Harmonic Oscillator Research Articles

Numerical Modal Analysis of Foams with Different Types and Configurations

Thanks to the perfect combination of mechanical properties like high strength and rigidity with functional properties like thermo-acoustic insulation and vibration damping, foam structures are becoming increasingly attractive in engineering applications. Most of the research done so far has been focused on the mechanical properties of foams. On the other hand, understanding the vibration behavior of foams is vital since most failures in engineering applications are associated with violent vibrations. In this research, it is focused on the vibration analysis of foams with different types and configurations. In the context of vibration, modal analysis is a highly preferred method for fully understanding the structural behavior of materials. The Finite Element Method is commonly employed for numerical modal analysis to reveal the vibration characteristics of structures, including natural frequencies and corresponding mode shapes. With this objective, the natural frequencies and mode shapes of these foams were defined under both clamped-free and free-free boundary conditions. Subsequently, the effects of material application and boundary conditions were examined. The findings and results obtained can provide valuable insights to researchers and engineers for design applications.

Harmonic Oscillator, Dissipation and Thermodynamics

Abstract A loss-free harmonic oscillator when treated as the working substance in a cylinder with a piston, exhibits dissipation characterized by hysteresis cycles. Dissipation in this case develops through conversion of potential energy of the springs and part of the work by piston motion to kinetic energy of the oscillator that represents its temperature. The results also yield analogies with several complex thermodynamic notions such as lost work, heating and cooling, Joule - Thompson expansion and temperature inversion, and regimes of maximum power and maximum efficiency as in finite thermodynamic systems. Use of multiple oscillators with different frequency distributions supports the notion of a dissipative constitutive relationship emerging from a dissipation-free model in which the stress depends both on strain and strain rate as in heuristic models used in solid mechanics as, for example, the Johnson-Cook model.

Parameter Estimation of a Partially Observed Hypoelliptic Stochastic Linear System

In this article, we address the problem of the parameter estimation of a partially observed linear hypoelliptic stochastic system in continuous time, a relevant problem in various fields, including mechanical and structural engineering. We propose an online approach which is an approximation to the expectation–maximization (EM) algorithm. This approach combines the Kalman–Bucy filter, to deal with partial observations, with the maximum likelihood estimator for a degenerate n-dimensional system under complete observation. The performance of the proposed approach is illustrated by means of a simulation study undertaken on a harmonic oscillator that describes the dynamic behavior of an elementary engineering structure subject to random vibrations. The unknown parameters represent the oscillator’s stiffness and damping coefficients. The simulation results indicate that, as the variance of the observation error vanishes, the proposed approach remains reasonably close to the output of the EM algorithm, with the advantage of a significant reduction in computing time.

Estimation of Probable Ground Vibration Spectra and Reaction Spectra Taking into Account Local Ground Conditions

Statement of the problem. Using the example of a strong earthquake that occurred in Dagestan in 1970 with a magnitude of M = 6.7, practical methods and results of forecasting the variable Fourier spectra and reaction spectra, taking into account the characteristics of the focal zone and local ground conditions under strong seismic influence, are shown. It became possible to consider the variability of reactions associated with the randomness of the phase angle of individual harmonics of the general oscillation and the uncertainties of the parameters of the ground oscillation. In turn, this will allow us to obtain a set of regional or local reaction spectra with given probabilities of not exceeding the loads, which allows designers to choose the initial loads depending on the type of building or structure (depending on the degree of its responsibility). Results. The reliability of estimates of Fourier spectra and reaction spectra obtained during a single event allows us to solve the problem of assessing seismic hazard in terms of Fourier spectra and reaction spectra. But, it should be noted that this method of assessing the seismic load can lead to an increase in the cost of construction, since in this case we lay the load with a large margin, so this technique is applicable for the design and construction of buildings and structures in which deformations are unacceptable (nuclear power plants, etc.). Conclusions. Consideration of soil factors in the probabilistic formulation should be carried out in the presence of a large amount of experimental data on the composition, properties and reaction of this type of soil, allowing to construct the probability density functions of the distribution of spectral characteristics, as well as the characteristics of the focal zone.

Active control of electromagnetically induced transparency based on vanadium dioxide microstructures

Abstract Electromagnetically induced transparency (EIT) based on metasurfaces has made significant advancements in the past decade. The ability to actively tune EIT is desirable for practical applications, and this has been accomplished by integrating metallic structures with tunable materials. Here, we propose a dynamically tunable EIT using a metasurface composed of vanadium dioxide (VO2) microstructures without additional metallic structures. A single cut wire and a pair of U-Shape split ring microstructures are combined to design the unit cell of the VO2 metasurface, which functions as bright and dark modes, respectively. The destructive interference between these two modes causes an EIT-like resonance at the terahertz band for VO2 in its metallic phase. However, when VO2 transitions into its insulating phase, the EIT resonance gradually vanishes. Theoretical analyses based on the electric field distribution and coupled harmonic oscillator model indicate that the tunable EIT is due to changes in the attenuation rate of two modes. Furthermore, the phase transition of VO2 can generate tunable group delays. The active EIT utilizing VO2 microstructures could be applied in terahertz modulators and tunable slow light devices.

Path Integral Analysis for a Damped Harmonic Oscillator with a Higher Derivative Term in the Damping

Path Integral Analysis for a Damped Harmonic Oscillator with a Higher Derivative Term in the Damping

METHODOLOGY FOR EXPERIMENTAL RESEARCH ON THE DISTRIBUTION OF ENERGY IN THE ELEMENTS OF THE «VIBRATION MACHINE – COMPACTING CONCRETE MIXTURE» SYSTEM

The paper presents a methodology for experimental research on the distribution of energy in the elements of a vibra-tion machine for compacting concrete mixtures. The development of this methodology is based on a thorough analy-sis of existing research methods and the determination of energies in mechanical systems and media. Within the general system of the "vibration machine – compacting concrete mixture," the following subsystems were identified: bearings of the vibration exciter, supports, vibration dampers, reactive and active masses, including the form mass and the compacting concrete mixture. Specific research methods for energy dissipation were determined for each of the mentioned subsystems, preceding relevant modeling. Energy dissipation depends on many factors: the composi-tion and structure of the material, cyclic deformation and stresses arising from the medium’s exposure, the type and parameters of the load, the duration of cyclic deformation, and more. The evaluation criterion for energy dissipa-tion in media is the energy absorption coefficient, which expresses the ratio of energy used to perform the techno-logical process of compaction to the potential energy. The ratio of these energies is considered an independent material characteristic, determined experimentally, taking into account actual technological and operational fac-tors. It was found that the following main methods are used to evaluate energy parameters: phase, damping oscilla-tions, hysteresis loops, energy, and resonance methods. The paper substantiates the methodology for experimental research of parameters and energy indicators of concrete mixture compaction processes. Two models—discrete and continuous—were used in the simulation of these processes.

A unified physics-based continuum theory for magnetorheological fluid deformation: Implications in magnetorheological fluid-based brake applications

Magnetorheological (MR) fluids are smart composites that can exhibit reversible behavior changes and quickly transit from a liquid state to a nearly solid state when exposed to magnetic fields. Existing theories, such as the Herschel–Bulkley (H-B) model and artificial neural network, are frequently employed to describe the deformation of MR fluids; however, these are limited to certain modes of deformation and have lagged in the physical interpretation of magneto–mechanical interaction. To address the limitations, this study provides an in-depth investigation of MR fluid behavior, highlighting its non-Newtonian characteristics and the occurrence of a yielding phenomenon under finite deformation. A unified framework is developed to describe solid and fluid characteristics using classical continuum mechanics and Ericksen's seminal work consistent with the second law of thermodynamics. To highlight the distinctive characteristics of MR fluids, the investigation explores different deformation modes, including shear, flow, and squeezing. This study comprehensively addresses essential phenomena in MR fluids, including yielding, rate-dependent viscosity, and the Weissenberg effect, by leveraging the physical insights from their interaction with magnetic fields. We performed experiments with a rheometer to validate these conclusions and contrasted the analytical findings with the experimental data. Additionally, we confirmed the theoretical predictions for flow mode deformation by comparing them with existing experiments, offering a thorough explanation of field-dependent flow properties. The presented theory is also used to analyze the breaking for the MR brake system analytically, which is then validated by comparing it with the experiment. The proposed framework serves as a valuable tool for understanding and predicting the behavior of MR fluids, enabling the realization of their full potential in practical applications, such as MR fluid-based clutches and vibration dampers.

Nonlinear periodic response analysis of mechatronic systems with friction

Nonlinearities are present in many coupling components of mechanical and mechatronic systems, with the most common nonlinear coupling property being that of friction force. Transient simulation of systems with nonlinear friction can be a challenge in terms of solver robustness and calculation time. Moreover, many manufacturing processes lead to periodic forces and motions such as in milling, or repetitive pick-and-place serial production operations. In this paper, a method and application for nonlinear periodic response analysis (NPRA) of reduced-order mechatronic systems is presented, which leverages the fact that the majority of components in common mechatronic systems (e.g. machine tools) are linear. The dynamic behaviour of these components can thus be represented using a linear reduced order model (ROM). The analysis is implemented using the Harmonic Balance Method (HBM), which is then applied to the ROM of a simple, structurally compliant mechatronic system with a motion controller and profiled rail guideways. A practical case encountered in industrial settings is analysed, that being the testing of a system’s frequency response. Periodic responses to a harmonic velocity setpoint input oscillation are analysed in both time and frequency domains and comparisons then made between measurement and simulation. This comparison shows that many significant effects of nonlinear friction in ROMs of mechatronic systems can be modelled using the NPRA method and a simple friction model with a presliding regime. The combination of HBM with model order reduction (MOR) opens up a field of applications for the efficient and robust simulative analysis of periodic processes with nonlinear couplings in complicated mechatronic systems.

Extreme events in the Higgs oscillator: A dynamical study and forecasting approach.

Many dynamical systems exhibit unexpected large amplitude excursions in the chronological progression of a state variable. In the present work, we consider the dynamics associated with the one-dimensional Higgs oscillator, which is realized through gnomonic projection of a harmonic oscillator defined on a spherical space of constant curvature onto a Euclidean plane, which is tangent to the spherical space. While studying the dynamics of such a Higgs oscillator subjected to damping and an external forcing, various bifurcation phenomena, such as symmetry breaking, period doubling, and intermittency crises are encountered. As the driven parameter increases, the route to chaos takes place via intermittency crisis, and we also identify the occurrence of extreme events due to the interior crisis. The study of probability distribution also confirms the occurrence of extreme events. Finally, we train the long short-term memory neural network model with the time-series data to forecast extreme events.

Seismic performance and vibration damping analysis for end reinforcement tunnel working shaft in complex geology

Seismic performance and vibration damping analysis for end reinforcement tunnel working shaft in complex geology

The Feynman propagator within three parameters generalized Dunkl derivative: One-dimensional case

In this paper, the Feynman path integral approach within three parameters Dunkl derivative is investigated in the one-dimensional case of nonrelativistic quantum mechanics. We successfully derive the propagator in Cartesian coordinates and give its exact expression for the free particle, inverse square, harmonic oscillator and pure Coulomb potentials. The energy eigenvalues and their corresponding wave functions are determined.

Transport parameter effects on controlling formation and shape of lotus-type pores in solid

Abstract This study explores sufficient conditions based on transport parameters to effectively manipulate the growth and shape of lotus pores during solidification. Specifically, spatial variations in mass transfer coefficients and solute transport parameters are considered. Solute transport is the key factor responsible for the evolution of lotus pores. The work investigates the influence of these conditions on the shape development of lotus pores, which find applications in diverse fields such as energy absorption, sound absorption, shock and vibration damping, heat sinks, filters and tissue and bone implants. The unsteady gas pressure within the pores, responsible for bubble entrapment, is influenced by gas, capillary and liquid pressures, as well as Sieverts’ or Henry's laws, and solute transfer at gas–liquid interfaces. Solute transport into the pore is determined by liquid convection as well as convection-affected segregation at the advancing liquid–solid interface. The study utilizes the MATLAB code to solve the resulting first-order time-derivative ordinary differential equations. It shows that the lotus pores are susceptible to entrapment as the mass transfer coefficient at a contact angle of 90° increases, while the solute transport parameters at the initial time and a contact angle of 90° decrease. The lotus pore length increases and decreases, respectively, with increases in the mass transfer coefficients as well as the solute transport parameter at the initial time and a contact angle of 90°. Predicted lotus pore shapes align closely with algebraic results, validated by experimental data from a prior study.

Deterministic periodic structures in a model of the human airways

Deterministic periodic structures in a model of the human airways

Alchemical harmonic approximation based potential for iso-electronic diatomics: Foundational baseline for Δ-machine learning.

We introduce the alchemical harmonic approximation (AHA) of the absolute electronic energy for charge-neutral iso-electronic diatomics at fixed interatomic distance d0. To account for variations in distance, we combine AHA with this ansatz for the electronic binding potential, E(d)=(Eu-Es)Ec-EsEu-Esd/d0+Es, where Eu, Ec, Es correspond to the energies of the united atom, calibration at d0, and the sum of infinitely separated atoms, respectively. Our model covers the two-dimensional electronic potential energy surface spanned by distances of 0.7-2.5Å and differences in nuclear charge from which only one single point (with elements of nuclear charge Z1, Z2, and distance d0) is drawn to calibrate Ec. Using reference data from pbe0/cc-pVDZ, we present numerical evidence for the electronic ground-state of all neutral diatomics with 8, 10, 12, and 14 electrons. We assess the validity of our model by comparison to legacy interatomic potentials (harmonic oscillator, Lennard-Jones, and Morse) within the most relevant range of binding (0.7-2.5Å) and find comparable accuracy if restricted to single diatomics and significantly better predictive power when extrapolating to the entire iso-electronic series. We also investigated Δ-learning of the electronic absolute energy using our model as a baseline. This baseline model results in a systematic improvement, effectively reducing training data needed for reaching chemical accuracy by up to an order of magnitude from ∼1000 to ∼100. By contrast, using AHA+Morse as a baseline hardly leads to any improvement and sometimes even deteriorates the predictive power. Inferring the energy of unseen CO converges to a prediction error of ∼0.1 Ha in direct learning and ∼0.04 Ha with our baseline.

Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator

Quantum technologies and experiments often require preparing systems in low-temperature states. Here we investigate cooling schemes using feedback protocols modeled with a quantum Fokker-Planck master equation (QFPME) recently derived by Annby-Andersson []. This equation describes systems under continuous weak measurements, with feedback based on the outcome of these measurements. We apply this formalism to study the cooling and trapping of a harmonic oscillator for several protocols based on position and/or momentum measurements. We find that the protocols can cool the oscillator down to, or close to, the ground state for suitable choices of parameters. Our analysis provides an analytically solvable case study of quantum measurement and feedback and illustrates the application of the QFPME to continuous quantum systems. Published by the American Physical Society 2025

Vertical kinematics of the young Galactic clusters

Abstract The young disc vertical phase is paramount in our understanding of Galaxy evolution. Analysing the vertical kinematics at different galactic regions provides important information about the space-time variations of the Galactic potential. The vertical phase snail-shell structure found after Gaia DR2 release encompasses a wide range of ages. However, the structure of the VZ vs Z diagram appears linear when the analysis is limited to studying objects younger than 30 Ma. Based on the vertical velocity and height-over-disc maps obtained for a sample of young open clusters, this method also allows the matter density in the Solar neighbourhood to be estimated using a completely different approach than previously found in the literature. We use two different catalogues of star clusters to confirm the previous result and study new age ranges. The linear pattern between VZ and Z shows different slopes, ∂VZ/∂Z, for various age groups. The results fit a simple model (harmonic oscillator) of in-plane decoupled vertical dynamics up to a certain age limit, corresponding to ∼ 30 Ma. This work also analyses the relationship between the local volumetric density of matter (ρ0) and the disc vertical kinematics for different age ranges, all below 50 Ma. The best estimates of the effective volumetric mass density in the Solar neighbourhood, 0.09-0.15 M⊙ pc−3, agree with those given by other authors, assessing the reliability of the proposed dynamical model. These values are a minorant of the actual matter density in the region.

Research on the Spiral Rolling Gait of High-Voltage Power Line Serpentine Robots Based on Improved Hopf-CPGs Model

The efficiency of helical locomotion in snake-like robots along high-voltage transmission lines is often hindered by low motion efficiency, high joint signal noise, and challenges in traversing obstacles. This study aims to address these issues by proposing a gait generation method that leverages a standardized Central Pattern Generator (CPG). We modify the traditional Hopf-CPG model by incorporating constraint functions and a frequency-tuning mechanism to regulate the oscillator, which allows for the generation of asymmetric waveform signals for deflection joints and facilitates rapid convergence. The method begins by determining initial and obstacle-crossing state parameters, such as deflection angles and helical radii of the snake-like robot, using the backbone curve method and the Frenet–Serret framework. Subsequently, a CPG neural network is constructed based on Hopf oscillators, with a limit cycle convergent speed adjustment factor and amplitude bias signals to establish a fully connected matrix model for calculating multi-joint output signals. Simulation analysis using Simulink–CoppeliaSim evaluates the robot’s obstacle-crossing ability and the optimization of deflection joint signal noise. The results indicate a 55.70% increase in the robot’s average speed during cable traversal, a 57.53% reduction in deflection joint noise disturbance, and successful crossing of the vibration damper. This gait generation method significantly enhances locomotion efficiency and noise suppression in snake-like robots, offering substantial advantages over traditional approaches.

Study on Dynamic Response of Damping Type Composite Floor Slabs Considering Interlayer Interaction Influences

In order to explore the vibration mechanism of vibration damping composite floor slabs and further enrich the theory of floor slab vibration calculation, the free vibration characteristics of vibration damped composite floor slabs and the dynamic response of vibration damped composite floor slabs under multi-source excitation is analyzed using first type Chebyshev polynomials to construct the displacement function and derive an analytical solution. The three-dimensional laminated theory is employed, considering the interlayer interaction. Based on the proposed method, the influences of loading types, positions, magnitudes, and frequencies on the vertical vibration of floor slabs are calculated. The study illustrates that, under the action of multi-source excitation, the displacement and acceleration responses calculated by the method proposed in this paper are always greater than those calculated by the single-plate theoretical solution. The dynamic responses of the vibration damping composite floor slab decrease with the increase of the thickness and elastic modulus of the vibration damping layer. Under different thicknesses of the vibration damping layer, the peak accelerations of the vibration damping composite floor slabs increase linearly with the growth of the load amplitude. In addition, the load movement path has a significant effect on the vibration response of the floor slab. When the moving load moves along the short side of the floor, the displacement response of the floor is generally greater than that along the long side of the floor.

Event-triggered synchronisation of unknown heterogeneous coupled harmonic oscillators

This note concentrates on event-triggered synchronisation problem of unknown heterogeneous coupled harmonic oscillators (CHOs). We develop an event-triggered synchronisation algorithm that does not rely on any continuous information transmission among oscillators and global topology information. For this end, we first design an observer to estimate unknown system parameter for each oscillator. Second, each oscillator uses information received from its neighbours to estimate the frequency of leader oscillator and its neighbours' states. Based on estimated frequencies and states, we design an adaptive synchronisation algorithm for CHOs to solve synchronisation problem. We prove that CHOs, under proposed synchronisation algorithm, reach state synchronisation, and there is no Zeno behaviour. In the end, a simulation is presented to check proposed synchronisation algorithm.