Harmonic Oscillator Research Articles

Synergistic effect of graphene and carbon black on the mechanical and vibration damping characteristics of styrene-butadiene rubber

Synergistic effect of graphene and carbon black on the mechanical and vibration damping characteristics of styrene-butadiene rubber

A piezoelectric nonlinear energy sink shunt for vibration damping

The theoretical study and experimental validation of a nonlinear shunt circuit for piezoelectric vibration damping is investigated here. The circuit consists of a resistor, an inductor and a nonlinear cubic voltage source. The shunt acts as an electrical analog to the mechanical nonlinear energy sinks (NESs). These mechanical NESs are passive vibration absorbers that typically have a cubic nonlinear stiffness. They have attractive properties such as saturation of the host system’s vibration amplitude and strongly modulated response. This increases its operational frequency bandwidth and robustness against variations in the properties of host systems compared to linear vibration absorbers. However, the nonlinear nature may induce isolated responses in the host system that induce high vibration amplitudes. This paper investigates if these attractive properties also occur in the electric nonlinear energy sink shunt. An analytical expression for the frequency response is derived through the complexification-averaging method. Bifurcations in the frequency response reveal the occurrence of a quasi-periodic vibration energy exchange between the host system and the voltage over the electrodes of piezoelectric material. This is the main mechanism behind the amplitude saturation of the host system. Other bifurcations also reveal the existence of isolated responses. The nonlinear shunt is then realized with analog multipliers and a synthetic inductor and its performance in vibration damping is experimentally verified for a cantilever beam.

Unveiling the temperature-dependent mechanisms of viscoelasticity of sand-enhanced epoxy

The viscoelastic behavior of epoxy is critical for its engineering performance and applications. This work focused on the improvement of its viscoelastic performance by using natural sand particles as fillers. Experiments were carried out to investigate the static and dynamic viscoelastic properties of epoxy with various sand particle contents. Static mechanical tests demonstrated an increase in the elastic modulus, albeit at the cost of reduced strength at a higher sand content due to stress concentrations. Dynamic tests indicated substantially improved storage modulus and damping of epoxy after being filled with sand particles. Moreover, the glass transition temperature of epoxy showed a substantial rise upon the addition of sand particles, signifying an augmentation in its heat resistance. Static viscoelastic characterization revealed an elevation in both room- and high-temperature relaxation moduli upon incorporating sand. By applying time–temperature superposition principles, long-term relaxation curves were obtained, which could provide a reference for engineering design. These viscoelastic investigations offer insights into the underpinning mechanisms governing the performance of sand-reinforced epoxy. This enables the rational design of sand-particle-reinforced epoxy for customized durability, heat resistance and vibration damping.

Hyperelasticity of blood clots: Bridging the gap between microscopic and continuum scales

The biomechanical properties of blood clots, which are dictated by their compositions and micro-structures, play a critical role in determining their fates, i.e., occlusion, persistency, or embolization in the human circulatory system. While numerous constitutive models have emerged to describe the biomechanics of blood clots, most of these models have primarily focused on the macroscopic deformation of the clots and the resultant strain-stress correlations without depicting the microscopic contributions from their structural components, such as fibrin fibers, fibrin network and red blood cells. This work addresses the gap in current scientific understanding by quantifying how changes in the microstructure of blood clots affect its mechanical responses under different external stresses. We leverage our previous published work to develop a hyperelastic potential model for blood clots, which incorporates six distinct strain-energy components to describe the alignment of fibers, the entropic and enthalpic stretching of fibrin fibers, the buckling of these fibers, clot densification, and clot jamming. These strain-energy components are represented by a combination of simple harmonic oscillators, one-sided harmonic potentials, and a Gaussian potential. The proposed model, which is C0, C1, and C2 continuous with a total of 13 parameters, has been validated against three datasets: 1) fibrin clot in tension, 2) blood clot in compression, and 3) blood clots in shear, demonstrating its robustness. Subsequent simulations of a microscopic blood clot model are performed to uncover mechanistic correlations for a majority of the hyperelastic potential's stiffness/strain parameters. Our results show that only one proposed term concerning fiber buckling needs further refinement, while the remaining five strain-energy terms appear to describe precisely what they were intended to. In summary, the proposed model provides insight into the behavior of thromboembolisms and assistance in computer-aided design of surgical tools and interventions such as thrombectomy.

Drop Behavior on Heterogeneous Ratchet-Structured Substrates Harmonically Vibrated in Lateral Direction.

We analyze numerically a new ratchet system: a liquid drop is sitting on a heterogeneous ratchet-structured solid plate. The coated plate is subject to a lateral harmonic oscillation. The systematic investigation performed in the frame of a phase field model shows the possibility of realizing a long-distance net-driven motion for isolated domains of the forcing parameters. The studied problem might be of considerable interest for controlled motion in micro- and nanofluidics.

Exact counterdiabatic driving in finite topological lattice models

Adiabatic protocols are often employed in state preparation schemes but require the system to be driven by a slowly varying Hamiltonian so that transitions between instantaneous eigenstates are exponentially suppressed. Counterdiabatic driving is a technique to speed up adiabatic protocols by including additional terms calculated from the instantaneous eigenstates that counter diabatic excitations. However, this approach requires knowledge of the full eigenspectrum meaning that the exact analytical form of counterdiabatic driving is only known for a subset of problems, e.g., the harmonic oscillator and transverse field Ising model. We extend this subset of problems to include the general family of one-dimensional noninteracting lattice models with open boundary conditions and arbitrary onsite potential, tunneling terms, and lattice size. We will derive a general analytical form for the counterdiabatic term for all states of lattice models, including bound and in-gap states which appear, e.g., in topological insulators. We also derive the general analytical form of targeted counterdiabatic driving terms which are tailored to enforce the dynamical state to remain in a specific state. As an example of the use of the derived analytical forms, we consider state transfer using the topological edge states of the Su-Schrieffer-Heeger model. The derived analytical counterdiabatic driving Hamiltonian can be utilized to inform control protocols in many-body lattice models or to probe the nonequilibrium properties of lattice models. Published by the American Physical Society 2024

Strain modal response and vibration damping optimization of tower for wind power equipment

The safety of wind power equipment under dynamic load is one of the key factors to ensure sustainable energy recovery. In order to effectively improve the reliability of tower structure, the damage identification of flange bolt fracture based on strain mode was studied, and the vibration control and optimization scheme was proposed and verified. The dynamic response of the tower to wind load was calculated using the theory of Davenport spectrum. Combined with computational fluid dynamics, the dynamic load change law of the tower was obtained. Based on ANSYS Workbench, the modal simulation and analysis of the tower were carried out. Under different bolt damage conditions, the distribution characteristics of the strain modal shape of the tower in the axial and radial directions were obtained. The vibration damper was applied to the inside of the tower, and the vibration and stress at different positions under wind load were compared and analyzed to verify the specific vibration reduction and optimization effect. The results show that the strain modal shape of the tower cylinder has a significant peak at the damage site, and the peak height is positively correlated with the damage degree, indicating that the strain modal shape is highly sensitive to the damage. In addition, the vibration and maximum stress of the flange and top position of the tower have been effectively reduced by the shock absorber. The average amplitude of tower top can be reduced by 22.5 %, and the peak stress at the bottom flange position can be reduced by about 38 %.

Coherent spin states and emergent de Sitter quasinormal modes

As a toy model for the microscopic description of matter in de Sitter space, we consider a Hamiltonian acting on the spin-j representation of SU(2). This is a model with a finite-dimensional Hilbert space, from which quasinormal modes emerge in the large-spin limit. The path integral over coherent spin states can be evaluated at the semiclassical level and from it we find the single-particle de Sitter density of states, including 1/j corrections. Along the way, we discuss the use of quasinormal modes in quantum mechanics, starting from the paradigmatic upside-down harmonic oscillator.

Experimental study on the effects of SS304 and Aluminium reinforcements on mechanical and vibration properties in jute‐epoxy composites

AbstractJute fiber has emerged as a promising reinforcement material in polymer composites, and researchers are actively exploring hybrid composite materials to overcome its individual mechanical property limitations and enhance overall performance. The paper introduces a unique hybridization of polymer composites that harnesses the advantages of stainless steel and aluminium offering a lightweight material for potential engineering applications. In this study, stainless steel 304 wire mesh (S), aluminium wire mesh (Al) and aluminium perforated sheet (Alp) are used as an additional reinforcement along with jute (J) and glass (G) fibers to fabricate hybrid polymer composites with varying volume fractions of SS304 and Al wire mesh. Seven laminates of hybrid composites namely J/J/J/S/J/J/J, J/J/S/J/J/S/J/J, J/J/J/Al/J/J/J, J/J/Al/J/J/Al/J/J, J/J/J/Alp/J/J/J, G/J/J/J/S/J/J/J/G, (J/J/S/J/J/S/J/J)450 along with virgin composite laminate J/J/J/J/J/J/J/J were fabricated and tested to obtain mechanical and vibration properties. Bonding between metal wire and matrix is investigated and reported through ILLS tests and SEM observations. Experimental findings indicate a notable 24% and 7% increase in tensile and ILSS strength, respectively, with SS304 reinforcement. Moreover, significant improvements in flexural and impact strength, approximately 48% and 33% for J/J/S/J/J/S/J/J, demonstrate the effectiveness of the hybrid approach. The J/J/S/J/J/S/J/J laminate excels in damping capacity under various boundary conditions. The study underscores the potential of metallic reinforcement to enhance the mechanical properties of jute fiber‐reinforced polymer composites, presenting opportunities for the development of lightweight, sustainable, and high‐performance materials in engineering applications.Highlights Developed jute fiber‐based hybrid polymer composites with metal wire reinforcement. Significant increase in strength and stiffness observed with addition of metal wires. Bonding between metal wire and matrix is investigated through ILLS tests and SEM observations. Vibration damping of all hybrid materials is reported. Study provides valuable data to develop sustainable, lightweight, and cost‐effective materials.

Young’s Modulus and Hardness Identification of Extruded Aluminum by Scratching Damper

A special vibration damper is proposed for Young’s modulus and hardness identification through a scratching process on extruded aluminum. This paper presents the design and working principle of a scratching damper based on a scratching device. A non-contact electromagnetic shaker is used to generate the shaking force for test sample vibration. The required forces on the scratched material during the scratching process are generated by an adjustable compression spring. The proposed damper is designed and tested on an extruded aluminum 3004 sample for the determination of its Young’s modulus and hardness, and validation is performed using the standard test instruments. The physical dimensions of the scratching tracks are measured using a microscope and utilized to compute the scratching energy factor. Load curves are obtained at different divisions of the scratching process. The loop energy during the scratching process of the tested object is measured and used for the determination of sample material properties. Furthermore, the energy conservation law, scratch energy release rate of semi-conical scratch head, and loop energy release rate are established to determine the Young’s modulus and hardness of the sample. Their estimation accuracies are evaluated. The proposed method has several advantages over the traditional methods, including low cost, directness, and high repeatability. The results suggest this to be used as an alternative to the standard modulus and hardness tester.

On periodic motions of a harmonic oscillator interacting with incompressible fluids

We consider a mass–spring system immersed in an incompressible fluid flow governed by the Navier–Stokes equations subject to a prescribed time-periodic flow rate (and possibly external time-periodic body forces on the fluid and the mass). We show that, with no restriction on the period of the flow rate (and of the external forces), when the flow rate is “small”, there exists a weak time-periodic solution to the coupled system. Under some more regularity and “smallness” conditions on the flow rate (and the external forces) we also show that these solutions are, indeed, strong solutions.

Frequency dependent polarizability of confined harmonic oscillators

The D-dimensional Schrödinger equation for a confined harmonic potential perturbed by a time-dependent dipole field is analysed. The model uses exact confined solutions for the harmonic potential whereas the time-dependent field is treated using first-order time-dependent perturbation theory. Exact analytic solutions are obtained in terms of generalised Laguerre functions. This system has applications to nanostructures where there are strong confinement potentials in some dimensions and example calculations are carried out to illustrate the effect of the dimension.

Numerical study on dynamic response of double drive shafts of dual-coupled axial piston pump under various load ratios

The dynamic response of the double drive shafts, as the core component of the dual-coupled axial piston pump, affects the stability and reliability of the pump. The double drive shafts bear complex dynamic loads accompanied by a certain degree of vibration during the transmission of power, which results in abnormal contact between the double drive shafts and the bearing, as well as between it and the splined coupler, leading to increased wear. In this study, addressing the fatigue failure issue of the double drive shafts in the dual-coupled axial piston pump, a rigid-flexible coupling dynamic model of the dual-coupled axial piston pump is established. The stress and strain conditions of the double drive shafts under various load ratios are analysed, along with the dynamic characteristics between the drive shaft and the barrel block, as well as between it and the spline sleeve in both time and frequency domains, and the variation pattern of the vibration displacement of the double drive shafts. Additionally, the fatigue damage of the double drive shafts under various load ratios is analysed using the fatigue cumulative damage model. The results show that under various load ratios, obvious stress and strain concentrations occur in the neck near the bearing connection and the spline sleeve connection. The safety factor of the double drive shafts is higher than 1.5 in the obtained safety load range. The contact force between the double drive shafts and the barrel block is mainly influenced by the reciprocating motion of the pistons, while the contact force between the double drive shafts and the spline sleeve is affected by the synergistic effect of the reciprocating motion of the piston and the rotation of the drive shaft. Furthermore, the increase in the rear pump load pressure results in irregular trends in the vibration displacement of the double drive shafts, as well as superimposed fatigue damage to the front shaft. This study provides a reference for fatigue failure prevention, noise reduction, and vibration damping of the double drive shafts under various load ratios.

Assessment of Different Levels of Blackcurrant Juice and Furcellaran on the Quality of Fermented Whey-Based Beverages Using Rheological and Mechanical Vibration Damping Techniques.

In the current study, fermented whey-based beverage models with different levels of blackcurrant juice (0; 10; 20; 100% (w/w)) and furcellaran (0.25% and 0.50% (w/w)) were produced and evaluated. Physicochemical, rheological, mechanical vibration damping, and sensory analyses were performed. During fermentation (48 h), the values of pH, density, and total soluble solids decreased. On the other hand, the ethanol content during fermentation increased up to a final content in the range of 0.92-4.86% (v/v). The addition of furcellaran was effective in terms of sediment content decrease to a level of 0.25% (w/w). In general, the samples exhibited non-Newtonian pseudoplastic behaviour. The sensory analysis revealed that the sample with a composition of 20% (w/w) blackcurrant juice and 0.50% (w/w) furcellaran received the highest score.

High signal-to-noise ratio harmonic mode-locking Mamyshev oscillator at 1550 nm

Harmonic mode-locking is the effective method to improve ultrafast pulse repetition rate for the current research. However, this way of increasing the repetition rate based on pulse splitting has inherent instability characteristics, manifested as low signal-to-noise ratio and loss of mode-locking. In this paper, Mamyshev regenerative oscillation mode-locking technique is used to effectively improve the signal-to-noise ratio of pulses by compressing the nonlinear chirp in the cavity under the condition of near-zero dispersion. In the experiment, we successfully achieved a harmonic mode-locked pulse of up to 16 orders, corresponding to a repetition rate of 78.56 MHz, and the signal-to-noise ratio of the highest harmonic order reached 70 dB. Our research not only solves the inherent defect of low repetition rate of Mamyshev oscillator, but also effectively improves the signal-to-noise ratio of harmonic mode-locked pulse. This mode-locked structure based on Mamyshev oscillator provides reference and operability for improving the stability of ultrafast fiber lasers.

Vibration damping method of cantilever structure considering redundant constraint of monocrystalline blade casting mold shell

Excessive vibrations of the mold shell during the manufacturing process of monocrystalline blades lead to dendirite and frekle defects in directional solidification. The dynamics of the casting lifting device-mold shell system is analysed theoretically to reveal the influence of key parameters such as excitation force, damping and stiffness on the monocrystalline blade casting. The effect of redundant constraint onto the system is analysed via the developed vibration model. A lifting device-mold shell system test bench is developed, a slide-support arm device is designed to provide redundant constraint. A self-developed high-precision sensor is used to test the vibration signals, and the effectiveness of the damping method is verified. The experimental results show that the redundant constraint can reduce the undesired vibration of mold shell by more than 77 %, which ensures the casting quality of monocrystalline blades. The proposed vibration damping method can provide a reference for the vibration damping of the cantilever machine.

Covariant density functional theory for nuclear fission based on a two-center harmonic oscillator basis

Covariant density functional theory for nuclear fission based on a two-center harmonic oscillator basis

Strong coupling in an asymmetric two-dimensional guided mode resonance metasurface structure and enhancement for optical third-harmonic generation

A two-dimensional guided mode resonance structure supports a transverse magnetic (TM) resonant mode in the direction of incident polarization and a transverse electric (TE) resonant mode in the direction perpendicular to the polarization. In this work, the coupling between the transverse magnetic and the transverse electric resonant modes in an asymmetric two-dimensional dielectric metasurface structure is investigated. The asymmetric structure consists of a two-dimensional square nanohole array etched in a titanium dioxide thin film on a transparent silica substrate. With finite difference time domain simulations, anti-crossing of the resonant spectra of the TM and TE modes is observed by adjusting the asymmetry of the structure. The anti-crossing indicates that the interaction between TM and TE resonant modes results in a strong coupling state. A coupled harmonic oscillator model is used to explain the strong coupling effect. The results of the coupled harmonic oscillator modeling agree well with the results of numerical simulations. Furthermore, it is shown that the strong coupling can significantly enhance the third harmonic generation intensity compared with the uncoupled TM and TE resonant modes.

Exploring Piezoelectric Actuation towards Its Applications in Laser Powder Bed Fusion Additive Manufacturing.

Piezoelectric materials, which exhibit a charge distribution across the surfaces in reaction to mechanical strain, find significant utility in actuation and sensing applications. Apart from actuation applications like acoustic devices, motors, and vibration damping, an emerging domain for ultrasonic actuators lies in additive manufacturing processes. Ultrasonic waves applied during solidification aim to modulate grain structure and minimize defects. This research focuses on a fixture designed to facilitate and optimize ultrasonic wave propagation through the build plate in laser powder bed fusion additive manufacturing by utilizing a piezoelectric transducer. Three implementations of piezoelectric transducers were evaluated based on their out-of-plane ultrasonic velocity transmissions. It was determined that a thin plate adhered to the surface of the piezoelectric transducer yielded the most favorable outcomes for implementation, achieving 100% transmission of velocity and energy. Preliminary analysis of melt pool morphology and defects in single-track laser scanning experiments demonstrated the impact of ultrasound on solidification, hinting at a novel approach to enhancing the printability of alloys in laser powder bed fusion additive manufacturing processes. The optimal fixture and the explored transducing efficiency could further guide advanced ultrasound testing to enable in situ defect and texture detection during the additive manufacturing processes.

Coherently Driven Quantum Harmonic Oscillator Battery

Coherently Driven Quantum Harmonic Oscillator Battery