in Multiple Modes of Soft Ferromagnetic Rectangular Thin Plate

In this article, the nonlinear principal and internal resonance properties of a soft ferromagnetic rectangular thin plate are investigated in a magnetic field environment. The nonlinear partial differential equation of motion of a soft ferromagnetic rectangular thin plate is derived under the effect of homogeneous simple harmonic excitation. The system of nonlinear differential equations with multiple degrees of freedom is established by the assumed one-sided fixed trilateral simply support condition using the Galerkin’s method. The system of nonlinear differential equations is solved by the multiscale method to obtain the response of two modes under the simple harmonic force at the principal and internal resonance. The numerical results of the system response show that when the frequency of the simple harmonic force is close to one of the modes (first-order or second-order mode) causing it to resonate, the other mode will also resonate internally. The magnetic field can have an inhibiting effect on the resonant response of the system and also affect the kinematic state of the system. The internal resonance provides a mechanism for transferring energy from a high mode to a lower mode.

Analyzing and Characterizing the Global Complexity of Bistable Structures Under Simple Harmonic Excitation

Analyzing and Characterizing the Global Complexity of Bistable Structures Under Simple Harmonic Excitation

Bifurcation and chaos of Li-doped 6,6,12-graphyne impacted by hydrogen atoms: A new way to explore hydrogen storage

Hydrogen energy, as a green new energy source, has great significance for environmental protection due to its widespread application. This article uses nonlinear dynamics theory to study the problem of hydrogen energy storage firstly, which is different from traditional methods by using simulation and experimental methods. In this paper, the bifurcation and chaos of Li-doped 6,6,12-graphyne impacted by hydrogen atoms are studied. The perturbation of 6,6,12-graphene by Li atoms is treated as the Gauss white noise. The incremental harmonic balance method (IHB) is used for drawing the amplitude-frequency response curve of the system under simple harmonic excitation. Theoretical analysis shows that the inhomogeneity of 6,6,12-graphyne stiffness can affect the system stability, which decides the actual hydrogen storage capacity of graphyne. And then simulation and experiment results confirm the results of theoretical analysis. The maximum increase hydrogen storage efficiency can be more than 10% by selecting appropriate distribution of Li atoms.The research results of this article have a certain promoting effect on the industrial application of hydrogen energy.

Dynamical characterization of a Duffing–Holmes system containing nonlinear damping under constant excitation

A Duffing-Holmes system containing nonlinear damping is used to investigate some dynamical properties of the system under the combined action of constant excitation and simple harmonic excitation. The harmonic balance method is used to find the main vibration equation of the system and obtain the amplitude-frequency response relationship. In the analysis of the global characteristics of the system, the Melnikov method is applied to analyze the necessary, insufficient conditions for the analysis of the system chaos, and the correctness of the analytical solution is verified by numerical calculations; the effect of the constant excitation amplitude on the global characteristics of the system is analyzed by the cell mapping method. The paper shows: gradually increasing the constant excitation amplitude causes the system amplitude-frequency response to appear rigidly asymptotic phenomenon; the boundary curve of the system generating chaos in the sense of Smale's horseshoe, with the increase of excitation frequency ω, the curve first decreases, then rises, finally tends to infinity, and the possibility of chaos occurs most near the resonance frequency of the system; with the change of the constant excitation amplitude, The number of attractor domains and attractors in the global attraction domain of the system changes substantially with the change of the constant excitation amplitude, and the attractor domains are entangled with each other.

Mechanism of time-delay feedback control of suspension damping with an annular vibration-absorbing structure

With the aim of enhancing both the ride comfort and the safety of the vehicle, we propose a new type of suspension with an annular vibration-absorbing structure, and establish a 3-DOF 1/4 vehicle model. The structure parameters and time-delay feedback control parameters are determined by particle swarm optimization algorithms, which take the root mean values of body acceleration, suspension dynamic deflection, and tire dynamic displacement as their optimization objectives. We analyze the stability of the suspension control system to ensure the stability of the time-delay control system through the Routh-Hurwitz stability criterion, characteristic root method, and stability switching method. Then, we compare and analyze the response characteristics of conventional suspension, new suspension without time-delay feedback control, and new suspension with time-delay feedback control under simple harmonic excitation and random excitation. The results show that the new suspension with time-delay feedback control has a significant damping effect on the body under the premise of ensuring the stability of the system.

Fundamental study on rapid detection of the insufficient lateral resistance of ballasted railway tracks by dynamic loading

To resume trains operation as soon as possible after disasters, it is necessary to quickly find out locations of ballasted railway with insufficient lateral ballast resistance. In this study, a new method was proposed to evaluate the lateral ballast resistance using dynamic lateral excitation. The dynamic method was performed on 1/9-scale ballasted railway models with ballast densities of 1.5 and 1.6 g/cm3. The simple harmonic excitation was generated from a pair of 20g flywheels, and the accelerations of the vibrator and the central sleeper were recorded by sensors attached on the central sleeper and the vibrator, respectively. Based on the obtained data sets, maximum accelerations as well as the maximum amplitudes of the lateral displacements of the vibrator and the central sleeper were analysed. It was found that the maximum accelerations of the vibrator were higher than those of the central sleepers. This was also true for the maximum amplitude of the lateral displacements. The ratio of the maximum amplitude of the lateral displacement of the central sleeper to that of the vibrator was evaluated. It was found that the amplitude ratio of the track model with the ballast density of 1.5 g/cm3 was higher than that with the ballast density of 1.6 g/cm3. This implies that the difference in the lateral ballast resistance owing to the difference in the ballast density may be detected based on the evaluation of the amplitude ratio.

Building Intelligence in the Mechanical Domain—Harvesting the Reservoir Computing Power in Origami to Achieve Information Perception Tasks

Herein, the cognitive capability of a simple, paper‐based Miura‐ori—using the physical reservoir computing framework—is experimentally examined to achieve different information perception tasks. The body dynamics of Miura‐ori (aka its vertices displacements), which is excited by a simple harmonic base excitation, can be exploited as the reservoir computing resource. By recording these dynamics with a high‐resolution camera and image processing program and then using linear regression for training, it is shown that the origami reservoir has sufficient computing capacity to estimate the weight and position of a payload. It can also recognize the input frequency and magnitude patterns. Furthermore, multitasking is achievable by simultaneously applying two targeted functions to the same reservoir state matrix. Therefore, it is demonstrated that Miura‐ori can assess the dynamic interactions between its body and ambient environment to extract meaningful information—an intelligent behavior in the mechanical domain. Given that Miura‐ori has been widely used to construct deployable structures, lightweight materials, and compliant robots, enabling such information perception tasks can add a new dimension to the functionality of such a versatile structure.

Propagation Characteristics of Vibration in Structure and Site Under Single-point Simple Harmonic Excitation

Propagation Characteristics of Vibration in Structure and Site Under Single-point Simple Harmonic Excitation

Field test study for evaluation of vibration control capacity of cracked mass concrete layer

Passive control is typically implemented to regulate ground vibration in advanced ultra-precision and large-scale synchrotron radiation facilities. This paper presents the field test to evaluate the influence of cracks on the vibration control capacity of a mass concrete layer used as a passive control method of an advanced synchrotron radiation facility. Simplified finite element model (FEM) analysis is utilized to simulate the cracks and analyze the key factor that influences the vibration control capacity of the mass concrete layer. In the field test, cracks are artificially formed by creating cuts in two orthometric directions on the surface of a 3-m-thick concrete layer. Measurement points and a vibrator capable of generating simple harmonic excitation (1–100 Hz) are positioned along a straight line. Velocity signals vertical to the ground are obtained to study the vibration attenuation in the vertical direction. Test results indicate that the velocity signals on the concrete layer are sensitive to the cracks; the vibration control ability of the concrete layer is slightly affected by the depth, length and location of the cracks in the frequency band of 1–100 Hz. The proposed simplified FEMs can reflect the cracked concrete layer’s vibration control ability from 1 to 100 Hz. Numerical study results indicate that the thickness of the concrete layer rather than the density or elastic modulus is the key factor in vibration control ability.

Reference Point-Free Measurement of Bridge Dynamic Deflection by Fusing Hydraulic Leveling and Accelerometer Signals

Structural health monitoring (SHM) is widely applied to assess the service condition of bridges. Deflection measurements are essential to determine a bridge’s performance, and in particular, dynamic deflection is increasingly required in SHM. However, continuous and high-precision measurements of the absolute dynamic deflection are challenging without a reference point placed at a distance from the bridge. We proposed a reference point-free dynamic deflection measurement system consisting of a level sensor and an accelerometer. The level sensor measures the low-frequency deflection components, while the accelerometer measures the high-frequency deflection components. We redesigned the level sensor from the hydrostatic level sensor and further provided a correction method to achieve the dynamic deflection measurement. A numerical algorithm fuses the signals from the level sensor and accelerometer to obtain the absolute dynamic deflection, and key parameters are calculated. The accuracy of the measurement system was tested in the laboratory, and the sensor results were similar to the ones obtained by the laser test under simple harmonic and random excitations. Field tests conducted on a T-shaped rigid frame bridge with random traffic flow indicate that the system can achieve continuous high-precision deflection measurements of bridges loaded by traffic flow.

Resonance and bifurcation of fractional quintic Mathieu-Duffing system.

In this paper, the main subharmonic resonance of the Mathieu-Duffing system with a quintic oscillator under simple harmonic excitation, the route to chaos, and the bifurcation of the system under the influence of different parameters is studied. The amplitude-frequency and phase-frequency response equations of the main resonance of the system are determined by the harmonic balance method. The amplitude-frequency and phase-frequency response equations of the steady solution to the system under the combined action of parametric excitation and forced excitation are obtained by using the average method, and the stability conditions of the steady solution are obtained based on Lyapunov's first method. The necessary conditions for heteroclinic orbit cross section intersection and chaos of the system are given by the Melnikov method. Based on the separation of fast and slow variables, the bifurcation phenomena of the system under different conditions are obtained. The amplitude-frequency characteristics of the total response of the system under different excitation frequencies are investigated by analytical and numerical methods, respectively, which shows that the two methods achieve consistency in the trend. The influence of fractional order and fractional derivative term coefficient on the amplitude-frequency response of the main resonance of the system is analyzed. The effects of nonlinear stiffness coefficient, parametric excitation term coefficient, and fractional order on the amplitude-frequency response of subharmonic resonance are discussed. Through analysis, it is found that the existence of parametric excitation will cause the subharmonic resonance of the Mathieu-Duffing oscillator to jump. Finally, the subcritical and supercritical fork bifurcations of the system caused by different parameter changes are studied. Through analysis, it is known that the parametric excitation coefficient causes subcritical fork bifurcations and fractional order causes supercritical fork bifurcations.

Unsteady Aerodynamic Lift Force on a Pitching Wing: Experimental Measurement and Data Processing

This work discusses the experimental challenges and processing of unsteady experiments for a pitching wing in the low-speed wind tunnel of the Vrije Universiteit Brussel. The setup used for unsteady experiments consisted of two independent devices: (a) a position control device to steer the pitch angle of the wing, and (b) a pressure measurement device to measure the aerodynamic loads. The position control setup can pitch the wing for a range of frequencies, amplitude, and offset levels. In this work, a NACA-0018 wing profile was used with an aspect ratio of 1.8. The position control and the pressure measurement setups operate independently of each other, necessitating advanced signal processing techniques to synchronize the pitch angle and the lift force. Furthermore, there is a (not well-documented) issue with the (sampling) clock frequency of the pressure measurement setup, which was resolved using a fully automated spectral analysis technique. The wing was pitched using a simple harmonic sine excitation signal at eight different offset levels (between 6° and 21°) for a fixed amplitude variation (std) of 6°. At each offset level, the wing was pitched at five different frequencies between 0.1 Hz and 2 Hz (that correspond to reduced frequencies k ranging from 0.006 to 0.125). All the experiments were conducted at a fixed chord-based Reynolds number of 2.85 × 105. The choice of operating parameters invokes the linear and nonlinear behavior of the wing. The linear unsteady measurements agreed with the analytical results. The unsteady pressure measurements at higher offset levels revealed the nonlinear aerodynamic phenomenon of dynamic stall. This confirms that a nonlinear and dynamic model is required to capture the salient characteristics of the lift force on a pitching wing.

Dynamics Modeling and Characterization of Sunk Screw Connection Structure in Small Rockets

Bolted flange joints are widely used in engineering structures. Sunk screw connection structures commonly used in small rockets and missiles exhibit significant nonlinear characteristics when subjected to forces. In this article, a study of the dynamic characteristics of sunk screw connection is conducted. A 3-dof trilinear dynamic model is proposed, based on the study of the stiffness characteristics of the connection structure and considering contact nonlinearities. The connection surface is simplified as two axial trilinear springs and a lateral linear spring. The motion of the system can be divided into nine regions by the turning point of the trilinear springs. So that the motion of the system in each region can be completely resolved, the dynamic characteristics of the 3-dof trilinear system under impulse load and simple harmonic load are studied by means of semi-numerical analytical method. It is found that the response frequency of the system remains unchanged under a small impulse load, and the response can be obtained by approximate analytical expressions. When the impulse load is large, the response frequency is fluctuant, which reflects the sensitivity of the nonlinear system to the magnitude of impulse load. Under the simple harmonic excitation of bending moment, the response frequency curve of the system presents good single peak characteristics when the excitation amplitude is small. When the amplitude is large, the peak frequency of the system shifts, and the phenomenon of multi-peak resonance is shown in a certain range.

An Optimization Algorithm of Time-Delayed Feedback Control Parameters for Quarter Vehicle Semiactive Suspension System

Time-delayed feedback control is commonly used on the vehicle semiactive suspension system to improve ride comfort and safety. However, its performance on the suppression of road random excitation is less significant than that on the suppression of simple harmonic excitation. Therefore, this paper proposes a strategy of time-delayed feedback control with the vertical displacement of wheel and the method of optimizing its parameters based on equivalent harmonic excitation. The optimal parameters of the time-delayed feedback control are obtained in this way for the vehicle semiactive suspension system in its effective frequency band. The results of numerical simulation verify that the time-delayed feedback control with vertical wheel displacement and its parameter optimization based on equivalent harmonic excitation can significantly improve the ride comfort and stability. Its performance is much better than that of the passive suspension system.

Process enhancement of vibrating classifier for tailings classification-dewatering and industrial application

To reduce environmental pollution and wastage of resources and to promote the large-scale utilization of tailings, classification-dewatering is a key technical challenge. The vibrating classifier efficiently separates minerals according to particle size, while the vibrating energy drives water out. However, the screen apertures of the vibrating classifier can be blocked easily, resulting in a poor classification-dewatering effect. In this study, an elastic screen surface for classification-dewatering is proposed to replace the rigid screen surface of a traditional vibrating classifier, eliminating the problems of easy plugging and low efficiency. The surface kinematics of the elastic screen under simple harmonic excitation is studied. The output energy of the screen surface increased by 10% compared with the input energy of the excitation source. In addition, the random elastic deformation of the screen's apertures contributed to the rupturing of water film in apertures. The effect of exciting parameters and concentrations of tailings on the classification-dewatering is also investigated. The optimum values for excitation force, working frequency, and the concentration of tailings are 9.66 kN, 15.62 Hz, and 35%, respectively. Moreover, the classification and dewatering efficiencies are 80% and 53%, respectively. Industrial production shows that coarse tailing sand exhibits a moisture content of 18%, while the fine particles are used for paste filling. These results provide support to the comprehensive utilization of tailings and promote green and safe production in mines

Dynamic Characteristics of a Variable Damping Isolator with Translating Cam

A variable damping isolator based on a translating cam designed especially is proposed in this paper. The nonlinear variable damping isolator is mainly comprised of translating cam with a pair of rollers arranged symmetrically and horizontally and two linear dampers. The damping force of this isolator increases with the increase of its vertical displacement. The dynamic equation is established when the variable damping isolator is applied to the active isolation system under simple harmonic excitation. And the dynamic response of the equation is obtained by Harmonic Balance Method. After that, the numerical simulations are conducted to discuss the effects of the parameters of the isolation system on force transmissibility. The results show that the effects on attenuating the resonance and the force transmissibility in the region of high-frequency ratio are superior to that of the corresponding linear damping vibration isolator when appropriate design parameters (cam profile and damping coefficient of the horizontal linear damper) of the variable damping isolator are selected.

Research on the Vibration Characteristics of Aviation Hydraulic Clamp and Pipeline Based on Hard Coating

Aviation hydraulic clamp-piping systems often experience damage due to vibration, which poses a great threat to the reliability and safety of the aircraft. In this paper, a hard coating is used as a new damping method to study the vibration characteristics of aviation hydraulic clamp-piping systems. Three kinds of coated clamp entities are obtained by optimization and preparation, and the combination of finite element simulation and experiment is used to analyze the vibration response of the high- and low-pressure rotor under fixed-frequency simple harmonic excitation, and the resonance response under sweep-frequency excitation of the aviation hydraulic clamp-piping system. Through orthogonal experiments, it is clear that 304 stainless steel clamps coated with 200-μm-thick YSZ-PTFE coating have the best vibration damping effect on the clamp-piping system; that is, the damping rate can reach 24.67% under fixed-frequency excitation, and swept frequency damping can reach 19.93%. The maximum error between the simulation and the experimental vibration response amplitude is 7.9%, which proves the correctness of the model and verifies that the YSZ-PTFE hard coating can significantly improve the vibration damping effect with very good application prospects.