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The hub motor driven vehicle (HMDV), due to the increase in unsprung mass and the influence of uneven electromagnetic radial forces from road excitations, results in the deterioration of body acceleration, significantly impacting ride comfort. This seriously impacts ride comfort. However, the inerter proves effective in reducing low-frequency vibrations in body acceleration, and skyhook control significantly enhances ride comfort. To fully exploit the benefits of the inerter, comprehensively elevate skyhook control performance, and effectively counteract the worsening of body acceleration caused by the hub motor, this study integrates skyhook control with an inertial suspension system. This integration markedly improves the suspension’s low-frequency isolation performance, thereby substantially enhancing vehicle ride comfort. Firstly, establish a quarter-vehicle dynamics suspension model based on the Switched Reluctance Motor (SRM) driven wheel motor system. Subsequently, confirm the constraints of two different generalized skyhook inertial suspension structures separately and optimize their parameters to determine the most suitable parameters for each structure. Finally, analyze the impact of these two suspension types on body acceleration to derive the optimal structure. Simulation results demonstrate that, compared to traditional suspensions, the optimized generalized skyhook inertial suspensions reduce the Root Mean Square (RMS) values of body acceleration and suspension working space by 18.8% and 22%, respectively. This reduction is particularly significant in the 0$\sim$2Hz frequency range, effectively enhancing ride comfort. It also adequately validates the effective utilization of the advantages of inertial suspensions and skyhook control.

With the swift advancement of microelectronic technology and MEMS, piezoelectric energy harvesting technology has garnered escalating attention due to its eco-friendly and sustainable attributes. In this paper, a bimorph piezoelectric energy harvesting system considering multi-nonlinearity complex factors is devised, and the approximate analytical solutions for vertical displacement, output voltage, and output power of the entire system are derived. Owing to inherent nonlinear softening characteristic of material nonlinearity, the effective frequency bandwidth of the energy harvesting system is significantly broadened. The result indicates that under horizontal excitation ranging from 0.2g to 0.3g, the peak output voltage of the energy harvesting system with a frequency of 3.2254Hz (open circuit) increases approximately by 7.9 times. At another frequency of 3.2054Hz (short circuit), the peak output voltage amplitude is multiplied by approximately 6.5 times. Considering material nonlinearity, it can be concluded that the system energy harvesting efficiency at low frequency can be greatly improved. The numerical result obtained is not only more accurate, but it is also more consistent with real situations. This conclusion provides a theoretical basis for research and analysis of similar systems in low-frequency ranges.

Ocean waves are abundant in energy; however, they also cause ships to sway and can disrupt the operation of precision equipment. Harvesting energy from ocean waves and isolating vibrations in marine precision equipment have long posed significant challenges due to the inherently low-frequency nature of ocean waves. This study proposes a dynamic-constrained nonlinear (DCN) stiffness method for low-frequency energy harvesting and vibration isolation. A generalized mathematical model of the DCN stiffness system is established, and its semi-analytical solution is derived using the harmonic balance method and the arc-length extension method. Finally, various application scenarios for energy harvesting and vibration isolation using the nonlinear stiffness method are explored. The results demonstrate that the DCN stiffness method can significantly enhance the performance of low-frequency wave energy, capture and provide excellent low-frequency vibration isolation. Notably, this method exhibits a strong adaptive capability to excitation compared to traditional nonlinear stiffness methods.

Primary dysmenorrhea is a common gynecological complaint among young women that is related to an autonomic nervous system (ANS) disturbance. Acupuncture is one of several therapeutic approaches for primary dysmenorrhea, since it can modulate ANS function. The heart rate variability (HRV) parameters such as high frequency (HF), low frequency (LF) and LF/HF ratio are generally accepted tools to assess ANS activity. The purpose of this study was to investigate the effects of acupuncture applied at Hegu (LI4) and Sanyinjiao (SP6) points on HRV of women with primary dysmenorrhea during the late luteal phase. The experimental design was a crossover and patient-blinded procedure. All subjects participated in Sham (SA) and Real Acupuncture (RA) procedure, separated by one month, in a crossover sequence. The participants included 38 women (mean age 22.3 years; weight 53.8 kg; height 162.6 cm). HRV measurement was 15 min before and 15 min after an acupuncture procedure. The RA procedure was performed at two bilateral acupoints, but needles were inserted subcutaneously to the acupuncture points for the SA procedure. The RA induced a significant decrease in LF/HF ratio and a significant increase in the HF power, while SA treatment caused a significant increase only in the HF power. Manual acupuncture at bilateral acupoints of LI4 and SP6 may play a role in dysmenorrhea treatment with autonomic nervous system involvement.

In this paper, we theoretically investigate the propagation characteristics of Lamb wave in a two-dimensional (2D) asymmetric phononic crystal (PC) plate composed of cylinder stubs of different radius deposited on both sides of a thin homogeneous plate. The dispersion relations, transmission spectra and displacement fields of the eigenmodes are calculated by using the finite element method (FEM). Two complete bandgaps (BGs) can be found in low-frequency range and the transmission spectra coincide with the band structures. We investigate the evolution of dispersion relations with the decrease of the upper stub radius. The physical mechanism of the upper stub radius effect is also studied with the displacement fields of the unit cell. Numerical results show that the symmetry of the stub radius can remarkably influence the band structures and the asymmetric double-sided plate exhibits a new bandgap (BG) in lower frequency range due to the coupling between the lower stub’s resonant mode and the plate’s Lamb mode becomes weak and the adjacent bands separate. Moreover, we further investigate the effect of the stub height on the dispersion relations and find that the BGs shift to lower frequency regions with the increase of the stub height. In addition, the BGs’ sensitivity to the upper stub radius and the stub height is discussed. The low-frequency BGs in the proposed PC plate can potentially be used to control and insulate vibration in low frequency range.

A broadband and wide-angled microwave absorber based on resistive-type metamaterial has been proposed and demonstrated in the low-frequency regime of 2–8 GHz. The minimum reflection loss of the absorption peak located at 5.27 GHz is −51.41 dB. Effective bandwidth better than −10 dB reflection loss is able to achieve 2.70 GHz in the range from 3.81 GHz to 6.51 GHz. The underlying physical mechanisms of electromagnetic wave energy attenuation are illustrated in detail by means of surface current, electromagnetic field and power loss density. Furthermore, the influence of structural dimensions on the attenuation properties of the proposed resistive-type metamaterial absorber is also investigated. More importantly, the designed resistive-type metamaterial absorber could operate well with incident angles changing from 0${}^{\circ }$ to 60${}^{\circ }$ under the transverse electric (TE) and transverse magnetic (TM) waves. Research results will be capable of providing guidance for the design and preparation of broadband microwave absorbing materials at low frequencies.

The experiment was carried out to study the low frequency surface waves due to the horizontal high frequency excitation. The feature of the phenomenon was that the big amplitude axisymmetric surface wave frequency was typically about 1/50 of the excitation frequency. The viscous effect of water was neglected as a first approximation in the earlier papers on this subject. In contrast, we found the viscosity was important to achieve the low frequency water wave with the cooperation of hundreds of "finger" waves. Photographs were taken with stroboscopic lighting and thereafter relevant quantitative results were obtained based on the measurements with Polytec Scanning Vibrometer PSV 400.

In this paper, extremely low frequency band gaps of beam-like inertial amplification metamaterials are investigated based on local resonance theory. Inertial amplification mechanism is proposed to obtain extremely low frequency band gaps by altering geometry parameters of the beam-like structures rather than modulating material properties, which allow first lower band gap (BG) to be attained easily compared to traditional local resonance structures. Band structures, frequency response functions (FRFs) plots and vibration modes of the beam-like structures are calculated and analyzed by employing finite element method. Numerical results show that first BG of the structure ranges from 23 Hz to 21 Hz. FRFs are in accordance with the dispersion relationship. It is found that interaction between inertial amplification and traveling wave modes in the proposed structure are responsible for formation of the first BG. This type of beam-like inertial amplification metamaterials has many potential applications in the field of low frequency vibration and noise reduction.

A metal-dielectric-metal (MDM) sandwich metamaterial perfect absorber (MPA) with magnetic nickel metal has been designed. An optimal absorption of 99.28% at 404 MHz is achieved for MPA with thickness of 5.54 mm. Resonant absorption is demonstrated to be main mechanism according to analyses on surface current distributions and electromagnetic field distributions. Furthermore, the electromagnetic energy is mainly dissipated in magnetic metal with magnetic loss proportion of 55.43% by comparatively analyzing the wave-absorbing performance of using magnetic metal, non-magnetic metal and perfect electric conductor (PEC) as metallic layers. These results would provide a guidance for the design of quasi-microwave absorbing/shielding materials.

In this paper, a comb-like locally resonant phononic crystal (LRPC) with optimal structural parameters, which has good low frequency and broadband band gaps (BGs) between 20–250 Hz, is investigated numerically. With the intention of obtaining the optimal structural parameters, based on the structures with different number of the short elastic beams, 2-factor (the two key structural parameters, i.e. the width of the scatterer and the thickness of elastic beams) and 7-level numerical experiments are designed to obtain simulations data using finite element method (FEM). The functional relationships are further constructed using the response surface method (RSM) analysis, i.e. the relationship of the starting frequency of the first BG and the two factors, the terminating frequency of the second BG and the two factors, and the relationship of the total bandwidth of the first two BG and the two factors. After calculation using interior point method, the BGs of LRPC with optimal structural parameters are determined with lower and wider BGs below 250 Hz.

Structural stiffness of phononic crystals (PnCs) can affect their bandgap properties. It thus needs to consider stiffness in the design of the unit cell of a PnC. In this paper, a local resonant (LR) rod composed of tri-wing rhombus ligament (TRL) resonators arranged periodically within a common hollow rod is proposed to create a low-frequency flexural vibration bandgap. The dispersion relations, mode of resonances and vibration transfer function are studied using a finite element method. Low-frequency forbidden bands can be effectively shifted by changing the resonator geometries. In addition, both numerical simulations and sample test are conducted to verify the low-frequency bandgap. The results show that the hollow rod with TRL resonators can create a low-frequency flexural vibration bandgap as well as have high support structure stiffness.

When an oscillator vibrates in a porous medium or along an unsmooth surface, a fractal model can be adopted using the two-scale fractal derivative. This paper elucidates a simple but effective method for fast and exclusive insight into the asymptotically periodic property at the initial stage and the extremely low frequency property when time tends to infinity. Some examples are illustrated to show the one-step solution process and the accurate results.

A nonlinear vibration system in a fractal space can be effectively modeled using the fractal derivatives, and the homotopy perturbation method is employed to solve fractal Duffing oscillator with arbitrary initial conditions. A detailed solving process is given, and it can be easily followed for applications to other nonlinear vibration problems.

The low and medium frequency - 1 Hz ≤ f ≤ 100 kHz - amplitude noise characteristics of 840 nm proton-implanted VCSELs (Vertical Cavity Surface Emitting Lasers) have been investigated. Experiments clearly show that the DBR (Distributed Bragg Reflector) structure represents the main electrical noise source of VCSELs. Furthermore, the electrical noise is somehow linked to the optical noise when the laser shows a "disturbed" optical spectrum with competition between very close modes.

Accurate models, optimization methods and improvement measures are three key issues in the design and optimization of complex structures in the field of vibration and noise. Due to the increase of passenger vehicle structure complexity and lightweight demand, nonlinear materials and structures increase obviously in the whole system. Not only different structural adhesives are used to strong body structures under the lightweight requirement, but also the influence of the windshield should be considered in the structural design process. The first point of this paper is to use the model matching method to build an accurate finite element model that takes into account nonlinear materials and structures for the next optimization. Although the optimization method can also achieve structural improvement, it cannot find the regular conclusion that has a significant impact on the performance of the structure inherently. The second innovation is to propose a combination method of sensitivity analysis and modal strain energy (MSE) indication. The method not only finds a specific weak structure, but also summarizes viewpoints that the whole stiffness mismatch characters and the weak local structure destroyed balance of the whole structure. These conclusions provide the basis for further improvement. It is a difficult problem to solve low-frequency vibration and noise problem because of their long wavelength and strong penetration ability. As the third innovation point, three-dimensional phononic crystal simulation is done to optimize the low-frequency noise of structure in this paper. The synthesis method including the above three key points has a very good effect in suppressing low-frequency vibration and noise in the vehicle. This method is also suitable for simulation and optimization of other complex structures.

Design, modeling, and analysis of an intelligent flexible isolation system for attenuating low-frequency micro-vibration are presented. The isolator consists of a payload platform, a supporting platform and four folded-beams with surface-bonded macro-fiber composites (MFCs). To accurately analyze the system performance, a piezoelectric finite element (FE) model is built and validated by the modal analysis results derived from ANSYS. This paper presents an attempt to widen the low-frequency isolation range for the micro-vibration using a modal frequency shift approach. The transfer functions of the active isolation system with different feedback controls are derived based on an FE model, in which feedback signals can be absolute and relative accelerations, absolute and relative displacement, relative velocity, and mixed responses. According to the numerical results, the expected performance of low-frequency vibration isolation can be easily achieved, especially by a kind of mixed responses feedback method. The time-domain simulations also show that the proposed piezoelectric isolation system exhibits a good isolation performance, endowing them with great potential for the micro-vibration restrain in aerospace application.