Amplitude-frequency Response Research Articles

Stability, bifurcation, and large-amplitude vibration analysis of a symmetric magnetic spherical pendulum.

Existing studies on the symmetric spherical pendulum are limited to small- and moderate-amplitude vibrations. This study was conducted to obtain accurate solutions for analysis of the large-amplitude vibration of a symmetric magnetic spherical pendulum using the continuous piecewise linearization method (CPLM). The stability conditions and bifurcation of the pendulum were derived based on the critical points, while the CPLM was used to estimate the frequency response and vibration histories to less than 0.1% and 1.0% relative error respectively when compared to numerical solutions. The CPLM was found to be significantly more accurate than the Laplace transform homotopy perturbation method and predicted the large-amplitude bi-stable vibrations accurately. The stability analysis that was conducted enabled the characterization of all bounded symmetric vibrations based on the relationship between the cyclotron frequency and azimuthal velocity, whereas the bifurcation analysis confirmed that the symmetric vibrations can undergo pitchfork bifurcation that results in transition from single-well to double-well (or bi-stable) vibrations and vice versa. Finally, a parametric analysis was conducted to study the effect of the cyclotron frequency and uniform azimuthal velocity on the frequency-amplitude response and vibration histories The parametric analysis showed that the frequency-amplitude response has a strong dependence on the cyclotron frequency and azimuthal velocity for all amplitudes. On the other hand, the oscillation profile only depends on the cyclotron frequency and azimuthal velocity for some amplitudes. The results of this study can be applied in the design of energy harvesters and elliptic tanks for liquid transport.

Weight Effects on Vertical Transverse Vibration of a Beam with a Nonlinear Energy Sink

Reductions in the vibration of a continuum system via a nonlinear energy sink have been widely investigated. It is usually assumed that weight effects can be ignored if the vibration is measured from the static equilibrium configuration. The present investigation reveals the dynamic effects of weight on the vertical transverse vibrations of a Euler–Bernoulli beam coupled with a nonlinear energy sink. The governing equations considering and neglecting weights were derived. The equations were discretized with some numerical support. The discretized equations were analytically solved via the harmonic balance method. The harmonic balance solutions were compared with the numerical solution via the Runge–Kutta method. Finite element simulations were performed via ANSYS software (version number:2.2.1). Free and forced vibrations, predicted by equations considering or neglecting the weights, were compared with the finite element solutions. For the forced vibrations, the amplitude–frequency responses determined by the harmonic balance method agree well with those calculated by the Runge–Kutta method. The free and forced vibration responses predicted by the equations considering the weights are closer to those computed by the finite element method than the responses predicted by the equation neglecting the weights. The assumption that weights can be balanced by static deflections leads to errors in the analysis of the vertical transverse vibrations of a Euler–Bernoulli beam with a nonlinear energy sink.

Nonlinear dynamics for cylindrical resonator of wave solid-state gyroscope with different number of electrostatic control sensors

The purpose of this work is to determine differences in the nonlinearities of mathematical models of dynamics and nonlinear effects of dynamics for the cylindrical resonator of wave solid–state gyroscope using a different number of electrostatic control sensors. Methods. In this article resonator oscillations nonlinearity caused by finite ratio of the small deflection of the resonator to the small gap of the electrostatic sensor is considered. To construct approximate mathematical models Tikhonov’s theorem on the passage to the limit is used and a small parameter singularly included in the system of differential equations is also taken into account. The equations of resonator dynamics are averaged by using the Krylov–Bogolyubov method. Results. The difference between the nonlinear terms in the equations of resonator dynamics with eight and sixteen control sensors is determined. It is found that nonlinear effects are more pronounced in the case of the gyroscope with sixteen control sensors. The angular drift velocity and the displacement of the resonant peak of the amplitude-frequency response are greater than in the case of eight control sensors. It is shown that in the case of eight control sensors, the angular drift velocity has a variable value and also contains a small uncompensated component. Conclusion. Mathematical models of the dynamics for the cylindrical resonator of wave solid-state gyroscope taking into account the nonlinearities caused by the excitation of oscillations by eight and sixteen electrostatic control sensors are deduced. The difference between the nonlinear effects of the resonator dynamics for wave solid-state gyroscope with different number of control sensors is shown. The angular drift velocity and the displacement of the resonant peak of the amplitude-frequency response are obtained. Conclusions about the applicability of gyroscope with eight control sensors are discussed.

Numerical investigation on the hydrodynamic wave forces on the three barges in proximity

Two-dimensional nonlinear hydrodynamic wave forces acting on three side-by-side barges are numerically investigated in this work. A finite volume viscous flow model, incorporating the volume of fluid method for free-surface capturing, is implemented based on OpenFOAM® platform to simulate interactions between nonlinear free-surface waves and multiple barges. The study explores the impact of fluid resonances in the gaps between three barges on the hydrodynamic wave forces. The initial transient and final quasi-steady wave forces are first examined to highlight the significance of transient evolution stage. The steady-state wave forces are subsequently concerned with the amplitude-frequency response of wave forces, along with the pressure and viscous force components. Relationship between wave forces and fluid oscillations within the gaps is then clarified to explain the mechanism of wave forces on the barges associated with gap resonance. Significant nonlinear higher-order harmonics are further demonstrated, with their origins closely linked to fluid oscillations within gaps between the barges. Contributions of higher-order harmonics to the overall wave force amplitudes are explored through harmonic analysis utilizing Fourier transformations. Finally, effects of the normalized incident wave amplitudes on the amplitudes of wave forces and higher-order harmonics are found to be highly dependent on frequency bands.

Vibration suppression analysis of iced transmission lines under axial time-delay velocity feedback strategy

To ensure the safety of power energy transmission channel and mitigate the harm caused by galloping of iced transmission lines, the axial time-delay velocity feedback strategy is adopted to suppress the galloping. The partial differential equation of galloping with axial time-delay velocity feedback strategy is established based on the variational principle for Hamiltonian. Then, the partial differential equation of galloping is transformed into ordinary differential equation based on normalization and the Galerkin method. The primary amplitude-frequency response equation, the first-order steady-state approximate solution, and the harmonic amplitude-frequency response equation are derived by the multiscale method. The impact of different parameters such as time-delay value, control coefficient, and amplitude of external excitation on the galloping response are analyzed. The amplitude under the primary resonance exhibits periodicity as time-delay value varies. The amplitude diminishes with increased control coefficient and increases with external excitation. Comprehensive consideration of various influences of parameters on vibration characteristics is crucial when employing the axial time-delay velocity feedback strategy to suppress galloping. Therefore, to achieve the best vibration suppression effect, it is crucial to adjust the time-delay parameter for modifying the range and amplitude of the resonance zone. The conclusions obtained by this study are expected to advance the refinement of active control techniques for iced transmission lines, and may provide valuable insights for practical engineering applications.

Method for Increasing the Linearity of The Phase in The Approximation Phase On 5G Antennas Using Modified Functions of The Subtractors

The possibility of reducing the phase distortion of the signal spectra in the input paths at the stage of approximation of frequency characteristics is shown. Noticeable progress in the technology of satellite and mobile telecommunications systems, as well as in radar systems, is largely associated with the use of broadband and ultra-broadband signals. Thus, in 2012-2013, the development of Wideband High Frequency (WBHF) radio technology (hereinafter referred to as broadband HF (HF) radio communication) took place in the direction of increasing data transmission rates over HF (HF) radio channels to meet the needs of subscribers of the armed forces of NATO countries. The development of broadband HF (HF) radio communication has led to the revision of the following NATO standards and their release in a new edition: - MIL-STD-188-110C «Interoperability and operational requirements for data modems», 03.01.2012; - MIL-STD-188-141C «Functional compatibility and operational requirements for medium and high frequency radio frequency systems», 12/27/2011. The work carried out experiments to compare frequency characteristics. The changes are also related to the introduction of broadband HF (HF) radio communication technology, which defines a family of broadband modulation types for a radio channel with the necessary bandwidth of the end-to-end amplitude-frequency response (AFC) of the transceiver path from 3 kHz to 24 kHz in 3 kHz increments.

Dynamic characteristic analysis and strength optimization of vibrating screen based on computer simulation technology

The dynamics and modal characteristics are important basis for the stable operation of vibrating screen. A multi-body dynamic model of vibrating screen was established based on ADAMS, and the laws of change in the center of mass and the dynamic response of the vibration isolation system were obtained. The amplitude-frequency response results of acceleration under varying stiffness and damping coefficients were compared and analyzed, providing a crucial foundation for enhancing vibration isolation performance. The vibrating screen was analyzed for its modal characteristics using ANSYS, and the natural frequencies and vibration patterns were investigated. The distribution and main causes of the maximum resonance displacement were discussed. Drawing on the results of stress and modal shapes, the strength of the vibrating screen was significantly enhanced through multi-objective optimization methods without increasing its weight. The findings indicate that the optimized structure can achieve a 32.2 % reduction in peak stress.

Nonlinear vibration and transient stress analysis of disc brake based on computer simulation technology

The nonlinear vibration and dynamic stress characteristics of disc brakes are key factors affecting braking noise and safety. Based on the working principle of disc brake, a six-degree-of-freedom dynamic model was constructed, and the amplitude-frequency response of vibration under diverse braking pressures and initial velocities was acquired. The modal characteristics of the brake disc were computed using the finite element simulation approach, and the natural frequency and vibration mode were obtained. The accuracy of the modal calculation was verified by means of the laser detection method. In order to study the dynamic stress variation law more accurately, a coupled model of temperature and displacement was established, and transient stresses on different paths were obtained. The results indicate that the finite element model has high accuracy, with a maximum calculation error of only 5.1 % for the natural frequency. Besides, temperature variations will lead to thermal deformation of the brake disc, which intensifies the random vibration characteristics associated with the friction process.

Torsional vibration of a static drill-rooted nodular pile embedded in elastic media

This study examines the vibration characteristics of static drill-rooted nodular (SDRN) piles in elastic soils under time-harmonic torsional loads via an analytical approach. SDRN piles, which are characterized by uniformly distributed nodes and enhanced surrounding cemented soil, are able to increase the vertical bearing capacity of piles in soft soils. Piles are modelled using elastic rod theory, while surrounding soils are separated into two sublayers along radial direction: a core zone made up of cemented soil and an outer semi-infinite natural soil layer. An analytical method is proposed to solve the problem after formulating the wave equations for pile and radial soil layer. This methodology rigorously considers the continuity of twist angle and shear stress across the interface of the pile and radial soil layers. The simulation of nodes in the SDRN pile involves discretizing the pile-soil system and applying the principle of impedance function recursion to accurately compute the torsional stiffness at the top of the pile. Developed results are validated against the existing benchmarks for a cylindrical pile in elastic soil. Detailed numerical examples are carried out to assess the effect of major factors on the torsional impedance of the pile. For improved comprehension in engineering applications, the impedance function is applied to derive the twist angle of the rigid foundation, with the amplitude-frequency response expressed in a closed form. Results indicate that the vibration behavior of the piles is significantly influenced by the inner radius, outer radius, the dimension of the node, the radial width of the cemented soil and the damping ratio of the radial soil layer. The developed solution offers valuable insights for the optimization design of SDRN piles under dynamic torsional loads.

The Nonlinear Dynamic Response and Vibration Transmission Characteristics of an Unloading System with Granular Materials

The aim of this study is to research the flow property of granular materials under nonlinear vibration, which directly affects the stability of the unloading system and the motion state of granules. According to the mechanical constitutive relation, the coupled suspension–tire model with nonlinear ordinary differential equations is established and the kinematic equations of granules are derived. Furthermore, the amplitude–frequency responses of the coupled system and force transmissibility are obtained by the incremental harmonic balance method (IHBM) with high-order approximation, and then the flow characteristics of granular materials are investigated based on the approximate analytic solution under nonlinear vibration. The theoretical analysis and numerical simulation show that the coupled suspension–tire system presents a softening nonlinear feature and the peaks are significantly smaller than that of the linear system, which further affects the motion rules of granular materials. As a result, different sliding states and flow paths are observed under the same operating conditions. This research not only shows the unloading mechanism and vibration transmission characteristics between the continuum structure and granular material but also theoretically explains the control mechanism of the coupled continuum–granular system. The research is instructive in improving the unloading efficiency of granules in practical engineering.

Analysis of the Response Characteristics of Ultra-Wideband Radio Fuze to Interference Signals

Abstract The response characteristics of the fuze to the interference signal with reasonable characteristic parameters are similar to the real echo signal, which may lead to the confusion of signal processing and recognition system. To solve this problem, this paper analyzes the influence of characteristic parameters of interference signal on the response characteristics of fuze in detail from two perspectives of time domain and frequency domain, Based on the analysis of receiver principle, the amplitude-frequency response model of sampling integral differential circuit is established, and the response characteristics of interference signal are analyzed from the perspective of frequency domain. Based on the analysis of the time-frequency characteristics of the echo signal of the UWB fuze, a time-frequency function cutting method is proposed to evaluate the anti-jamming performance of the UWB fuze. This methodology was applied to the evaluation of the anti-jamming performance of the UWB fuze to sinusoidal amplitude-modulation interference signal and the results show that the theoretical analysis and simulation results are consistent, and the research provides theoretical guidance for the anti-interference of fuze.

Vibration characteristic, quality factor and sensitivity analysis of a resonant micro-gyroscope based on the blue-sideband parameter modulation

In this paper, we design a nonlinear resonant micro-gyroscope based on the blue-sideband parameter modulation (BSPM), and Coriolis force acts in the axial direction of the resonant beam in the form of a twice-frequency parameter excitation. Considering the geometrical nonlinearity of the micro-beam, the dynamic equations of the resonant beam are derived and discretized according to Hamilton principle and Galerkin method. The discretized equations are subjected to perturbation analysis by using the multi-scale method, and the quality factors of the resonant beams are calculated by the half-power bandwidth method. Moreover, the sensitivity of micro-gyroscope is characterized by the amplitude ratio changes before and after the bifurcation of the nonlinear resonant beam. We conducted a detailed study on the effects of Coriolis force dynamic input, and BSPM on the amplitude-frequency response of resonant beam and the sensitivity of micro-gyroscope. The results indicate that when Coriolis force acts on the resonant beam in the form of a twice-frequency parameter excitation, it not only causes the resonant frequency of the micro-beam to shift but also significantly increases the amplitude of the resonant beam. The addition of BSPM significantly improves the quality factor of the resonant beam and enhances the signal-to-noise ratio. Under nonlinear conditions, when the modulation voltage is sufficiently large, the amplitude-frequency response of resonant beam exhibits two unstable regions near the resonant frequency. Although BSPM reduces the amplitude ratio sensitivity, there is still a 60 times improvement over conventional frequency shift sensitivity. Furthermore, BSPM reduces the nonlinearity degree of the amplitude ratio sensitivity by 64%, which is important for the design and fabrication of high-sensitivity resonant micro-gyroscope.

Method for determining the effect of destabilizing factors of digital filters on the multicriteria synthesis of radio communications of aviation robotic devices

The purpose of the research is development of a method for determining the influence of destabilizing factors, such as the unevenness of the amplitude-frequency response (AFC) and the nonlinearity of the phase-frequency response (FFC), in non-recursive digital frequency selection filters on the target function of multicriteria structural-parametric synthesis of radio communications from the payload of aviation robotic devices.Methods. In conducting scientific research, probability theory, mathematical statistics, statistical radio engineering and computational mathematics were used. The study obtained mathematical expressions of the dependence of the probability of error per bit (BER) on the average signal-to-noise ratio when signals pass through symmetrical non-recursive digital filters with quadrature amplitude modulation with a positivity of no more than 4096, signal constellation irregularities of no more than 5, which are the basis for the energy balance of radio lines with aviation robotic devices. The expressions obtained are one of the "foundations" for the implementation of a multi-criteria synthesis of radio systems adaptive to a cognitively formed flight task. In this paper, all the results of the probability of reliability of the received data by means of communication are reflected for the case of rigid decision-making (Gray coding).Results. In the course of the conducted research: 1) a mathematical model of the structural-parametric synthesis of radio communications with aviation robotic devices is demonstrated, which is based on the criteria for minimizing: electronic computing resources with a given noise immunity; radiation outside the operating frequency band; peak factor signals; the effects of narrowband, broadband and structural interference in the radio channel at a given bandwidth; the use of structural and functional nodes specific to the existing information and communication environment; 2) the analytical dependence of the influence of the parameters of one of several structural and functional nodes - digital filters of frequency selection, on the criteria for the synthesis of communication means has been revealed. The paper considers the most common approximating functions - Kaiser, Tukey, Barlett-Khan, Chebyshev, and also shows the influence of the filter order on the equivalent of energy loss in information communication lines of aviation robotic devices.Conclusion. The scientific article presents a method for determining the effect of the uneven frequency response of a symmetrical non-recursive digital filter in devices for receiving and processing radio signals of multicriteria means of communication with the payload of aviation robotic devices. The proposed approach increases the reliability of determining the values of criteria for minimizing electronic computing resources for a given noise immunity, radiation outside the operating frequency band, as well as the use of structural and functional nodes characteristic of the existing information and communication environment.

A Numerical Study of Dynamic Behaviors of Graphene-Platelet-Reinforced ETFE Tensile Membrane Structures Subjected to Harmonic Excitation

This study presents a numerical investigation of the dynamic behavior of graphene platelet (GPL)-reinforced ethylene tetrafluoroethylene (ETFE) tensile membrane structures subjected to harmonic excitation. Modal and harmonic response analyses were performed to assess both the natural frequencies and the dynamic responses of the ETFE membrane. GPLs were employed as the reinforcements to enhance the mechanical properties of the membrane materials, whose Young’s modulus was predicted through the effective medium theory (EMT). Parametric studies were conducted to examine the impact of pre-strain and the attributes of the GPL reinforcements, including weight fraction and aspect ratio, on the natural frequencies and amplitude–frequency response curves of the membrane structure. The first natural frequency substantially increased from 5.46 Hz without initial strain to 31.0 Hz with the application of 0.1% initial strain, resulting in a frequency shift that moved the natural frequency out of the range of typical wind-induced pulsations. Embedding GPL fillers into ETFE membrane was another potential solution to enhance the dynamic stability of the membrane structure, with a 1% addition of GPLs resulting in a 48.6% increase in the natural frequency and a 45.1% reduction in resonance amplitude. GPLs with larger aspect ratios provided better reinforcement, offering a means to fine-tune the membrane’s dynamic response. These results underscore that by strategically adjusting both pre-strain levels and GPL characteristics, the membrane’s dynamic behavior can be optimized, offering a promising approach for improving the stability of structures subjected to wind-induced loads.

Switched preselector of a multichannel receiver

The development of wideband radio receivers is an important technical task, and its solution is being addressed by numerous enterprises and researchers. Among the well-known enterprises-developers of professional radio-receiving devices it is necessary to mention ANII "Vector" (St. Petersburg), JSC SPE "Istok" (Fryazino), JSC "Salyut" (Nizhny Novgorod), Rostov Research Institute of Radio Communications, Voronezh Research Institute of Radio Communications, "Scard-Elektronics" (Kursk), Omsk NIIP. There are even more manufacturers of broadband radio receiving devices abroad, but it is not appropriate to list them here. Modeling and experimental study of a preselector for a multichannel receiver is carried out. The functional scheme of the preselector, the circuit diagram of one channel out of four, the model of this filter in the program CST Studio Suite and the amplitude-frequency characteristics are given. The structural scheme of the experiment and amplitude-frequency characteristics in the near and far zones are presented. The achievement of the following parameters is shown: Bandwidth from 3.5 to 4.0 GHz; Bandstop from 4.5 to 18.0 GHz; Transmission coefficient greater than 10 dB in the passband; Gain at frequencies 3f0 and 5f0 not less than 60 dB; Wave impedance of 50 ohms. The studied preselector has a wide frequency and dynamic range, high selectivity, so it allows to realize a modern receiver. The basis of the preselector consists of four bandpass filters on counter rods, on the air-strip transmission line. Each of the filters contains 11 resonators. To suppress false pass-bands, the preselector contains a low-pass filter on microstrip transmission lines. To obtain the required transmission coefficient, the preselector contains an amplifier, and to reduce the diversity of channels - a corrector of the amplitude-frequency response.

Direction finding receiver

Bearing receivers are an important component of electronic warfare equipment, but their technical level today seems to be insufficient in a number of parameters. Aim of work – to create a receiver with a small unevenness of the frequency response, which significantly affects the bearing error. Design documentation has been developed, a mock-up has been made and an experimental study of the bearing receiver has been carried out. The functional diagram and description of the receiver design are given. A bearing receiver with a wide frequency range and a dynamic range of 40 dB has been created. It surpasses previous developments in terms of the unevenness of the amplitude-frequency response.

Ultra-low frequency and broadband flexural wave attenuation using an inertant nonlinear metamaterial beam

Attenuation of elastic waves in the extremely low frequency range is a considerable challenge. While linear acoustic metamaterials can manipulate elastic waves, their effectiveness is often limited to a narrow frequency range. The present paper proposes a novel inertant nonlinear metamaterial beam to address the challenging problem of the ultra-low frequency broadband flexural wave attenuation. The amplitude-frequency response and dispersion relations of the flexural waves are obtained using the first-order harmonic balance method, where four different resonant units are investigated and the resulting band gaps are compared. Finite element (FE) simulations are also conducted to evaluate the transmission spectra of the flexural vibration through a finite metamaterial beam. The good consistency between the band gaps predicted by the analytical model and the FE simulation verifies the correctness and effectiveness of the developed analytical approach. The results of this study demonstrate that introducing the inertance and softening nonlinearity into the resonant units can significantly widen the flexural wave band gaps within the low-frequency range. This finding provides a viable solution for engineering applications that require low-frequency vibration suppression and isolation.

A composite structure device: vibration control and energy harvesting of tool system in aviation thin-walled parts milling process

Abstract The intense vibration generated by the high-speed milling cutter in the processing process not only seriously affects the surface roughness but also may damage important components of the machine tool, resulting in significant economic losses. Therefore, a composite structure of piezoelectric energy-collector (PEC) and nonlinear energy sink (NES) is innovatively constructed by combining theoretical research and numerical analysis to achieve more efficient vibration suppression and energy recovery in milling. Using the Hamilton principle, the electromechanical model of the composite structure is developed. Then, based on the Galerkin truncation to discretized displacement functions, we solve the amplitude-frequency response of the tool structure by using the harmonic balance method. The validity analysis of the proposed method can be verified by rigorous comparison with the results of the Runge-Kutta method. A novel NES-PEC composite structure presented in this work shows excellent vibration suppression capability in the milling process. More importantly, the structure also enables self-powered sensing of the tool system, significantly reducing dependence on external power sources. This innovative design substantially improves the stability and reliability of milling processes and opens up new ways to optimize the energy efficiency of tool systems. In summary, this paper’s modeling and solving methods, vibration reduction techniques, and energy harvesting strategies have laid a solid foundation for applying a high-speed milling cutter system. More relevant literature on applying vibration suppression and energy harvesting devices in milling must be reviewed. This paper fills in the research gap and provides a valuable reference for future tool systems design and optimization.

Application of Graphene in Acoustoelectronics.

An interdigital transducer structure was fabricated from multilayer graphene on the surface of the YZ-cut of a LiNbO3 ferroelectric crystal. The multilayer graphene was prepared by CVD method and transferred onto the surface of the LiNbO3 substrate. The properties of the multilayer graphene film were studied by Raman spectroscopy. A multilayer graphene (MLG) interdigital transducer (IDT) structure for surface acoustic wave (SAW) excitation with a wavelength of Λ=60 μm was fabricated on the surface of the LiNbO3 crystal using electron beam lithography (EBL) and plasma chemical etching. The amplitude-frequency response of the SAW delay time line was measured. The process of SAW excitation by graphene IDT was visualized by scanning electron microscopy. It was demonstrated that the increase in the SAW velocity using graphene was related to the minimization of the IDT mass.

Nonlinear resonance of fractional order viscoelastic PET films under temperature loading

The effects of oven temperature during printing on nonlinear vibration for fractional-order PET films are considered in this paper. The effect of temperature, fractional order modelling and some other parameters are analysed with respect to the response of the resonance. Fractional order kelvin-Voigt ontological relationship is used to describe the characteristics of viscoelastic materials. The differential equations for nonlinear vibrations are inferred according to the second law of Newton and the theory of von Karman. Discretization for nonlinear equations on locomotion using the Bubnov–Galerkin method. Forced co-oscillatory amplitude-frequency response equations for thin-films systems under temperature loading were calculated using the multiple scales method. Results of numeral results show that temperature, and fractional-order visco-elastic modelling influence the membrane's response to resonance. These results provide a basis for studying fractional-order visco-elastic films vibrations and identifying regions of stable operation in moving systems to prevent divergent instabilities for flexible electronic device manufacturing.