External Excitation Frequency Research Articles

Topologically tunable local-resonant origami metamaterials for wave transmission and impact mitigation

Origami metamaterials can control the propagation and energy transmission of elastic waves via the flexible design of microstructure topology, which has great application prospects in the field of structural impact resistance. In this paper, by integrating the Bloch theorem and the local resonance (LR) mechanism, a tunable hybrid origami metamaterial (HOM) is proposed to achieve low-frequency and broad bandgaps (BGs) for realizing wave transmission and impact mitigation. The elastodynamic wave equation of the HOM is established based on the Mindlin plate theory and discretized with the higher-order spectral elements, and band structures of the HOM are obtained through the semi-analytical periodic spectral plate (PSP-SAFE) methods. Effective dynamic properties of the HOM are numerically calculated to explain wave transmission behavior. Interestingly two complete BGs in the low-frequency range are found, and the proposed metamaterial can broaden the low-frequency bandgaps by coupling the polarization BGs and local resonance BGs. The influences of three significant parameters on two complete BGs within the region of interest are then discussed. Furthermore, the wave mitigation capacity of locally resonant HOM is investigated under impact pulses. It is noted that the reaction peak force of the HOM possesses an approximately 25.7% better reduction than that of origami structures with no mass inclusion. Especially when the external excitation frequency is consistent with local-resonance BGs, the transmission rate shows dramatically decrease due to the dramatic dissipation of energy in space. The locally resonant hybrid origami metamaterial shows promising potential for applying low-frequency wave attenuation and impact mitigation.

Optimization design on resonance avoidance for 3D piping systems based on wave approach

Vibration of liquid conveying piping systems in a closure may cause noising problem and degrade living comfort inside, it can even lead to fatigue failure of the system. Therefore, vibration alleviation in such circumstance is highly demanded. Traditionally, a piping system is designed to satisfy basic key functions as liquid conveying or heat exchange. Once the global arrangement of a piping system is determined for such key functions, local modifications with hangers on the piping system are then made to reduce its vibration. Here, we propose a method to optimize globally the shape and rigid hanger locations for a 3D piping system in order to achieve resonance avoidance. To this end, the wave approach is employed to estimate in a fast and accurate way the fundamental frequency of any 3D liquid conveying piping system, assembled from some basic elements. Based on genetic algorithm, optimization on shape and rigid hanger locations for a 3D piping system can be obtained with a maximal fundamental frequency, which is far away from the external excitation frequency. It shows that the shape optimization can be used to increase the fundamental frequency of a piping system if rigid hangers are not available, while the fundamental frequency can be increased more effectively with rigid hangers of optimized locations. Our work provides a systematic method for global optimization design of 3D piping systems.

Optimal design of double-link trapezoidal boom suspension for high gap self-propelled sprayer based on ANSYS

The high gap self-propelled sprayer has the characteristics of wide boom width and high working efficiency. Aiming at the problem that the spray boom is prone to mechanical vibration along with the body and affects the spraying effect, the static analysis and modal analysis of the boom suspension of its two-link trapezoidal mechanism are carried out, based on the ANSYS simulation method. The results show that the optimized stress at the end boom suspension connection is reduced from 161MPa to 22MPa, and the maximum displacement is reduced from 35mm to 7mm. The maximum stress of the inner boom suspension was reduced from 128.36MPa to 88.07MPa Stress distribution and displacement conditions achieve the desired effect. The modal analysis results show that the first six natural frequencies of the boom suspension do not coincide. And this frequency reasonably avoids the external excitation frequency range, and avoids unnecessary damage caused by the resonance of the boom suspension in the actual operation of the sprayer.

Modal analysis of the liquid sheet breakup with and without acoustic forcing

• The coupling between the acoustic field and the liquid sheet atomization process is studied. • Modal decomposition techniques like Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are employed. • Frequency response of the liquid sheet is found to be dependent on the laminar or turbulent nature of the impacting jets. • Liquid sheet breakup gets coupled with the external forcing when the acoustic energy goes into low frequency modes. • Decoupling occurs when the acoustic energy goes into the dominant modes which are higher ones having a higher frequency. The objective of the present study is to understand the coupling between the acoustics and the sheet atomization process. The phenomenon is studied through modal decompositions of time-resolved images of acoustically perturbed liquid sheets by employing the proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques. The injector operating conditions are selected in order to allow the transition of a smooth liquid sheet to a highly turbulent sheet or fully developed spray. The sheet is destabilized by the traveling acoustic waves of known frequency and sound pressure level. POD modes of the smooth sheets and DMD modes of the turbulent sheets clearly highlight distinct effects of the acoustic perturbations on the liquid sheets. The frequency response of the liquid sheet is found to be dependent on the laminar or turbulent nature of the impacting jets. When the impinging jets are laminar, interestingly the dominant POD mode frequencies are either equal to or harmonics of the external acoustic excitation frequency which confirms the coupling of the atomization process with the acoustic perturbations. Below the lower cutoff frequency, the POD mode having frequency equal to the forcing frequency always dominates other modes. Also, for laminar jets, the DMD growth rate is maximum for the mode having frequency equal to the external forcing. However, for the turbulent impinging jets, the first DMD mode frequency is not always equal to the external forcing frequency but one of the mode in the DMD frequency spectrum show the frequency which is either close to the forcing frequency or close to its integer multiple.

Piezoelectric vibration energy harvesting with asymmetric hybrid bracing beam

In order to reduce the natural frequency of the piezoelectric vibration energy harvester, improve the output power of the piezoelectric vibration energy harvester, and meet the demand of power supply for the low-power wireless switch in the low-frequency vibration environment, an asymmetric hybrid supported beam piezoelectric vibration energy harvester is proposed. The theoretical model of the hybrid support beam was established. The correlation factors affecting the open-circuit voltage and the total output power of the hybrid braced beam were analyzed. The dimensional parameters of the hybrid supported beam piezoelectric energy harvester were optimized by using the optimization method of orthogonal experiments. Different coincidence degrees experiments were used to further optimize the structural design of the hybrid support beam. The test results show that the maximum output power is 770 μW, when the external excitation frequency is 1.0 g and the external resistance is 50 kΩ. Finally, a wireless switch test system was established, and the piezoelectric vibration energy harvester was experimentally verified to be capable of powering the wireless switch.

Time-varying dynamic analysis of a plate entering the finite subsonic airflow field

Devices entering rigid wall constrained finite airflow field are commonly seen in engineering practice. The devices gradually move from the infinite airflow field to the finite airflow field, which makes the device and the outside flow field a complicated time-varying fluid–structure interaction system. During the entry process, the stiffness, damping and mass of the devices change constantly over time, which makes the dynamic behaviors of the system show complex time-varying properties. Hence, it is needed to study the stability and vibration characteristics of the devices entering the finite airflow field. In this study, based on the von Karman nonlinear plate theory and the linear potential flow theory, the governing equation of the plate entering the finite airflow field is established by employing the Hamilton’s principle. By using the generalized eigenvalue method to linear system, the variations of the natural frequencies of the plate in the process of entering the finite airflow field are investigated, from which the stability change rules of the system are obtained. The vibration properties of the system are studied by analyzing the displacement time response of the plate in the process of entering the finite flow field. From the results, the different system parameters such as entry position, entry velocity, aspect ratio, external harmonic excitation amplitude and external harmonic excitation frequency have significant impacts on the stability and vibration properties of the plate entering the finite airflow field.

Encapsulations of Magnetorheological Fluids Within 3-D Printed Elastomeric Cellular Structures

In this study, magnetorheological fluid (MRF) was successfully encapsulated in a 3-D printed elastomeric cellular structure. To this end, an MRF, which was composed of (40% volume fraction) carbonyl iron particles (6– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10~\mu \text{m}$ </tex-math></inline-formula> in diameter) suspended in silicone oil, was encapsulated in a thermoplastic polyurethane (TPU) elastomeric cellular structure. A 3-D printer was used to print a TPU elastomer with a rectangular cellular structure in the shape of a circular cylinder. The MRF was injected into the rectangular voids within the TPU cellular structure (hereinafter MRF-TPU elastomeric composite), and then sealed into the composite by 3-D printing a capping or sealing layer on top. The mechanical stiffness and damping properties of the MRF-TPU elastomeric composite with respect to external magnetic fields (0, 2, and 7 kG) and excitation frequencies (1, 5, and 10 Hz) were measured via uniaxial dynamic mechanical testing. Also, the effects of excitation and prestrain amplitude on the mechanical properties of the MRF-TPU elastomeric composite were investigated in these experiments. The complex stiffness and dissipated energy measured via dynamic mechanical testing were used as the performance index.

A Bridge-Shaped Vibration Energy Harvester with Resonance Frequency Tunability under DC Bias Electric Field.

A vibration piezoelectric energy harvester (PEH) is usually designed with a resonance frequency at the external excitation frequency for higher energy conversion efficiency. Here, we proposed a bridge-shaped PEH capable of tuning its resonance frequency by applying a direct current (DC) electric field on piezoelectric elements. A theoretical model of the relationship between the resonance frequency and DC electric field was first established. Then, a verification experiment was carried out and the results revealed that the resonance frequency of the PEH can be tuned by applying a DC electric field to it. In the absence of an axial preload, the resonance frequency of the PEH can be changed by about 18.7 Hz under the DC electric field range from −0.25 kV/mm to 0.25 kV/mm. With an axial preload of 5 N and 10 N, the resonance frequency bandwidth of the PEH can be tuned to about 13.4 Hz and 11.2 Hz, respectively. Further experimental results indicate that the output power and charging response of the PEH can also be significantly enhanced under a DC electric field when the excitation frequency deviates from the resonance frequency.

Bursting dynamics and the zero-Hopf bifurcation of simple jerk system

We characterize the zero-Hopf bifurcation at a singular point of a parameter jerk system. By employing the second order averaging theory, we demonstrate that up to three periodic orbits generated as disturbance parameters tend to zero. Again, both the bifurcation mechanism and bursting dynamics of the 3D jerk system with external periodic excitation are systematically explored. While an order difference exists between the frequency of external excitation and the average frequency of the system, the system exhibits bursting oscillations. The mechanisms of different bursting oscillations are investigated by means of the equilibrium point curve and the transformed phase portraits. As the amplitudes of the excitation change, the system displays “delayed symmetric pitchfork/point, delayed symmetric pitchfork/supHopf, and delayed pitchfork/supHopf/homoclinic connection bursting”. Finally, an analog circuit is designed to verify the complex bursting phenomena of the system.

Vibration Fatigue Analysis of a Simply Supported Cracked Beam Subjected to a Typical Load

In order to realize the accurate prediction of the vibration fatigue life of the beam in service, a loose coupling analysis method is proposed to carry out vibration fatigue analysis of a beam with an initial crack. In modal analysis, the initial crack segment is replaced with a torsion spring, and the damping loss factor is introduced by the complex modulus of elasticity; for the simply supported beam, the inherent vibration characteristic equation of the cracked beam is derived. In vibration fatigue analysis, the interaction between the crack’s growth and vibration analysis is considered, and a loose coupling analysis method is proposed to conduct modal dynamic response and vibration fatigue analysis simultaneously. Results indicate that the crack’s relative location and depth determine the modal of the cracked beam, and crack parameters, damping loss factor and external excitation frequency are important factors for the vibration fatigue life of the beam.

The numerical calculation method based on equivalent frequency-independent time-domain damping model

In order to realize the time-domain analysis based on hysteretic damping model, the frequency-independent time-domain damping model of single degree of freedom (SDOF) system is constructed. Based on the assumed relationship of vibration responses, the equivalent frequency-independent time-domain damping model in complex domain and real domain are proposed. The characteristic that the dissipated energy in each cycle is not related to the vibration frequency of external excitation is retained for the two equivalent damping models. Combined with Newmark- β method, the corresponding numerical methods are obtained. The numerical examples show that the free vibration responses are stably convergent based on equivalent damping models. The numerical results of vibration responses of SDOF system due to earthquake wave have high calculation accuracy. Compared with equivalent frequency-independent time-domain damping model in real domain, the computational accuracy of equivalent frequency-independent time-domain damping model in complex domain is higher, and the computational efficiency is lower.

An experimental study of two-layer liquid sloshing under pitch excitations

The non-resonant and resonant responses of a two-layer liquid system in a tank under pitch excitation were investigated experimentally in this study. The movement of both the free surface and the interface was automatically identified simultaneously by an image processing method, which can rectify the visually tilted frames in a moving system. When the frequency of external excitation was near the natural frequency related to upper layer liquid, free surface resonance can be triggered. On the other hand, when the frequency of the external excitation was close to the natural frequency related to lower layer, resonant response of the interface between two liquids occurred. It is also found that Kelvin-Helmholtz instabilities with different length scales can be generated due to the reverse direction of velocities near the interface under different conditions. Such length scale of the Kelvin–Helmholtz instability can be estimated by using the critical Richardson number. In addition, the bottom of the tank may restrict the development of wave trough on the interface when the depth of lower layer was relatively shallow, while the free surface may limit the wave crest of interface when the thickness of the upper layer was small. Further investigations of the interface displacements for both non-resonant and resonant responses were also conducted in frequency domain.

Supercritical nonlinear transverse vibration of a hyperelastic beam under harmonic axial loading

Dynamics of a hyperelastic beam in a buckled state subjected to a harmonic axial load is investigated in this work. For the static case, the buckled configuration of the hyperelastic beam is first determined through an asymptotic method when the axial load is in excess of its critical load. Then, the governing equation of vibration of the buckled beam is derived, which is a complex nonlinear partial differential equation with varying coefficients. The first natural frequency of the buckled beam is obtained by linear analysis and effects of material and geometrical parameters on it are numerically investigated. By applying the Galerkin method, the governing equation for nonlinear transverse vibration of the beam in the buckled state is transformed into a series of strongly nonlinear ordinary differential equations. Dynamic characteristics of the hyperelastic beam are investigated by the Runge–Kutta method. Bifurcation diagrams, time traces, phase-plane portraits, and Poincare sections are obtained for different values of the external excitation frequency and amplitude of variation of the axial load. Results show that different dynamic behaviors of the hyperelastic buckled beam such as periodic, multi-periodic, quasiperiodic, and chaotic motions can be found when the amplitude of the axial load is varied. Amplitude–frequency responses of the hyperelastic buckled beam are obtained by the Runge–Kutta method and harmonic balance method. Results from the Runge–Kutta method are in good agreement with those from the harmonic balance method. Lastly, effects of the external mean axial load, amplitude of variation of the axial load, geometrical and material parameters on amplitude–frequency responses of the buckled beam are numerically investigated.

Bursting oscillations with adding-sliding structures in a Filippov-type Chua’s circuit

In this paper, a modified Chua’s circuit, possessing an external excitation current and a piecewise nonlinear resistor, is considered to investigate bursting oscillations and the dynamical mechanism in the Filippov system, focusing on the effects of sliding bifurcations on the bursting dynamics. Five typical representative bursting oscillations are observed when there is a gap between the external excitation frequency and the natural one. Codimension-1 bifurcations of the fast subsystem are discussed by regarding the whole excitation term as a bifurcation parameter. The necessary conditions of conventional bifurcations of the equilibria and the bifurcations of boundary equilibria are obtained via theoretical analysis. Both the local adding-sliding bifurcation, crossing-sliding bifurcation, non-smooth fold bifurcation, the fold bifurcation of non-smooth limit cycle in the fast subsystem and the adding-sliding bifurcation in the slow–fast coupling system are observed via numerical method. Based on slow–fast analysis method and the bifurcation analysis, the dynamical mechanism is discovered. Research found that the non-smooth fold bifurcation of the boundary equilibrium can lead to jumping behaviors of the trajectory from the switching manifold to the attractors of the subsystem. The crossing-sliding bifurcation may not cause the transition between spiking state and quiescent state. The local adding-sliding bifurcation in the fast subsystem can lead to adding-sliding bifurcation of non-smooth limit cycle in the coupling system. There may exist adding-sliding structure in bursting oscillations before or after the adding-sliding bifurcation.

Resonant sloshing in a rectangular tank under coupled heave and surge excitations

This paper investigates the resonant sloshing excited by coupled surge and heave excitations. A rectangular tank with a width-to-length ratio of W/L = 1/2 and an intermediate liquid depth of h/L = 0.2 are considered. Through laboratory experiments and numerical simulations, the nonlinear characteristics of the sloshing wave and dynamic pressure are investigated, and their correlations with the external excitation frequency are explored. It is found that when the sum or difference of the surge and heave frequencies approach to the system's odd-number-order natural frequencies, the resonant sloshing occurs even though neither the surge nor the heave excitation triggers resonance by itself. Nevertheless, the most violent sloshing happens when both heave and surge excitations locate in their corresponding resonant regions. The excitation frequency that induces the maximal resonance is slightly larger than that of the analytical value due to the effect of wave nonlinearity. The rising time and impact pressure during slamming under different excitation conditions are also analysed and discussed.

Dynamic model of vibrating plate coupled with a granule bed

A dynamic model is proposed to study the nonlinear behavior of a granule-bed–vibrating-plate coupling system based on the theory of a completely inelastic bouncing ball. The process of interactions between the ball and plate is divided into three stages: synchronized motion, separation, and impact. The discrete-element method is used to obtain the form of the impact function inspired by the bird impact model, and the analytical solutions of the overall process are derived. Furthermore, parametric research is performed to demonstrate the influence on the motion of the plate of system parameters including the amplitude of the excitation force, particle mass, and damping. The calculation results indicate that the model can be used to analyze the coupling dynamic behaviors of particles and plates, and abundant nonlinear phenomena, such as period-doubling bifurcations, can be observed. The motion of the plate always shows chaos in particular frequency bands (the ratio of external excitation frequency to natural frequency was between 0.63 and 0.75 for the conditions in this study).

Numerical analysis of combined optimization of turbine runner flow pattern and shafting System

This paper attempts to solve the turbine failures reported by a hydropower station, namely, the violent vibration in the runner region under a special working condition and the blade cracking on the outlet edge near the lower ring. For this purpose, the entire flow channel of the turbine was simulated by computational fluid dynamics (CFD) on ANSYS, and the runner strength and mode of shaft assembly system (SAS) were computed by the liquid-solid coupling algorithm. The calculation results show that severe low (negative) pressure appeared on the outlet edge near the lower ring, excess stress was observed in that area, and the resonance occurred as the fifth and sixth order natural frequencies of the SAS were the same with the rotation frequencies of the blade. On this basis, the original blade was modified repeatedly. Through the modification, the flow field distribution in the runner region and the blade strength were both greatly improved, and the SAS natural frequencies were kept away from the various external excitation frequencies, laying a solid basis for the safe and stable operation of the turbine.

Finite element modal analysis and experiment of rice transplanter chassis

The vibration problem during the operation of rice transplanters is the most common phenomenon. In order that the static and dynamic characteristics of the rice transplanter chassis can meet the requirements of more stable operation, the research took the 2ZG-6DK rice transplanter as the research object to carry out a vibration reduction optimization study. In the research, the Pro/Engineer 5.0 software was first used to model the chassis of the rice transplanter. The constructed finite element model was revised by using the structural parameter revision method and the mixed penalty function method. The model was imported into ANSYS Workbench to solve the modal frequency and vibration shape of the rice transplanter chassis. Based on the MAC (modal assurance criterion) criterion, modal tests were carried out to verify the accuracy of the finite element theoretical analysis. Through the analysis of the characteristics of the external excitation frequency, the chassis is structurally optimized to avoid resonance caused by the natural frequency of the chassis falling within the road excitation frequency range. The final optimization results showed that the first four orders of modal frequencies of the chassis were adjusted to 32.083 Hz, 33.751 Hz, 42.517 Hz, and 50.362 Hz, respectively, in the case that the chassis mass was increased by 6.714 kg (8.8%). They all avoid the range of road excitation frequency (10-30 Hz) so that the rice transplanter can effectively avoid the resonance phenomenon during operation. This study can provide a reference for the design and optimization of the chassis structure of transplanter. Keywords: transplanter chassis, vibration, finite element analysis, modal experiment, MAC criterion, optimization design DOI: 10.25165/j.ijabe.20221505.6230 Citation: Chen K K, Yuan Y W, Zhao B, Jin X, Lin Y, Zheng Y J. Finite element modal analysis and experiment of rice transplanter chassis. Int J Agric & Biol Eng, 2022; 15(5): 91–100.

An optimal control method for time-delay feedback control of 1/4 vehicle active suspension under random excitation

Time-delay feedback control can effectively broaden the damping frequency band and improve the damping efficiency. However, the existing time-delay feedback control strategy has no obvious effect on multi-frequency random excitation vibration reduction control. That is, when the frequency of external excitation is more complicated, there is no better way to obtain the best time-delay feedback control parameters. To overcome this issue, this paper is the first work of proposing an optimal calculation method that introduces stochastic excitation into the process of solving the delay feedback control parameters. It is a time-delay control parameter with a better damping effect for random excitation. In this paper, a 2 DOF one-quarter vehicle suspension model with time-delay is studied. First, the stability interval of time-delay feedback control parameters is solved by using the Lyapunov stability theory. Second, the optimal control parameters of the time-delay feedback control under random excitation are solved by particle swarm optimization (PSO). Finally, the simulation models of a one-quarter vehicle suspension simulation model are established. Random excitation and harmonic excitation are used as inputs. The response of the vehicle body under the frequency domain damping control method and the proposed control method is compared and simulated. To make the control precision higher and the solution speed faster, this paper simulates the model by using the precise integration method of transient history. The simulation results show that the acceleration of the vehicle body in the proposed control method is 13.05% less than the passive vibration absorber under random excitation. Compared with the time-delay feedback control optimized by frequency response function, the damping effect is 12.99%. The results show that the vibration displacement, vibration velocity, and vibration acceleration of the vehicle body are better than the frequency domain function optimization method, whether it is harmonic excitation or random excitation. The ride comfort of the vehicle is improved obviously. It provides a valuable tool for time-delay vibration reduction control under random excitation.

Vibration and stability analysis on the water entry process of a thin plate

In this study, the stability and vibration characteristics of a thin plate in the water entry process are investigated. In the water entry process, the mass, damping and stiffness of the system change continuously with time to make the stability of the fluid-structure system exhibit the time-varying characteristics. Based on the nonlinear plate theory and the linear potential flow theory, the equation of motion of the plate interacting with external airflow and water flow is established. For the linear equation, the changes of the natural frequencies of the plate entering the water are researched by applying the generalized eigenvalue method, from which the stability of the system is analyzed. For the nonlinear equation, the displacement time responses and phase portraits of the plate subjected to harmonic excitation are discussed by numerical simulations. When the plate enters the water, the stability of the plate becomes worse. The range of the external excitation frequency makes significant effects on the vibration characteristics of the plate. The plate falls into instability with the entry velocity increasing. Finally, the effects of the fluid density, the aspect ratios and the length-to-thickness ratios of the plate on the stability and vibration characteristics of the plate are discussed.