External Excitation Frequency Research Articles

Modal and harmonic analysis of femur bone using different boundary conditions by Finite Element Analysis.

The longest and largest bone in the human body is the femur. Pelvic bone sustains the weight of the body to which the femur bone is connected. Many researches have been carried out to identify the behaviour of the femur bone. The study aimed to explore the natural frequencies and mode shapes of vibrating devices to gain insights into the dynamic behavior of the femur bone during various physical activities. Examining the impact of patient-specific bone shape and density on bone natural frequencies is crucial. The primary goals of femur bone analysis involve employing computer simulations for fracture detection and employing Finite Element (FE) models to determine natural frequencies and vibration modes. To obtain the natural frequency of the femur bone, different boundary conditions such as free-fixed and fixed-fixed are applied. Avoiding the coincidence of the natural frequency with external excitation frequencies is crucial to prevent femur bone fractures. Also, for different magnitude of loads, femur bone is involved in harmonic analysis is to identify the amplitude and stress against acceleration.

Energy management optimization of a gravitational energy harvester powering wireless sensor nodes for freight trains monitoring

Energy harvesting is a promising solution for the realization of self-powered wireless sensor nodes (WSNs), minimizing battery waste and environmental impact. The harvesting devices studied in this paper are gravitational vibration-based energy harvesters (GVEHs), converting the ultra-low-frequency ambient vibrations of structures or vehicles into electric power. The main efficiency losses are related to the AC/DC rectification and battery storage processes. Experimental tests confirm the optimized layout of negative voltage converter (NVC) using MOSFETs and a schottky diode with a 1000 μF smoothing capacitor, achieving power rectification efficiency of 65%. The rectified and smoothed power is stored in a Li-Ion 3.6 V 40 mAh coin cell and supplied to the load, consisting of a 3.3 V micro-controller unit, temperature sensor and sub-GHz wireless communication module. A nano power boost charger with buck converter manages power between the battery and the load. Experimental battery charge tests are performed for charging power evaluation at different external excitation amplitudes and frequencies. WSN average power consumption is analyzed with master–slave communication tests at different signal strengths and relative distances between the nodes. Finally, a duty cycle between active and sleep phase is defined to guarantee continuous activity of the WSN and net positive charge to the battery.

Experimental and numerical study on dynamic response of a photovoltaic support structural platform with a U-shaped tuned liquid column damper

A tuned liquid column damper (TLCD) is widely used in offshore structures as a passive energy dissipation device to reduce the harm of wind, wave, and current loads to the safety of offshore platforms. This investigation explores the dynamic response and interaction mechanism of a photovoltaic support structural platform (SSP) equipped with a TLCD by experimental and numerical analysis. The vibration mitigation performance of the TLCD under varying liquid depth ratios, external excitation frequencies, and amplitudes is systematically evaluated. The experiments focus on assessing the structural dynamic response and wall pressure to determine the vibration reduction efficiency of the TLCD for structures with fundamental frequencies more than 2 Hz. The experimental results indicate that the TLCD can reduce the structural response maximally near the natural frequency (2.52 Hz) of the structure, with vibration reduction effectiveness ranging from 42.0% to 85.1%. Additionally, one develops a two-way fluid-structure interaction (FSI) model to investigate further the impact of hydrodynamic pressure caused by sloshing inside the TLCD on the SSP motion response, which providing a more detailed explanation for the different phenomena observed in the experimental results.

Nonlinear vibration characteristics of thermo-viscoelastic coupling of moving PET films with temperature-dependent elastic modulus

In order to improve the transport stability of roll-to-roll produced polyethylene terephthalate films (PET films) in high temperature environments, this paper investigates the nonlinear vibrational properties of moving PET films under a uniform temperature field by considering the temperature dependence of the elastic modulus. Firstly, constant tensile tests were conducted to test the elastic modulus values of PET films at different hot air temperatures, and the Wachtman model was improved to establish a temperature-dependent elastic modulus model for PET films. Secondly, based on the Kelvin-Voigt model, the nonlinear vibrational equilibrium differential equations of the system were established by applying the Bubnov-Galerkin method of discretization according to D’Alembert’s principle. Finally, numerical simulations based on the 4th-order Runge-Kutta method were carried out to analyze the effects of films width, external excitation frequency, external excitation amplitude, transfer velocity, ambient temperature, damping coefficient and viscoelasticity coefficient on the nonlinear vibration of the system. This provides a theoretical basis for the commissioning of stabilized transfer parameters for roll-to-roll production of PET films.

Nonlinear dynamic analysis of a spring coupled double beam based piezoelectric energy harvester under parametric base excitation

This paper proposes a base excited, spring coupled double cantilever beam with attached tip mass based piezoelectric energy harvester. The dimensions of the beams are so chosen that the system experiences 1:1 internal resonance. The governing coupled electro-mechanical equations of motion of the system are obtained by using the Lagrange principle which is reduced to the temporal form by using generalized Galerkin’s method. The governing temporal equations of motion are in the form of that of a parametrically excited coupled system with geometric and inertial nonlinearities. These nonlinear equations are solved using the method of multiple scales and the results are compared with those solved by numerical method (4th order Runge Kutta method) for principal parametric resonance conditions. Parametric studies are conducted by varying the tip masses of the beams, coupled spring stiffness, load resistance, external excitation frequency and excitation amplitude. Results show that by introducing spring coupling, the system operational frequency range increases significantly and also energy transfer process takes place due to the internal resonance. Significant enhancement of voltage and power are observed in the present work in comparison to the earlier studied equivalent single beam-based energy harvester.

Optimization Design of Straw-Crushing Residual Film Recycling Machine Frame Based on Sensitivity and Grey Correlation Degree

This paper takes the frame as the research object and explores the vibration characteristics of the frame to address the vibration problem of a 1-MSD straw-crushing and residual film recycling machine in the field operation process, and an accurate identification of the modal parameters of the frame is carried out to solve the resonance problem of the machine, which can achieve cost reduction and increase income to a certain extent. The first six natural frequencies of the frame are extracted by finite element modal identification and modal tests, respectively. The rationality of the modal test results is verified using the comprehensive modal and frequency response confidences. The maximum frequency error of modal frequency results of the two methods is only 6.61%, which provides a theoretical basis for the optimal design of the frame. In order to further analyze the resonance problem of the machine, the external excitation frequency of the machine during normal operation in the field is solved and compared with the first six natural frequencies of the frame. The results show that the first natural frequency of the frame (18.89 Hz) is close to the external excitation generated by the stripping roller (16.67 Hz). The first natural frequency and the volume of the frame are set as the optimization objectives, and the optimal optimization scheme is obtained by using the Optistruct solver, sensitivity method, and grey correlation method. The results indicate the first-order natural frequency of the optimized frame is 21.89 Hz, an increase of 15.882%, which is much higher than the excitation frequency of 16.67 Hz, and resonance can be avoided. The corresponding frame volume is 9.975 × 107 mm3, and the volume reduction is 3.46%; the optimized frame has good dynamic performance, which avoids the resonance of the machine and conforms to the lightweight design criteria of agricultural machinery structures. The research results can provide some theoretical reference for this kind of machine in solving the resonance problem and carrying out related vibration characteristics research.

Design and test of liquid sloshing piezoelectric energy harvester

The energy harvester based on the piezoelectric effect can convert the vibration energy in the environment into electricity to power the network nodes. In order to broaden the effective frequency bandwidth of the piezoelectric energy harvester and reduce the resonant frequency of the system, a liquid slosh-type piezoelectric energy harvester is proposed in this paper. Based on the theory of the piezoelectric effect, the mechanical model and electromechanical coupling model of the piezoelectric energy harvester were established, and the dynamic characteristics of the liquid slosh piezoelectric energy harvester were analyzed. Based on theoretical model and experimental test, the liquid slosh piezoelectric energy harvester is studied. By making a prototype and building a vibration experiment platform, the energy capture characteristics of the piezoelectric energy harvester were tested experimentally. The experimental results show that when the external excitation frequency is close to the first resonant frequency, the maximum output power of the liquid sloshing piezoelectric energy harvester is 0.068 mW, and the optimal matched impedance is 440 kΩ. When the external excitation frequency is close to the second resonant frequency, the maximum output power of the liquid sloshing piezoelectric energy harvester is 0.178 mW, and the optimal matching load resistance is 600 kΩ. Compared with the traditional cantilever beam piezoelectric energy harvester, the liquid slosh piezoelectric energy harvester has a lower resonant frequency and achieves two resonant peaks in the range of 1–20 Hz, which greatly widens the effective frequency bandwidth and improves the energy capture efficiency of the piezoelectric energy harvester.

Approximate analytical solutions of the 1:3 internal resonance response of piezoelectric energy harvester considering two types of coupled frequency components

The 1:3 internal resonance effect in the L-shaped piezoelectric vibration energy harvester leads to an expanded frequency band for energy harvesting and better matching of external excitation frequency in the environment. The electromechanical-coupled governing equations for this vibration energy harvester have been validated in our previous work (Nie et al., 2019). The effect of load resistance on the energy harvester’s natural frequency and damping ratio is addressed. The quadratic and cubic nonlinearities in this system leads to two types of coupled frequency components appear, they ultimately affect the approximate solution of the voltage response. The method of multiple scales is used to derive the two types of coupled frequency components of the system along with their contribution to the output responses. The revised approximate analytical solutions of the output responses are then presented. The system’s stability is assessed through the Jacobi matrix of modulation equations. The nonlinear softening phenomenon that favors the broadening of the bandwidth of the energy harvester is analyzed. The vibration patterns in regions with nonlinear softening and non-softening behavior are investigated through frequency spectra, phase trajectories, and Poincaré cross-sections. The findings reveal that the load resistance significantly affects the damping ratio of the harvester. Inclusion of quadratic and cubic nonlinearities results in three frequency components in the output responses spectrum, with an approximate ratio of 1:2:3. Two types of coupled frequency components appeared in the spectrum of the system’s output responses. The contribution of coupled frequency components to the output response proves crucial, and the revised approximate solutions are in good agreement with that of numerical solutions. The output responses are significantly affected by the initial conditions in the nonlinear softening region, the large and small initial conditions yield solutions in the upper and lower branches, respectively.

Enhancing low-orbit vibration energy harvesting by a tri-stable piezoelectric energy harvester with an innovative dynamic amplifier

Piezoelectric energy harvesting faces a primary challenge in effectively capturing low-orbit vibration energy across a broad frequency range. In this paper, we present a tri-stable piezoelectric energy harvester that incorporates a dynamic amplifier (TPEH + DM), specifically designed for efficient collection of low-orbit vibration energy. The TPEH + DM comprises a piezoelectric cantilever beam connected to an innovative dynamic amplifier at its restrained end, which enhances both the rotational and lateral displacement of the piezoelectric cantilever beam simultaneously. The governing coupled differential equations of motion for the system is derived based on the Lagrange equation, and analytical expressions for its steady-state response are obtained using the multi-scale method. The influence of factors such as the mass and the stiffness ratio of the dynamic amplifier on the steady-state dynamic output characteristics of the system is investigated using the theoretical analysis and numerical simulation. The results indicate that TPEH + DM exhibits significantly improved energy harvesting performance compared to TPEH under low-orbit external excitations. The bandwidth of inter-well motion and the TPEH + DM power output may be further increased by suitably modifying the relative stiffness between the cantilever beam and the dynamic amplifier. In addition, we analyze the time-domain behavior of the system’s output voltage using the ode45 solver under various external excitation frequencies and intensities. The results demonstrate that with appropriate adjustments to the mass of the tip magnet and the stiffness ratio of the dynamic amplifier, the proposed TPEH + DM system can harvest energy efficiently across a broad frequency range, even under low-orbit excitations.

Experiment, Simulation, and Theoretical Investigation of a New Type of Interlayer Connections Enhanced Viscoelastic Damper

A conventional plate-type viscoelastic damper (VED) can easily crack at the interfaces of steel plates and viscoelastic components. In the present work, grooved VEDs, which are a new type of interfacial enhanced VEDs with interfacial grooves, are designed to improve the damping capacity and anti-cracking ability of conventional dampers. The dynamic property experiments of the normal and grooved VEDs are carried out and the interfacial cracking failure of the VEDs are simulated and analyzed by using bilayer cohesive constitutive model with ABAQUS. The grooved VED exhibits excellent dynamic performance and energy dissipation capacity at different temperatures, frequencies, and displacement amplitudes. Experiments and finite element analysis prove that the energy dissipation performance and interfacial bonding strength of the grooved VED are effectively improved. A modified fractional standard linear solid model, in which the Payne effect and temperature–frequency equivalent principle are combined and implemented, is proposed. This model can portray the influence of the excitation displacement, surrounding temperature and external excitation frequency on damper properties at the same time. The fillers and molecular chains affections at micro- and meso-scale are also taken into account. The model’s numerical calculations and experimental results comparisons present that the modified fractional standard linear solid model has sufficient accuracy and performs well in depicting the dynamic properties of the interfacial grooved VED. The errors between the theoretical and experimental values of [Formula: see text] and [Formula: see text] for the grooved VED are mostly within 20% at representative conditions. The interfacial groove structures can well enhance the interfacial bonding and improve the service life of conventional dampers. The modified fractional standard linear solid model is simple and has clear physical meanings for each macro/micro parameters, making it convenient for application in engineering practice. The present research is of great significance in improving the work stability of VEDs and promoting the application of viscoelastic damping technology.

Analysis of stress and deformation of an exponentially graded viscoelastic coated half plane under indentation by a rigid flat punch indenter tip

This paper solves the dynamic contact problem when a rigid flat punch indents into an exponentially graded (FG) viscoelastic coated homogeneous half-plane. A harmonic vertical force is applied to the FG coating, and the solution is obtained for the stress and displacement for both the FG viscoelastic coating and the half-plane using the Helmholtz functions and the Fourier integral transform technique. By applying specific boundary conditions, the contact mechanics problem is converted into a singular integral equation of the first kind. This equation is then solved numerically using the Gauss-Chebyshev integration formulas. The analysis provides detailed insights into how various parameters—such as external excitation frequency, loss factor ratio, Young’s modulus ratio, density ratio, Poisson’s ratio, indentation load, and punch length—affect the dynamic contact stress and dynamic in-plane stress.

Interface coupling effect and multi-mode Faraday instabilities in a three-layer fluid system

We investigate the Faraday instabilities of a three-layer fluid system in a cylindrical container containing low-viscosity liquid metal, sodium hydroxide solution and air by establishing the Mathieu equations with considering the viscous model derived by Labrador et al. (J. Phys.: Conf. Ser., vol. 2090, 2021, 012088). The Floquet analysis, asymptotic analysis, direct numerical simulation and experimental method are adopted in the present study. We obtain the dispersion relations and critical oscillation amplitudes of zigzag and varicose modes from the analysis of the Mathieu equations, which agree well with the experimental result. Furthermore, considering the coupling strength of two interfaces, besides zigzag and varicose modes, we find a beating instability mode that contains two primary frequencies, with its average frequency equalling half of the external excitation frequency in the strongly coupled system. In the weakly coupled system, the $A$ -interface instability, $B$ -interface instability and $A$ & $B$ -interface instability are defined. Finally, we obtain a critical wavenumber $k_c$ that can determine the transition from zigzag or varicose modes to the corresponding $A$ -interface or $B$ -interface instability.

Oblique impact dynamic analysis of wedge friction damper with Dankowicz dynamic friction

<abstract> <p>Aiming at the wedge friction damper for freight train bogie, considering Dankowicz dynamic friction, the mechanical model of a three-degree-of-freedom inclined impact vibration system with gap and dynamic friction, is simplified. The mechanical model of the system is established, the motion equation of the system is obtained, and the motion state and conditions of the system are analyzed. The Poincare map is constructed by selecting a fixed collision section, and the response of the system is solved by the fourth-order Runge-Kutta numerical method with variable step size. The transition process of the system motion and the phenomenon of sticking and chatter are analyzed by numerical simulation when the external excitation frequency changes. The results show that: 1) Under certain parameters, with the change of excitation frequency, the system undergoes periodic doubling bifurcation, inverse periodic doubling bifurcation, Grazing bifurcation and Hopf bifurcation, and there is a "periodic bubble" phenomenon in the system motion. When the system excitation frequency is between 3.35–3.55, 4.425–6.12, and 7.34–7.758, the system motion has chatter and sticking phenomena; when the system excitation frequency is between 1.75–3.24 and 3.92–4.425, the sticking phenomenon disappears, and only the chatter phenomenon exists. 2) When other parameters remain unchanged, and the mass ratio decreases from 1.15 to 0.85, nonlinear dynamic phenomena such as the transition between periodic bubbles and chaotic bubbles will be found. In this paper, the bifurcation and chaos characteristics of the impact vibration system of the wedge friction damper are studied, and the rich friction-induced vibration forms such as chatter and sticking are revealed, which provides a reference for improving the stability of vehicle operation and the selection of parameters in vehicle vibration reduction design in engineering practice.</p> </abstract>

Numerical study of liquid sloshing using smoothed particle hydrodynamics with adaptive spatial resolution

Liquid sloshing is a typical problem of free surface flow in a number of engineering applications. The efficient simulation of liquid sloshing, particularly the large deformation and breakup of free surface, is a challenge for numerical methods. This paper presents a numerical method based on smoothed particle hydrodynamics with adaptive spatial resolution (SPH-ASR) for liquid sloshing. The SPH-ASR method can adaptively adjust the spatial resolution based on the distance to the free surface and the moving boundary. The numerical method was validated against experimental results from literature. Then the SPH-ASR method was applied to study the liquid sloshing problem in a prismatic tank and a rectangular tank. The effects of liquid fill level, external excitation frequency and amplitude on liquid sloshing were investigated. The pressure at different points on the tank wall and the total moment on the rotating shaft of the tank were compared and analyzed.

Analysis of vibration characteristics of face gear powering-split transmission system

A nonlinear dynamic model of the face gear powering-split transmission system was established, and the nonlinear dynamic characteristics of the face gear powering-split transmission system were studied by considering various factors such as support stiffness, time-varying meshing stiffness, lateral clearance of teeth, comprehensive transmission error and bearing stiffness. The Runge–Kutta integral method is used to solve the differential dynamics of the system. The nonlinear behavior of the system is described by the phase plane diagram, time history diagram, frequency domain diagram, and Poincare section diagram. The influence of external excitation frequency on the nonlinear behavior of the system is described by the bifurcation diagram. In addition, the multi-scale method is used to analyze the superharmonic resonance of the system and determine the stability conditions of the superharmonic resonance of the system. The influence of meshing damping, time-varying meshing stiffness, and time-delay control parameters on the amplitude-frequency characteristics of the system is studied by numerical analysis of the superharmonic resonance. The results show that the system will show periodic chaotic alternating motion characteristics under external excitation. Selecting meshing damping, meshing stiffness, and time delay control parameters in a reasonable range can effectively reduce the superharmonic co-amplitude and keep the system in a stable state.

Study on wave propagation in the modulation structure with gradually changing impedance according to specific waveform based on magneto-rheological fluid

This work proposes a novel hierarchical modulation structure with gradually-changed impedance built by magneto-rheological (MR) fluid and investigates its wave propagation characteristics theoretically and experimentally. Based on the impedance tunable property of the MR fluid, applying multiple magnetic fields to MR fluid realizes the modulation of this proposed structure, and regulating its magnetic field distribution law can effectively change the impedance variation forms in the structure. Establish the elastic wave propagation model of this modulated structure, and analyze the variation trends of its elastic wave propagation characteristics with different impedance distribution patterns, taking the vibration level difference as an indicator. Subsequently, conduct experimental testing for the transmissibility of elastic waves. The results show that the elastic wave transmission characteristics of the proposed modulation structure mainly depend on its impedance variation rate and the frequency of external excitation. On a broader band of the frequency range (20–300 Hz) studied in this paper, the gradual impedance distribution of MR fluid enhances the transmission loss of elastic waves compared to a uniform distribution of its impedance. Moreover, in the lower frequency range (40–125 Hz), the layered modulation structure with a non-monotonic variation of impedance following a wave-like waveform presents more significant attenuation on elastic waves than the structure whose impedance varies monotonously in a gradient waveform. This work contributes to expanding the design thoughts of the structure with gradually changing impedance and providing new ideas and means for the control of elastic waves.

Quasi-periodic oscillation characteristics of a nonlinear energy sink system under harmonic excitation

Quasi-periodic oscillation characteristics of a nonlinear energy sink (NES) system under harmonic excitation are studied in this work. It is found that there exist uniformly distributed sidebands in frequency spectra of quasi-periodic oscillations. The traditional incremental harmonic balance (IHB) method and the IHB method with two time-scales are used to obtain accurate frequency components and amplitudes of periodic responses and two different quasi-periodic oscillations of the system, respectively, with variations of the external excitation frequency and amplitude. The two different quasi-periodic oscillation characteristics are analyzed; energy absorption of the NES system under different excitation frequencies and amplitudes is also analyzed. Stability of quasi-periodic solutions obtained from the IHB method with two time-scales is analyzed by the Floquet theory. Analytical results obtained from the traditional IHB method and the IHB method with two time-scales agree very well with those from numerical integration using the fourth-order Runge–Kutta method. Results show that the efficiency of energy absorption of a strongly quasi-periodic oscillation is greater than those of a periodic response and a weakly quasi-periodic oscillation.

Complex gravity-acoustic impact on V-flame structure

Development of efficient and safe energy systems for space objects includes ensuring fire safety. This problem requires a deep understanding of influence of gravitational forces on combustion processes, which explains the importance of studying this issue. The paper analyzes the dynamics of inverted conical methane-air flame under conditions of normal and reverse gravitational force with external acoustic excitation. Applied frequencies of acoustic excitation could be parasitic or be produced during proper work of different technical systems of aircraft. High speed recording of flame chemiluminescence and PIV analysis were conducted. Decomposition of flow vector pictures into the modes was calculated using POD method. Energy contribution into the flow was analyzed for its separate elements at the different frequencies of excitation. At the high excitation frequencies vortex generation intensity in the shear layer with reverse gravity is about the same as it was observed in the experiments with normal gravity direction, that could indicate dominance of acoustic mechanism of the vortexes stimulation over the mechanism of shear instability. At external excitation frequency equals 240 Hz significant growth of shear vortex diameters and increasing of perpendicular oscillations amplitude of flame branches were obtained. Thereby in such experiment with 240 Hz external acoustic excitation the most intensive large scale instability of flow was observed.

Complex mode superposition method of non-classically damped systems based on hysteretic damping model with frequency-dependent loss factors

For non-classically damped systems, it is easy to construct a damping matrix based on a hysteretic damping model. However, the damped natural frequency is non-physical, and the frequency response function is non-causal. These two drawbacks can be overcome by the hysteretic damping model with frequency-dependent loss factors. In this paper, a complex mode superposition method for non-classically damped systems based on the hysteretic damping model with frequency-dependent loss factors is proposed. Frequency-dependent loss factors of the natural frequencies are considered in the transient vibration response, while frequency-dependent loss factors of the external excitation frequencies are considered in the steady state vibration response. By decoupling complex modes in state space and physical space, non-proportional damping characteristics of hybrid structures can be effectively considered. Therefore, the proposed method can be used to calculate the time-domain dynamic responses of hybrid structures, whose loss factors are sensitive to frequency variation and have strong non-proportional damping characteristics. The time-domain dynamic responses of numerical examples are compared based on different mode superposition methods. Shaking table tests are performed on cantilever plates with different damping characteristics. The numerical and test results validate the proposed method. Moreover, the proposed method has a wide range of applications.

Vibration Analysis of Traction Drive System Components Based on the Field Test for High-Speed Train

The traction drive system of a high-speed train is the key subsystem of a high-speed train, which controls the driving and braking of the train through electromechanical coupling, and determines the running speed, power quality, and comfort of the train. The traction drive system is subjected to many internal and external excitation sources and frequency bandwidth, and the dynamic response and dynamic characteristics of the system are extremely complex. The results of the traction motor field vibration test showed that 100 Hz vibration frequency occurred during traction and braking of high-speed trains when the inverter output voltage frequency was close to 100 Hz, and its vibration amplitude was higher than other frequency bands. When traction power was cut-off, the 100 Hz frequency was not significant. Through simulation analysis of fatigue damage, it was found that 100 Hz DC-link voltage pulsation would aggravate the fatigue damage of the motor hanger. The line vibration test and bench test of the gearbox showed that there was a natural frequency of the gearbox at about 2500 Hz, when the meshing frequency was close to it. Thus, the resonance characteristic became significant.