External Excitation Frequency Research Articles

Numerical researches of three-dimensional nonlinear sloshing in shallow-water rectangular tank

The Boussinesq-type equations in terms of velocity potential are adopted for the solutions of three-dimensional nonlinear sloshing motions in a shallow-water rectangular tank. The total velocity potential is divided into two parts: a particular solution and the rest which is calculated by the Boussinesq-type equations. Particular solutions of six degrees of freedom motions are constructed. The fully nonlinear free surface boundary conditions are satisfied and finite difference scheme is adopted for the spatial derivatives. The free surface profiles in tank with external excitation frequencies close to the first natural frequency are presented. Numerical results demonstrate that the Boussinesq-type equations with particular solutions can accurately model nonlinear sloshing waves in shallow-water rectangular tank.

Study on Torsional Vibration of RV Reducer Based on Time-Varying Stiffness

The torsional vibration of RV reducer is the key factor affecting the positioning accuracy and trajectory accuracy of industrial robots. It is of great significance to study the torsional stiffness periodic fluctuation and parametric torsional vibration to improve the torsional vibration performance and transmission accuracy of RV reducer. Based on the torsional stiffness test device of RV reducer, the torsional stiffness is measured and the torsional stiffness curve with periodic fluctuation is obtained. The trigonometric function fitting and mathematical description of torsional stiffness curve are carried out, and the torsional vibration equation of RV reducer parameters is established. The parametric torsional vibration response of RV reducer is simulated by Runge–Kutta method, and the combined frequency characteristics and system stability are analyzed. The torsional vibration test device of RV reducer is developed to study the torsional stiffness fluctuation and torsional vibration fault. The torsional stiffness fluctuation of RV reducer can be divided into a short period and long period, corresponding to different manufacturing errors, and the mechanism of torsional stiffness fluctuation is found out. The frequency spectrum of torsional vibration under working condition is highly consistent with the simulated response spectrum, and the harmonic resonance interval obtained by frequency sweeping is close to the peak of the torsional vibration–speed curve, so the correctness of the established torsional vibration model is verified. Using the mechanism of RV reducer stiffness fluctuation to realize rapid diagnosis of defective parts of RV reducer has a strong engineering application value. The time-varying torsional stiffness of RV reducer will cause the phenomenon of parametric torsional vibration. The vibration response characteristic frequency is a linear combination of internal reference variation frequency and external excitation frequency. The parametric torsional vibration will cause the harmonic resonance of RV reducer and aggravate the torsional vibration. Therefore, it is of great engineering value to study the time-varying torsional stiffness and torsional vibration of RV reducer.

A fractional nonlocal time-space viscoelasticity theory and its applications in structural dynamics

To overcome the long wavelength and time limits of classical elastic theory, this paper presents a fractional nonlocal time-space viscoelasticity theory to incorporate the non-locality of both time and spatial location. The stress (strain) at a reference point and a specified time is assumed to depend on the past time history and the stress (strain) of all the points in the reference domain through nonlocal kernel operators. Based on an assumption of weak non-locality, the fractional Taylor expansion series is used to derive a fractional nonlocal time-space model. A fractional nonlocal Kevin–Voigt model is considered as the simplest fractional nonlocal time-space model and chosen to be applied for structural dynamics. The correlation between the intrinsic length and time parameters is discussed. The effective viscoelastic modulus is derived and, based on which, the tension and vibration of rods and the bending, buckling and vibration of beams are studied. Furthermore, in the context of Hamilton’s principle, the governing equation and the boundary condition are derived for longitudinal dynamics of the rod in a more rigorous manner. It is found that when the external excitation frequency and the wavenumber interact with the intrinsic microstructures of materials and the intrinsic time parameter, the nonlocal space-time effect will become substantial, and therefore the viscoelastic structures are sensitive to both microstructures and time.

Finite Element Analysis of Marine Weapon Lift Based on ANSYS

In order to improve the dynamic characteristics of a shipborne weapon elevator and reduce the adverse effects of harmonic vibration on the elevator under sea conditions, the finite element model of weapon elevator is established by ANSYS/Workbench, and the modal analysis, harmonic response analysis and static strength analysis of the elevator under dynamic load are carried out. The analysis results are obtained: The harmonic frequency is far less than the first natural frequency of the elevator under the external sea condition, so the system will not suffer from resonance damage and meet the strength requirements; the external excitation frequency of the elevator should be avoided from 20 to 40 Hz, and the deformation of the side plate in motion is the largest, but within the control range, it does not affect the docking of adjacent components. Improvement measures are put forward to increase safety factor and anti-vibration ability.

Enhanced design considerations on the buckling and dynamics of Gannet-inspired systems during water entry

To provide a more complete analysis of Gannet birds and Gannet-inspired drones during diving, this work considers an improved beam model to describe the static and dynamic characteristics of Gannet and Gannet-like drones at impact. The beam model consists of two different geometric and material property beams under continuity conditions to better understand the geometrical and material parameters’ influence on the structural statics and dynamics of these kinds of systems. Using Hamilton’s principle, the equations of motion, continuity, and boundary conditions considering Euler–Bernoulli and Timoshenko theories are derived. Then, applying the continuity and boundary conditions, the static and dynamic analyses are conducted to examine the impact buckling speeds, the buckled shapes, the natural frequencies at different impact velocities for bioinspired drone design, and the post-buckled mode shapes. The buckled configurations suggest that the body of the Gannet most likely has a different bending and torsional stiffness than the neck. The results indicate that the amount of softening in the joints contributes significantly to not only the speed at which the bird will buckle, but also the buckling profile of the bird. To obtain a physical buckling profile of the Gannet, a stiffer boundary condition at the end of the bird body model is needed due to the increased bending stiffness properties of the body compared to the neck as well as the position of the wings and feet surpassing the end of the body. The results also demonstrate that to build a bioinspired diving drone that falls within a smaller air-vehicle range, the amount of error between theories in predicting the static and dynamic buckling behavior of the system becomes significantly more evident. The dynamic characteristics and mode shapes of the Gannet-like systems are provided for further drone design insight on the impact speeds the drone can achieve without responding to an external excitation frequency from a propeller or actuator.

Numerical and experimental study of tuned liquid damper effects on suppressing nonlinear vibration of elastic supporting structural platform

A liquid storage container installed on the top of a fixed offshore platform is used as a tuned liquid damper (TLD) to suppress structural vibration through sloshing motion and viscous energy dissipation. To further optimize TLD capability on suppressing vibration and accurately predict nonlinear coupled processes between TLD and offshore platform, a two-way coupling numerical model was developed to investigate the nonlinear vibration of TLD and elastic supporting structural platform (SSP). Meanwhile, laboratory experiments of TLD interaction with the SSP were also conducted on a six-degree-of-freedom motion simulator to validate the developed model. The bottom plate of the SSP was fixed to the motion simulator and subjected to sinusoidal excitation in the horizontal direction. The natural frequency of bare SSP was obtained firstly by shaking table tests at a wide range of external excitation frequencies and finite element modal analysis. The developed numerical model was validated by using the present experimental data in terms of both the roof plate displacements of the SSP and the free surface elevation and waveforms in TLD. Effects of TLD in suppressing the nonlinear vibration of the elastic SSP were further investigated numerically by varying the mass and frequency ratio of TLD to the SSP. Wavelet transform was used to analyze the nonlinear interaction and energy distribution characteristics of the sloshing wave in TLD. It was shown that the peak displacement response of the roof plate had been significantly reduced, and at the same time a frequency shift occurred after TLD installed on the SSP. In addition, the sudden excitation breaks the balance of energy absorption and production in fluids, resulting in larger wave height. Finally, a mass ratio of 2% and a frequency ratio of 1 were found to be optimal by considering the frequency shift and energy dissipation.

3D full-space triboelectric-electromagnetic hybrid nanogenerator for high-efficient mechanical energy harvesting in vibration system

Mechanical energy with low frequency is a widely distributed energy in environment. Triboelectric nanogenerator (TENG) and electromagnetic energy harvester (EMG) are considered as promising methods to harvest low-frequency mechanical energy. In this study, a three-dimensional (3D) full-space triboelectric-electromagnetic hybrid nanogenerator (FSHG) based on a magnetic ball and Polystyrene (PS) spherical shells is presented. The external excitation can be transformed into the relative motion between different units. The mover composed of the PS spherical shell 3 and a magnet ball transforms 3D full-space mechanical energy into electrical energy through friction electrification and electromagnetic induction effect. The results of experiments show that the performance of TENG and EMGs can be influenced by the direction of external vibration and excitation frequency. The output performances of TENG and EMGs increase as the excitation frequency increases. The results show that the maximum output power of TENG is 18 μW at an external loading resistance of 200 MΩ, and the maximum output power of EMG is 640 μW at an external loading resistance of 1000 Ω. The FSHG demonstrates a quick charging ability for capacitor and the capability to power hundreds of LEDs. After storing energy in the capacitor, the DC signal can power a humidity/temperature sensor.

Effects of Silicone Oil on Stiffness and Damping of Rubber-Silicone Oil Combined Damper for Reducing Shaft Vibration

The helicopter tail drive shaft system is a typical multi-point supported drive shaft system, with a long span that can lead to serious vibration problems. Shaft vibration can be effectively reduced by installing a rubber-silicone oil combined damper between the bearing and bearing pedestal at the support point along the tail drive shaft. Stiffness and damping characteristics of the rubber-silicone oil combined damper are important factors affecting shaft vibration. In this study, the effects of silicone oil on the stiffness and damping of rubber-silicone oil combined damper were analyzed through simulations. The simulation method was experimentally verified and factors influencing the static stiffness, dynamic stiffness, and damping characteristics of the damper were investigated. In addition, the influence of damper dimensions and external excitation frequency on the stiffness and loss factor of the damping ring in the presence and absence of silicone oil were examined. The presence of silicone oil increases the difference between the dynamic stiffness and the loss factor. As the viscosity of the silicone oil increases, the static stiffness, dynamic stiffness, and loss factor of rubber-silicone oil combined dampers increase. The results have important guiding significance in the design of dampers for shafting systems.

Experimental study on characteristic of sloshing impact load in elastic tank with low and partial filling under rolling coupled pitching

A series of experiments covering lowest three natural frequencies of rolling coupled pitching were conducted to investigate liquid sloshing with low liquid depth. The test results show that the most violent liquid sloshing in rolling and pitching is located in the vicinity of the first order natural frequency (f1). When the excitation frequency of rolling and pitching is located between 0.98f1 and 1.113f1, roof-bursting phenomenon of liquid appeared, and the maximum impact pressure is at 1.09f1. When the external excitation frequency is at 1.113f1, the number of sloshing shocks decreases sharply. Furthermore, the space distribution of the impact pressure on the left bulkhead and the top bulkhead was analyzed. It is concluded that with low liquid filling, the impact load is greater near the free surface and the top of tank, and the impact position of the side bulkhead increases with the increasing of the frequency near the resonant frequency.

Nonlocal and strain gradient effects on nonlinear forced vibration of axially moving nanobeams under internal resonance conditions

Based on the nonlocal strain gradient theory (NSGT), a model is proposed for an axially moving nanobeam with two kinds of scale effects. The internal resonance-accompanied fundamental harmonic response of the external excitation frequency in the vicinities of the first and second natural frequencies is studied by adopting the multivariate Lindstedt-Poincare (L-P) method. Based on the root discriminant of the frequency-amplitude equation under internal resonance conditions, theoretical analyses are performed to investigate the scale effects of the resonance region and the critical external excitation amplitude. Numerical results show that the region of internal resonance is related to the amplitude of the external excitation. Particularly, the internal resonance disappears after a certain critical value of the external excitation amplitude is reached. It is also shown that the scale parameters, i.e., the nonlocal parameters and the material characteristic length parameters, respectively, reduce and increase the critical amplitude, leading to a promotion or suppression of the occurrence of internal resonance. In addition, the scale parameters affect the size of the enclosed loop of the bifurcated solution curves as well by changing their intersection, divergence, or tangency.

Modeling and Performance Investigation of a Piezoelectric Vibrating Gyroscope

An improved mathematical model of a piezoelectric vibrating gyroscope is constructed with the effects of electromechanical coupling and rotary inertia taken into account. The gyroscope consists of a cantilever beam with tip mass attached to its free end. The piezoelectric materials are adhered to the four surfaces of the rectangular beam. By using two Euler angles and extended Hamilton’s principle, the electromechanical coupled partial differential equations governing the flexural-flexural motions of the piezoelectric gyroscope are obtained. The accuracy and effectiveness of the comprehensive mathematical model are validated by the existing models in literature. The necessity of taking rotary inertia into account is discussed. The natural frequencies of the rotating piezoelectric beam in both drive and sense directions have been investigated by considering the effects of the tip mass, angular speed, and external impedance. The dynamic behaviors of the piezoelectric gyroscope with different parameters, such as the tip mass, the lengths of piezoelectric materials and beam, and the external impedance, have been studied. In particular, the optimal combination of the external excitation frequency and the external impedance for the best calibration curve of the piezoelectric gyroscope is identified. Finally, the dynamic performance of the piezoelectric gyroscope under varying boundary conditions has been investigated for the potential practical applications.

Dynamic Response of a Coated Half-Plane with Hysteretic Damping Under a Harmonic Hertz Load

This paper investigates the dynamic response of a coated half-plane subjected to a harmonic Hertz load on the coating surface. The complex modulus is used to describe the hysteretic damping of the elastic homogeneous coating and half-plane. Using the Helmholtz decomposition and Fourier integral transform technique, we derive the stresses and displacements of the coating and half-plane from Navier’s elasticdynamic equations in the form of complex integrals. Then, the global adaptive quadrature algorithm is exploited to solve the complex integrals numerically. The effects of Young’s modulus ratio, density ratio, coating thickness, loss factor and external excitation frequency are discussed. It is found that the dynamic response of displacements and stresses becomes increasingly oscillatory with the increase in excitation frequency.

Dynamic responses of base-isolated concrete liquid storage structure under two types of resonances

One important characteristic of base-isolated liquid storage structure (LSS) is that the vibration periods of structure and liquid are different, namely, there are two kinds of periods in the system. As a result, structure or liquid resonance may occurs under external excitation. In order to reflect the nonlinear characteristics of liquid sloshing, subsonic potential-based element is used to simulate the liquid. The governing equations of liquid field and fluid-structure interaction (FSI) equations are established; the initial and boundary conditions of liquid sloshing in dynamic coordinate system are obtained. Harmonic functions used to conduct time history analysis are generated by the first order vibration frequencies of structure and liquid respectively. The dynamic responses of base-isolated rectangular liquid storage structure (RLSS) under two types of resonance are studied comparatively. Results show that when the external excitation frequency is equal to the first order vibration frequency of isolated structure or liquid sloshing, wall tensile stress, structure displacement, base shear force and liquid sloshing wave height will appear resonance amplification phenomenon. The dynamic responses of structure itself caused by structure resonance are greater than that of liquid resonance; while the liquid sloshing wave height caused by liquid resonance is greater than that of structure resonance. Under structure resonance, the wall is prone to be cracked; and under liquid resonance, the liquid velocity field will become unusually violent, and liquid overflow will be caused easily.

An integrated three-dimensional micro-solenoid giant magnetoimpedance sensing system based on MEMS technology

In this paper, we proposed an integrated three-dimensional (3D) micro-solenoid giant magnetoimpedance (GMI) sensing system. The sensing system is composed by a 3D micro-solenoid inside which patterned Cobalt-based ribbon is kept as magnetic core and this system was fabricated by Micro-electromechanical Systems (MEMS) technology. The system was measured by non-contact method, which has the advantages of high sensitivity, low power consumption and widespread application prospect. The influence of external magnetic field direction and excitation frequency on micro-solenoid GMI sensing system has been discussed respectively. The fabricated system exhibits an optimum magnetoimpedance (MI) ratio of 4360±40 % at the excitation frequency of 13 MHz under longitudinal external magnetic field. In consequence, 3D micro-solenoid GMI sensing system offers great magnetic performance and this integrated sensing system has potential applications in the field of weak magnetic field detection.

Design and analysis of ground-based operation test bench for complex optical machine functional components

In order to solve the problem of high cost investment in the detection and debugging of complex optical machine functional components by Unmanned aerial vehicle (UAV), especially the aerial camera, a novel ground-based operational test bench is presented in this paper, which can realistically simulate the attitude of UAV and could be used for research of the control system. Based on the Lagrange’s equations of motion, the exact dynamic equation of the flight simulation platform for ground-based operational test bench is derived. The structure is driven by Brushless DC motor (BLDCM) torque motor and simplifying the equations under conditions of practice, we derive the mathematical model. The static and dynamic characteristics were carried out by using the finite element theory to explain rationality of the ground-based operational test bench. Through modal analysis, the first six natural frequencies range is between 99.362Hz and 262.37Hz. The natural frequency of the first mode is much larger than the external excitation frequency. So, it is verified that the frequency response of the structure will not resonate. The ground-based operational test bench that is designed in this paper has the advantages of simple structure and low cost.

Selective frequency conversion with coupled time-modulated cavities

Time dependence in photonic structures leads to a number of intriguing and useful phenomena such as optical isolation, topological states of light, and frequency conversion. Here we present a mechanism to achieve efficient and selective frequency conversion using a system of two time-modulated cavities. This setup allows us to fine-tune the conversion process by controlling important parameters such as the intercavity coupling and the external excitation frequency. Both symmetric and asymmetric (up- or down-conversion) outputs can be targeted at will. We describe the processes extensively, with for example a leading role for the dynamic modes of the coupled system, the Floquet modes.

Levitation Height Drifts of HTS Bulks under a Long-Term External Disturbance

High-temperature superconducting (HTS) maglev owns the capability of passive stabilization and has the potential to operate at a high speed with low energy consumption. However, the excitation caused by the irregular surface and inhomogeneous magnetic field of the permanent magnet guideway (PMG) will result in vibration between the superconductors and PMG, which could lead to some stability problems such as drift. To study the reliability of HTS maglev systems under a long-term disturbance, a tailored experimental device composed of a vibration table, a fixture, and HTS maglev model was employed. The effects of field-cooling height (FCH), external excitation frequencies, and amplitudes on the levitation height drift were investigated. It is found that under the same operating conditions, large excitation amplitude, high frequency, and low FCH would lead to a greater levitation height drift. There are three kinds of drift trends, i.e., downward, upward, or downward at first and then upward, and the phenomenon of drifting upward is more likely to occur under small excitation amplitude, high frequency, and low FCH conditions. Meanwhile, two simulation models employing the flux flow model and the flux flow and creep model were applied respectively. The simulation results show that the flux flow and creep model are more consistent with the experimental phenomena and the flux flow has a greater influence on the drift in the initial time period, while the flux creep has a slighter impact on the drift for a long time. These researches reveal the levitation height drift rules of the HTS maglev system and introduce proper simulation model for levitation height drift so that this work provides a reference for the design and safe operation of HTS maglev vehicles.

Maximization of Eigenfrequency Gaps in a Composite Cylindrical Shell Using Genetic Algorithms and Neural Networks

This paper presents a novel method for the maximization of eigenfrequency gaps around external excitation frequencies by stacking sequence optimization in laminated structures. The proposed procedure enables the creation of an array of suggested lamination angles to avoid resonance for each excitation frequency within the considered range. The proposed optimization algorithm, which involves genetic algorithms, artificial neural networks, and iterative retraining of the networks using data obtained from tentative optimization loops, is accurate, robust, and significantly faster than typical genetic algorithm optimization in which the objective function values are calculated using the finite element method. The combined genetic algorithm–neural network procedure was successfully applied to problems related to the avoidance of vibration resonance, which is a major concern for every structure subjected to periodic external excitations. The presented examples illustrate a combined approach to avoiding resonance through the maximization of a frequency gap around external excitation frequencies complemented by the maximization of the fundamental natural frequency. The necessary changes in natural frequencies are caused only by appropriate changes in the lamination angles. The investigated structures are thin-walled, laminated one- or three-segment shells with different boundary conditions.

Theoretical analysis of an impact-bistable piezoelectric energy harvester

In recent years, piezoelectric energy harvesting has attracted growing attention due to its great potential in the application of Internet of Things. However, traditional linear harvesters have limited operation bandwidth, resulting into the sharp decline of the output power when the excitation frequency shifts from the resonance thus a low efficiency for stochastic excitations in the ambient environment. In order to overcome these issues, this paper analyzes the performance of an impact-bistable piezoelectric energy harvester. Influence of critical parameters including the clearance between two collision parts of the harvester, and external excitation frequencies and amplitudes upon the harvester performance are theoretically studied using the dimensionless model. Phase portraits, time histories, bifurcation diagrams and 0-1 test are employed to analyze the characteristics of the harvesting system. The results show that by choosing appropriate physical parameters, the proposed energy harvester could exhibit high-energy interwell motion with an 80% frequency bandwidth under both the harmonic excitation and broadband random excitation.

Simulation and experiment on bridge-shaped nonlinear piezoelectric vibration energy harvester

There is abundant of vibration energy in environment. Using piezoelectric energy harvesters to power ultra-low power wireless sensors has become a hot topic in recent years. Most piezoelectric energy harvesters have satisfactory output only at one resonant frequency, while once the external excitation frequency deviates from the resonant frequency, the voltage output will drop significantly. Therefore, this paper proposes a bridge-shaped piezoelectric energy harvester to broaden the frequency band for energy harvesting, and the harvester can adaptively adjust the natural frequency of the system to match the external excitation. Based on the two-dimensional nonlinear Euler–Bernoulli beam hypothesis and the Hamilton principle, the distributed-parameter dynamic model of the nonlinear energy harvesting system is set up. By use of variation operator and nondimensionalization, we derive the dimensionless electromechanical coupling equations. With the harmonic balance method, the approximate equations for calculating voltage amplitude and average power are derived. And then the model is numerically solved and analyzed by considering the influence of excitation frequency, excitation amplitude, mass position and load on the output performance of the bridge-type piezoelectric energy harvester. Finally, various comprehensive experiments are performed to verify the results of simulation, and the dynamic effects of the moving mass on the output characteristics are studied. It can be noted that the moving mass can improve the voltage output of the bridge type energy harvester by changing the resonant frequency of the bridge-type piezoelectric energy harvester and impacting the piezoelectric beam. The proposed vibration energy collection device can adaptively tune the resonant frequency and has practical value in engineering.