Free Oscillations Research Articles

Determination of hydrodynamic coefficients for open-frame ROVs through free oscillation tests in 1-DOF

ABSTRACT This study introduces an economical experimental approach for measuring the hydrodynamic inertia ( C M ) and drag ( C D ) coefficients of an open-frame ROV to support the stock assessment of scallops in the North Sea of Peru. A 1:3 scale ROV model was tested, suspended on springs, and set to oscillate freely in still water. The multiple spring groups provide equivalent stiffness, initial displacement, and natural frequencies for different cases. Three damping models—linear, quadratic, and linear-plus-quadratic—were applied to describe the motion equations, with the linear plus-quadratic model best fitting the experimental data. The coefficients and were analyzed against Reynolds (Re) numbers from 0.2×10 5 and 0.6×10 5 and Keulegan Carpenter (KC) numbers from 0.5 to 2. A strong correlation was observed with previous forced oscillation tests on cylinders and irregular bodies; thus, this methodology can be used to determine the hydrodynamic coefficients of ROVs.

Detection of Earth’s free oscillation and analysis of the non-synchronous oscillation phenomenon of normal modes

Earth’s free oscillation can provide essential constraints for refining Earth models, inverting seismic source mechanisms, and studying the deep internal structure of the Earth. Large earthquakes can simultaneously excite numerous normal modes. Due to the Earth’s ellipticity, rotation, and internal heterogeneities, these normal modes undergo splitting, with the frequencies of singlets of normal modes becoming very close (only a few µHz apart). This imposes greater demands on the detection of normal modes. This paper introduces a novel method for normal mode detection based on the normal time–frequency transform (NTFT). Compared to classical FT spectrum methods and recent optimal sequence estimation (OSE), the proposed method not only detects more weak normal modes but also reveals the spatial distribution of the phase of each normal mode. Taking the detection of 0S2 as an example, the phase measurements of each singlet are spatially inconsistent. This phenomenon can provide prior information for other methods, such as product spectrum analysis (PSA), spherical harmonic stacking (SHS), multistation experiments (MSE), and OSE. Additionally, understanding the phase distribution patterns contributes to further study of geological structures, offering crucial foundational data and observational support.

Coupling analysis between wave resonance in the moonpool and heave motion of the twin hulls with mooring effect

Fluid resonance in the moonpool formed by two identical rectangular hulls in water waves is investigated by employing the Computational Fluid Dynamics (CFD) package OpenFOAMⓇ. The influence of vertical stiffness on the behavior of moonpool resonance coupling with the heave motion response is presented. Numerical simulations show that the free surface oscillation in the moonpool exhibits a two-peak variation with the incident wave frequency, defined as the first and second peak frequencies. A local Keulegan–Carpenter (KC) number is introduced for describing the influence of fluid viscosity and flow rotation on the fluid resonance and heave motion resonance. At the first peak frequency, the free surface oscillation and heave motion response show an in-phase relationship, where increase in the vertical stiffness can increase the relative motion between them. This finally leads to an increase in the KC number, indicating the increased effect of energy dissipation with increase in the vertical stiffness. At the second peak frequency with an out-of-phase relationship between the free surface oscillation and heave motion response, the variation of the KC number is not sensitive to the vertical stiffness. Correspondingly, the influence of energy dissipation is not strongly dependent on the vertical stiffness.

Searching the InSight Seismic Data for Mars’s Background-Free Oscillations

Abstract Mars’s atmosphere has theoretically been predicted to be strong enough to continuously excite Mars’s background-free oscillations, potentially providing an independent means of verifying radial seismic body-wave models of Mars determined from marsquakes and meteorite impacts recorded during the Interior Exploration using Seismic Investigations, Geodesy, and Heat Transport (InSight) mission. To extract the background-free oscillations, we processed and analyzed the continuous seismic data, consisting of 966 Sols (a Sol is equivalent to a Martian day), collected by the Mars InSight mission using both automated and manual deglitching schemes to remove nonseismic disturbances. We then computed 1-Sol-long autocorrelations for the entire data set and stacked these to enhance any normal-mode peaks present in the spectrum. We find that while peaks in the stacked spectrum in the 2–4 mHz frequency band align with predictions based on seismic body-wave models and appear to be consistent across the different processing and stacking methods applied, unambiguous detection of atmosphere-induced free oscillations in the Martian seismic data nevertheless remains difficult. This possibly relates to the limited number of Sols of data that stack coherently and the continued presence of glitch-related signal that affects the seismic data across the normal-mode frequency range (∼1–10 mHz). Improved deglitching schemes may allow for clearer detection and identification in the future.

Defining and Mitigating Flow Instabilities in Open Channels Subjected to Hydropower Operation: Formulations and Experiments

A thorough literature review was conducted on the effects of free surface oscillation in open channels, highlighting the risks of the occurrence of positive and negative surge waves that can lead to overtopping. Experimental analyses were developed to focus on the instability of the flow due to constrictions, gate blockages, and the start-up and shutdown of hydropower plants. A forebay at the downstream end of a tunnel or canal provides the right conditions for the penstock inlet and regulates the temporary demand of the turbines. In tests with a flow of 60 to 100 m3/h, the effects of a gradually and rapidly varying flow in the free surface profile were analyzed. The specific energy and total momentum are used in the mathematical characterization of the boundaries along the free surface water profile. A sudden turbine stoppage or a sudden gate or valve closure can lead to hydraulic drilling and overtopping of the infrastructure wall. At the same time, a PID controller, if programmed appropriately, can reduce flooding by 20–40%. Flooding is limited to 0.8 m from an initial amplitude of 2 m, with a dissipation wave time of between 25 and 5 s, depending on the flow conditions and the parameters of the PID characteristics.

The topological characteristics of the bifurcation and chaos in the motion of combustion fronts in solids.

We investigate the geometric features in the bifurcation and chaos of a partial differential equation describing the unsteady combustion of solid propellants. Driven by the interaction of the unsteady combustion at the surface and the diffusion inside solids, the motion of the combustion fronts can be steady, harmonically oscillatory, and become more complicated to chaos through a series of bifurcations. We examined the dynamics in both free and forced oscillations. In the free oscillation, by varying a parameter related to the solid property, the intrinsic instability of the combustion is discovered. We find the typical period-doubling to chaos route and verify it via both qualitative and quantitative universalities. In the forced oscillation case, the system is perturbed by an external pressure excitation, leading to a more complicated bifurcation diagram with richer dynamics. Concentrating on the topological characteristics of the periodic orbits, we discover two new types of bifurcation other than the period-doubling bifurcation. In present work, we extract a series subtle topological structures from an infinite-dimensional dynamical systems governed by a partial differential equation with free boundary. We find the results provide an explanation for the period-3 orbits in the experimental data of a full-scale motor.

A generalized mathematical model for the damped free motion of a liquid column in a vertical U-tube

A one-dimensional mathematical model is developed to analyze the unsteady characteristics of arbitrary damped free motion, denoted as Z(τ), in a rigid, constant-diameter vertical column of a U-tube filled with an incompressible Newtonian liquid, where τ represents time. This model utilizes a simplified unsteady momentum equation derived from the Navier–Stokes equations in a circular coordinate system. Moreover, it incorporates assumptions about the periodicity of arbitrary damped free oscillations and employs the Fourier series representation to characterize the damped free motion. The combination of assumptions made for periodicity, the simplified momentum equation, and the Fourier series representation makes the current mathematical model unique and novel compared to prevailing models in the literature. In this model, the governing partial differential equation contains two dependent variables: Z(τ) is the known variable, as one can measure from experiments, and the instantaneous velocity uz is the unknown variable. Fitting the experimental data into the Fourier series provides the Fourier coefficients associated with the specific experiment. The Laplace transform method is used to determine the analytical solution for uz corresponding to the known Z(τ). The analytical expressions for instantaneous flow characteristics of practical importance, including area-averaged velocity, wall shear stress, and acceleration/deceleration, are deduced from uz. The analytical solutions presented are valid for generalized unsteady motions, including underdamped oscillations with varying amplitudes and periods, underdamped oscillations with varying amplitudes and constant period, and overdamped motion that does not exhibit a single oscillation. The findings from the present model offer insights for formulating a new friction model.

Numerical investigation of the damping rates of free oscillations in fluid energy acquired due to sloshing in rectangular tanks

Numerical investigation of the damping rates of free oscillations in fluid energy acquired due to sloshing in rectangular tanks

Control of deposits on pipeline systems by the method of free oscillations

RELEVANCE. There are a large number of heat exchangers in operation enterprises that operate under various temperature conditions. Steam, hot water, heated products of oil refining and other industries, which may contain oxides of iron, aluminum, calcium sulfate silicates, etc., are used as a heating agent. The efficiency of the heat exchange equipment depends on the condition of the heating surfaces. Contamination of these surfaces with various deposits dramatically reduces the heat transfer coefficient, which leads to a significant increase in heat consumption. The nature of the deposits depends on the properties of the heating agent and the heated medium.THE PURPOSE. The purpose is to assess the possibility of controlling deposits on the surfaces of heat exchange equipment by the free oscillation method. The presence of deposits changes the mass of structures and, consequently, the natural frequencies of vibrations, the analysis of which can determine not only the presence and thickness of deposits, as well as their appearance.METHODS. The paper shows the results of experimental studies conducted using a hardware and software package and calculations of natural vibrations of the surfaces of heat exchange equipment in the ANSYS software package to identify their dependence on the thickness and density of deposits. A plate, a pipe, and a pressurized pipe were modeled as heat transfer surfaces.RESULTS. The results obtained experimentally and computationally coincided, and it was concluded that the free oscillation method makes it possible to determine not only the presence of deposits on heat exchange surfaces, but their thickness and appearance.CONCLUSION. The free oscillation method can detect deposits in a timely manner and monitor their condition, which in turn will, reduce overall operating costs, increase energy efficiency and extend service life.

ANALYTICAL DESCRIPTION AND ALGORITHM OF CALCULATIONS OF MECHANICS OF STRUCTURES WITH BERNOULLI – EULER BEAMS USING SCAS KIDY

The problems of developing a universal analytical description and algorithm for automatic computer calculations of dynamics, statics and kinetostatics of mechanical models of structures including a beam lattice are considered. This can be calculations of transient processes, steady-state free and forced oscillations, determination of equilibrium positions and stress-strain states under static and dynamic loads, etc. The structure itself can be flat or spa- tial, stationary or moving on a plane or in space. Various instruments and devices can be attached to it. Arbitrary connections can be taken into ac- count. It is shown how it is possible to succinctly, using a special language for preparing computer data, analytically describe a part of a structure rep- resenting a beam lattice. Based on the theory of elasticity of Bernoulli-Euler beams, 2 forms of the canonical representation of the potential energy of an elastic beam are obtained. This makes it possible to introduce into the language of description of mechanical models of the special computer algebra system KiDyM (SCAS KiDyM) a new beam element, for which the position of the coordinate systems associated with the extreme sections is indi- cated. The positions of these sections are determined by lattice nodes, like solid bodies. Angular and linear coordinates of such solid bodies give gen- eralized coordinates of the mechanical model. An algorithm has been developed for the formation of elements adopted to describe mechanical models in SCAS KiDyM. Thus, the elastic structure of the mechanical model is formed. Using the available tools in this program, equations of dynamics and statics are automatically constructed, that is, a mathematical model is formed, and dynamic and static calculations can be carried out. The proposed method is demonstrated in detail on the example of calculating the deformation of an elastic lattice, with is the basis of a UAV (unmanned aerial vehi- cle). The results are compared with calculations using the ANSYS program

Free Vibrations of Thin-Walled Gas Pipelines Taking into Account the Influence of Longitudinal Force During Trench Laying

A numerical experiment was carried out to determine the frequencies of free oscillations of an inhomogeneous pipeline at various mechanical and geometric parameters.This made it possible to establish the influence of factors such as longitudinal force, thickness of the reinforced concrete shell, internal working pressure and the coefficient of the soil bed on the system’s own vibrations. For calculations, a model of an inhomogeneous cylindrical two-layer shell of finite length consisting of a steel pipe and a protective reinforced concrete layer was chosen.

An isogeometric approach for nonlocal bending and free oscillation of magneto-electro-elastic functionally graded nanobeam with elastic constraints

An isogeometric approach for nonlocal bending and free oscillation of magneto-electro-elastic functionally graded nanobeam with elastic constraints

Определение диссипативных потерь в гидравлическом приводе газораспределительного механизма двигателя внутреннего сгорания

Controlling the opening and closing times of intake and exhaust valves can improve the efficient parameters of an internal combustion engine and reduce the toxicity of combustion products. The valves are moved by an electronically controlled hydraulic drive. The energy consumption for the operation of a hydraulic valve drive is greater than when using a traditional mechanical drive. The dissipative energy losses in the accumulator one-way hydraulic valve drive are investigated. The working fluid of the hydraulic drive is SAE 5W-30 motor oil. The oil pressure behind the pump is 8 MPa, the diameter of the hydraulic cylinder is 16 mm. The main items of energy consumption are identified, and a methodology for their determination is proposed. The assessment of the efficiency of the hydraulic drive was based on the law of conservation of energy. To determine energy costs, a hydraulic drive model was compiled in the Simulink environment. A law of valve movement similar in shape to trapezoidal was obtained. The maximum speed of valve movement during the opening process is 4 m/s, during the closing process 3.8 m/s. During the period when the valve is held near the maximum lift of 14 mm, free oscillations with an amplitude of about 1 mm are observed. The energy consumption for a single actuation of the valve, which has a progressively moving mass of 0.5 kg, amounted to 25.9 J. Of this, a little more than 70% is spent on filling the hydraulic cylinder with liquid, the rest is spent when emptying it. As a result of throttling the fluid flow in the hydraulic cylinder rod stroke limiter and hydraulic brake, 56% of the energy is lost. Large energy losses are observed between the hydraulic accumulators and the hydraulic cylinder. When the cylinder is filled, 21.1% is lost here, and when it is emptied, 10.4%. Increasing the capacity of the supply and drain lines between hydraulic accumulators and hydraulic cylinders allows you to increase the speed of opening and closing valves. The main ways to increase the energy efficiency of the drive are to shift the hydraulic accumulators to the hydraulic cylinder, increase the diameter of the connecting lines, and increase the throughput of the solenoid valves.

Exact solution for free vibration analysis of non-uniform thickness functionally graded porous nanosheet with surface effect based on variable nonlocal and length-scale parameters

In this article, the analytical solution for free oscillation of non-uniform thickness functionally graded porous (FGP) rectangular nanosheets resting on a Pasternak foundation with various boundary conditions (BCs) based on the nonlocal strain gradient theory and surface effect are discovered. The nonlocal stress and strain effects are captured on the nonlocal strain gradient hypothesis, while the surface energy effects are based on the surface elasticity hypothesis. The FGP nanosheet has a nonlinear thickness change in both x and y directions and is placed on the Pasternak elastic foundation. The unique point of this study is to investigate the change of nonlocal and length-scale coefficients along the thickness as mechanical properties of the material. Applying classical shear deformation theory (ignore the effect of shear deformation) combined with Hamilton’s principle, the motion balance equation of non-uniform thickness nanosheets is established. The accuracy of the proposed method is verified through reliable publications. A set of results of natural vibration frequencies of variable thickness FGP nanosheets under the influence of factors are discovered and discussed. The results of this study can be used in design calculations of MEM and NEMs systems in mechanics.

Muzzle bubble dynamics characterization of underwater launching

To comprehensively understand the dynamic behavior of muzzle bubbles during underwater launching, an emptying process aligned with the muzzle flow characteristics is established and an evaporative condensation mechanism is modeled according to the high temperature and pressure properties of the propellant gas. Utilizing the spherical bubble theory, which comprises the inflation process and evaporative condensation effects, the dynamics of muzzle bubbles and their corresponding pressure waves are investigated. The numerical simulation results well agree with the experimental observations in terms of bubble radius and near-field pressure waves. Furthermore, the influence of two key factors on the bubble dynamics is examined: underwater launching depth and initial muzzle pressures. The results illustrate that the inflation process needs to be accurately described for precise pressure wave predictions. Using the evaporation condensation model, the bubble radius and frequency can be accurately characterized. Moreover, the launching depth influences the free expansion radius and oscillation frequency mostly due to the increase in hydrostatic pressure, which decreases by 33% and increases by 150% in the 1–20 m range, respectively. The initial muzzle pressure affects the initial expansion velocity and initial shock wave mainly due to the increase in the mass flow rate, which increase by 56% and 82% in the 35–65 MPa range, respectively.

Experimental Determination of Pitch Damping Coefficient Using Free Oscillation Method

This paper outlines an experimental investigation conducted at the INCAS trisonic wind tunnel, focusing on the determination of pitch damping coefficient. The model used for this investigation is the Basic Finner Model, a standard model for dynamic tests which consists in a cone-cylinder body with four rectangular fins. The study aims to evaluate the influence of various parameters—including the Mach number, angle of attack, reduced frequency, center of rotation, and roll angle—on pitch damping coefficient. The employed method for determining these coefficients is the free oscillation method which consists in measuring the model oscillation in free stream after an initial perturbation. In order to perform these dynamic tests in the wind tunnel, a dedicated rig was developed to initiate the model’s oscillation using a linear servo-actuator and to record its oscillation using a strain gauge. The results obtained from the experiments illustrate how each parameter impacts the pitch damping coefficient, highlighting the precision of the measurements. The paper’s conclusion presents that the developed rig and the method used provide accurate results, and the variation in different parameters can change the damping coefficient.

Vibrational and Dissipative Characteristic Measurement of Solid-state Wave Gyroscope Resonators: Algorithms Based on the Identification of Free Oscillation Equations

The article describes the methodological basis for constructing computational circuits of different complexity degrees and different purposes for solving a wide range of industrial and laboratory problems to measure angular irregularity of vibrational-dissipative resonatorcharacteristics of integrating solid-state wave gyroscopes. The main method to solve such problems is the identification of the coefficients of the differential equations of quartz hemispherical resonator state in the mode of its free oscillations. The resonator oscillation equations both in the fixed measuring axes and in the moving axes of standing waves were chosen as the equations of state. After reduction to slow variables, only slowly changing amplitudeequations are left for identification problems. In all the described circuits, it is assumed that the information signals for the solved identification tasks are formed in a measuring device similar to the standard gyroscope device. These algorithms make it possible to measure the vibrational and dissipative characteristics of resonators with different degrees of completeness and directionality for different standard initial requirements to themeasurement accuracy and experimental modes, which makes it possible to reduce the measurement time and labor intensity of the established set of production control operations. Among the tasks to be solved for the free run-down mode of the resonator wave pattern are the following: angular irregularity measurement of the gyroscope resonator dissipative properties under conditions of low and significant residual frequency difference; angular non-uniformity measurement of gyroscope resonator vibrational properties (its different frequency); simultaneous measurement of resonator oscillatory and dissipative characteristics for fixed and special rotating gyroscope modes. The detailed processing of the computational schemes for the implementation of these algorithms is focused on their practical application for various tasks of production operational control. At the same time, the choice of the most suitable computational algorithm from the considered options depends on the conditions, requirements and specifics of measurements.

Experimental Study On Bubble Pairs And Induced Flow Fields Using Tomographic Particle Image Velocimetry

Gas-liquid two-phase flows, such as bubbly flows, are widely used across various engineering and military applications due to their distinctive fluid dynamics. This study utilizes advanced imaging techniques, including shadowgraphy and laser-induced fluorescence tomographic particle image velocimetry (LIF-TPIV), to provide a quantitative analysis of bubble motions and the resulting flow fields. We systematically investigate the effects of orifice distances (s) set at 10, 15, 20, and 25 mm to assess the impact of spacing on bubble behavior and interactions. Our findings indicate that at orifice distances of 20 mm or less, the proximity of bubbles facilitates interactions, promoting dynamic bubble behaviors. In contrast, at distances greater than 25 mm, interactions become markedly weaker, leading to increased separation between bubbles during their free oscillation stages. This weak interaction directly influences the characteristics of bubble-induced flow fields. As orifice spacing increases, there is a noticeable decrease in the velocity of the flow field between bubbles, particularly noticeable at spacings of 20 mm and above. At these larger spacings, a low-velocity zone develops between the bubbles at higher heights, which, according to Bernoulli's principle, corresponds to a high-pressure area. This high pressure contributes to a reduction in bubble volume with increasing orifice spacing. Furthermore, the intensity of wake vortices between two bubbles is observed to be highest at the smallest spacing of 10 mm, closely resembling the flow structure characteristic of a single rising bubble. For spacings of 15 and 20 mm, the induced flow fields of the bubbles continue to interact significantly. However, at a spacing of 25 mm, the flow fields appear to function independently, suggesting a threshold beyond which bubble interactions stop to significantly affect their surrounding fluid environments. These findings are helpful for comprehending the two-phase flow dynamics, particularly in multi-orifices bubbly flow.

Laser beam effect on the entanglement of elastic collisions in quantum plasma

In the quantized field formalism, using Kramers–Henneberger unitary transformation as the semi-classical counterpart of Block–Nordsieck transformation, the dynamics of entanglement during the low energy scattering processes in bi-partite systems at the presence of a laser beam fields are studied. The stationary-state Schrodinger equation for the quantum scattering process is obtained for such systems. Then, using partial wave analysis, we introduce a new form of entanglement fidelity considering the effect of high-intensity laser beam fields. The effective potential of hot quantum plasma including plasmon and quantum screening effects is used to obtain the entanglement fidelity ratio as a function of the laser amplitude, and plasmon and Debye length parameters for the elastic electron-ion collisions. It is shown that the plasma free electrons oscillations under interaction with laser beam fields improve the correlations between charged particles and consequently lead to the increase in the system entanglement.

On the stability of prestressed beams undergoing nonlinear flexural free oscillations

We study the nonlinear free undamped motions of a hinged-hinged beam exhibiting geometric stretching-induced nonlinearity and arbitrary initial conditions. We treat the governing integral-partial-differential equation of motion as an infinite dimensional Hamiltonian system. We analytically obtain a quantitative Birkhoff Normal Form via a nonlinear coordinate transformation that yields the reduced (modulation) equations describing the free oscillations to within a certain nonlinear order with an estimate of the reminder. The obtained solutions provide a very precise description of small amplitude oscillations over large time scales. The analytical optimization of the involved estimates yields time stability results obtained for plausible values of the physical quantities and of the perturbation parameter. The role played by internal resonances in determining the time stability of the solution is highlighted and discussed. We show that initial conditions with a finite number of eigenfunctions yield bounded solutions living on invariant subspaces of the involved modes at all times. Conversely, initial conditions comprising the full (infinite) spectrum of eigenfunctions provide solutions for which time stability for all times cannot be stated.