Dynamic Equations Research Articles

Design of active vibration isolation system for satellite optical load based on Stewart platform

According to the requirements of hyperstatic environment of a satellite optical load during in orbit operation, the Stewart active vibration isolation platform was designed, and its dynamic equation was established by Newton Euler method. The virtual prototype model was established in ADAMS, and the accuracy of the model was verified by comparing the numerical solution and simulation solution of the modal frequency of the platform; On this basis, the dynamic model is decoupled into six SISO systems, and the optimal controller is designed for each subsystem. Finally, the whole system is simulated by ADAMS/MATLAB, and the displacement response curves of the load before and after control are obtained. The simulation results show that the Stewart active vibration isolation platform can effectively suppress the vibration.

The TDHF code Sky3D version 1.2

The Sky3D code has been widely used to describe nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The approach is based on Skyrme forces or related energy density functionals. The static and dynamic equations are solved on a three-dimensional grid, and pairing is been implemented in the BCS approximation. This updated version of the code aims to facilitate the calculation of nuclear strength functions in the regime of linear response theory, while retaining all existing functionality and use cases. The strength functions are benchmarked against available RPA codes, and the user has the freedom of choice when selecting the nature of external excitation (from monopole to hexadecapole and more). Some utility programs are also provided that calculate the strength function from the time-dependent output of the dynamic calculations of the Sky3D code. New version program summaryProgram Title: Sky3DCPC Library link to program files:https://doi.org/10.17632/vzbrzvyrn4.2Developer's repository link:https://github.com/manybody/sky3dLicensing provisions: GPLv3Programming language: Fortran, with one post-processing utility in Python.Journal reference of previous version:: Schuetrumpf, B., Reinhard, P.G., Stevenson, P.D., Umar, A.S., and Maruhn, J.A. (2018). The TDHF code Sky3D version 1.1. Comput. Phys. Commun. 229 (2018) 211–213.Does the new version supersede the previous version?: Yes.Reasons for the new version: The capability of reproducing the nuclear strength function for a variety of newly-coded external boosts has been added.Nature of problem: Calculating nuclear multipole strength functions is a crucial probe that can help model the nuclear system and its structure properties. A variety of models exist for this task, such as QRPA (Quasiparticle Random Phase Approximation) and its variants, but such approaches are often limited due to symmetry constraints. Time-dependent Hartree Fock (TDHF) has been used to simulate nuclear vibrations and collisions between nuclei for low energies without assuming any symmetry in the system. This code extends the TDHF to calculate the multi-pole strength functions of atomic nuclei. We showcase its reliability by comparing it with the established RPA codes for the calculation of such strength functions.Solution method: We extended previous versions of the Sky3D code [1,2] to include an external boost of multipole type where the user can provide custom input that decides the nature of the multipole (monopole, quadrupole, octupole, and so on) boost. The principal aim is to calculate the multipole strength function, which is the Fourier transform of the time-dependent expectation value of the multipole operator, which has the same form as the external boost. The proper unit conversion is done so that one can extract the exact unit of the thus calculated strength function, which is comparable to the available literature in the field. The boundary conditions are chosen such that a Woods-Saxon-like function cuts off the external field, driving it to zero at the boundary.Summary of revisions: The ability to give a more general external field for excitation has been implemented, which can be of a chosen multipolarity and isospin nature. Then, as a function of time, moments for both isospins and for multipolarities up to L=5 are followed. A new analysis program is included to calculate strength functions and energy weighted sum rules. The ability to specify a mixing parameter in the pairing force is included. This allows a mixed surface-volume pairing to be selected in a way more compatable with QRPA codes for comparison. An updated Makefile is included which makes compilation on Apple silicon computers easier.

Constant-roll inflation with a complex scalar field

We consider inflation with a constant rate of rolling in which a complex scalar field plays the role of inflaton during the inflationary epoch. We implement the inflationary analysis for an accredited angular speed θ̇ which satisfies our dynamical equations. Scalar and tensorial perturbations generated in the framework of constant roll inflation with a complex field are studied. In this respect, we find analytically solutions to the gauge invariant fluctuations, with which an expression for the scalar power spectrum together with its scalar index spectral in this scenario were found. By comparing the obtained results with the observations coming from the cosmic microwave background anisotropies, the constraints on the parameters space of the model and also its predictions are analyzed and discussed.

Analytical solutions for hydrodynamic responses of arrays of floating truncated cylinders using multi-term Galerkin method and its application to a new wave energy converter device

In the context of linear water wave theory, the analytical solutions for the diffraction and radiation of a truncated cylinder array are developed in the presence of ambient incident waves. Each cylinder in the array can oscillate with five degrees of freedom (DOFs), i.e., surge, sway, heave, roll, and pitch. This paper adopts the multi-term Galerkin method to expand the fluid velocity at the interface of different regions into a set of basis functions containing Gegenbauer polynomials, which accurately and efficiently characterizes the cube root singularity of the fluid velocity near the edges of the truncated cylinders. Using the dynamic equilibrium equations, the amplitudes of each DOF of the cylinders in the array are solved. The analytical solution presented in this paper converges rapidly, and high-precision hydrodynamic response results can be obtained using just a few truncated terms (e.g., the upper bounds of m0 = 5 and p0 = 22 can yield results of five-figure accuracy). For the 4-cylinder array, under the same accuracy conditions (the error less than 1%), the computation time of the conventional method developed by Zeng et al. [“Hydrodynamic interactions between waves and cylinder arrays of relative motions composed of truncated floating cylinders with five degrees of freedom,” J. Fluids Struct. 115, 103785 (2022d)] based on the exact algebraic method [Kagemoto and Yue, “Interactions among multiple three-dimensional bodies in water waves: An exact algebraic method,” J. Fluid Mech. 166, 189–209 (1986)] is 3.9 times longer than that of the present method. As the number of cylinders increases, the advantage of the present method in terms of convergence speed becomes more apparent, e.g., for the 16-cylinder array, the conventional solution takes 6.3 times longer than the present solution. To extract wave energy more efficiently, a new 5DOF wave energy converter (WEC) device that can extract energy in 5DOFs is proposed. The present method is adopted to investigate the hydrodynamic performance of the 5DOF WEC arrays. Compared with the traditional 1DOF (heave) WEC, the 5DOF WEC can significantly improve the energy capture performance of arrays, especially in the high-frequency wave region.

Bifurcation analysis and new waveforms to the fractional KFG equation

This study presents novel waveforms and bifurcation analysis for the fractional Klein-Fock-Gordon (KFG) structure, which is widely used in particle and condensed matter physics. To examine the bifurcation, chaos, and sensitivity of the model, we derive the dynamic system equation from the Galilean transformation. We present and explore a diverse range of waveforms, including periodic waves, quasi-periodic waves, bright and dark solitons, kink waves, and anti-kink waves. Graphic diagrams from simulations illustrate the diverse features and existence of these solutions. Nonlinear models can benefit from the potency, brevity, and effectiveness of integration procedures used in contemporary scientific and engineering contexts.

Opto-magnonic reservoir computing coupling nonlinear interfered spin wave and visible light switching

Physical reservoir computing is a promising approach to realize high-performance artificial intelligence systems utilizing physical devices. Recently, it has been experimentally found that nonlinear interfered spin wave multi-detection shows excellent performance for processing nonlinear time-series data due to its outstanding features: nonlinearity, short-term memory, and the ability to map in high dimensional space. However, said performance is considerably inferior to reservoir computing utilizing an optical circuit with a large volume. Herein, we develop reservoir computing with nonlinear interfered spin wave coupled with light switching, namely opto-magnonic reservoir computing. The spin wave was modulated through a crystal field transition that occurred in two different Fe3+ sites of Y3Fe5O12 by visible light switching, and it was found that the spin wave modulated by visible light switching dramatically reduced normalized mean square errors to 4.96 × 10−3, 0.163, and 3.66 × 10−5 for NARMA2, NARMA10, and second-order nonlinear dynamical equation tasks. Said excellent performance results from the strong nonlinearity caused by chaos and large memory capacity induced by reservoir states diversified by visible light switching.

Fluid-structure interaction dynamic analysis of large civil aircraft tank sloshing

To meet the requirements of passengers, the tank volume of large civil aircraft is gradually increasing, which brings certain risks. Under different 0 pertaining conditions during the flight, the liquid in the tank will cause structural failure and affect the aircraft’s safety. Therefore, based on the assumption of an ideal fluid, the smooth particle method (SPH) combined with the finite element method (FEM) is used to establish the coupling dynamic equation between the tank and the liquid. The effects of sloshing impact on the water tank under different filling rates were studied, and the influences of the water wave shape, the center of gravity shift, stress distribution, and deformation of the tank were obtained. The results show that the mass accumulation of water particles occurs in the acceleration stage, the relative center of gravity changes greatly in less water, and the accumulated liquid greatly influences the tank under the action of inertia. The more liquid in the tank is, the more the impact effect on the tank increases. The analysis results provide some reference for the analysis and design of tank anti-sway plates and flight attitude adjustment.

A simple model for evaluating the performance of sparker source with multi-electrode array

Sparker sources have been widely applied in high-resolution seismic explorations. However, to date, there exists no model that can directly predict the electro-acoustic characteristics of a sparker source with a multi-electrode array. In this Letter, we propose an analytical water-resistance model that yields a more accurate loop current. A simplified energy conservation model and the multi-bubble dynamics equations are used to evaluate the electro-acoustic process. Considering the bubble interaction will give a better prediction of multi-bubble dynamics. Regardless of the bubble interaction, the model is also able to obtain the desirable loop current and shockwave. Finally, with the influence of electrode considered, we use the model to evaluate the performance of a 50 × 8 array. The modeling results agree well with the field trials.

One-order closed model of fluctuating particle coagulation term in the Reynolds averaged general dynamic equation for nanoparticles

One-order closed model of fluctuating particle coagulation term in the Reynolds averaged general dynamic equation for nanoparticles

Stability and nonlinear vibration characteristics of cantilevered fluid-conveying pipe with nonlinear energy sink

Considering the midline non-expansion theory and nonlinear coordinate method, this paper mainly investigates the stability and nonlinear vibration characteristics of cantilevered fluid-conveying pipe with energy sink. Based on Hamilton 's variational principle, the dynamic equation of a cantilevered pipe conveying fluid with nonlinear energy sink (NES) under pulsating flow is established. The system equation is processed by Galerkin method, a novel matrix equations of single-degree-of-freedom and multi-degree-of-freedom coupling system is established. The results show that the physical factors in the flow pipe system have a great influence on the critical flow velocity of the whole system, comparing with the case of adding NES. Increasing the proportion of the mass of the fluid will have a greater impact on the real part frequency, thereby increasing the critical velocity of the fluid-conveying pipe system. Addition of nonlinear energy sink can significantly suppress the amplitude and decrease the unstable vibration of the pipe.

Theory of elastic wave propagation in a fluid-saturated multi-porous medium with multi-permeability

This paper establishes the concept of elastic wave propagation in a multi-porous medium with different permeabilities by assuming there are n distinct pore fluid phases. The dynamic equation of motion of elastic wave propagation through this multi-porous medium is derived based on Lagrangian mechanics. In this regard, the generalized form of mass coefficients and then the energy loss due to the fluid phases in terms of dissipation coefficients are presented for low-frequency limits with the help of Darcy’s Law of multi-phases system. The elastic coefficients of the constitutive equation in terms of compliance matrix are identified using a series of Gedanken experiments. Some significant results regarding the compressional and rotational waves in a multi-porosity medium are derived. The validation of the theory has been shown by comparing it with the existing theory of single and double porosity. It is observed that there are ( n + 1 ) compressional waves corresponding to solid and fluid phases, whereas only one rotational wave is associated with the solid phase. The concept of multi-porosity theory can contribute to a deeper understanding of wave behaviour in a porous medium.

Analysis of dynamic wave model for unsteady flow and sediment transport in alluvial rivers

The coupling interactions between flood propagation, sediment transport, and river morphology in alluvial rivers are mathematically described by the high-order dynamic wave model. The coupling capability of currently used dynamic wave models is systematically conducted. The results indicate that the propagation of a dynamic flood wave only depends on the Froude number, but is independent of the coupling of sediment transport and river mobility. Furthermore, based on the continuum hypothesis, the dynamic equations describing the motion of the active bed layer are obtained. A renewed dynamic wave model is established. Four families of asymptotic solutions to the eigenvalues of the renewed four-order hyperbolic system are obtained by means of the singular-perturbation technology. The results demonstrate that the interactions between flood propagation, sediment transport, and riverbed mobility are coupled. Propagation of the main dynamic flood wave and the dynamic sediment wave will be slower with the increasing deposition rate, but will be faster when the erosion intensity is enhanced. These mainly occur in the lower flow regime. In the process of deposition, the second dynamic flood wave and the dynamic bed wave will propagate both upward and downstream. Besides, the dynamic bed wave will propagate downstream and the second dynamic flood wave will only propagate upstream, regardless of the flow regime.

Evolutionary Tripartite Game Model in the Coal Mine Risk-Hazard Double Pre-Control and Management in China

The classification, investigation, and management of the safety risk (namely, risk-hazard double pre-control management mechanism) in coal mines were introduced into a behavioral evolution game to assess the decision-making processes of coal mine workers, regulators, and supervisors. A tripartite game tree and a revenue perception matrix were constructed, and the evolutionary stability strategy (ESS) achieved by the evolutionary system under different conditions was obtained according to the replication dynamic equation (RD). The numerical simulation of the evolution game was conducted in MATLAB, which verified the influence of various parameters on the behaviors adopted by all parties. The results show: (1) When the safety, regulatory, and supervisory costs are high, the average expected value of mine workers, regulators, and supervisors to choose safety behaviors is low, so they adopt an unsafe behavior. By contrast, reducing costs can encourage the adoption of safety behaviors. (2) When the punishment for accident losses caused by unsafe behavior and the lack of regulations and supervision is higher than 50% of the initial state, the actors in the tripartite game are more inclined to avoid risks when facing cost losses in the short term, which can lead them to choose a safety behavior. (3) When the actors in the tripartite game face different accident probabilities and accident loss, with the severity of the accident increasing to 80% of the initial state, mine workers and regulators gradually adopt safety and regulation behaviors, and supervisors quickly adopt supervision methods.

Modal frequency identification using the predictor subspace approach for a space solar power station

The system’s modal frequency parameters are determined by using a technique known as predictor-based subspace identification (PBSID), which is based on the dynamic properties of space solar power stations’ huge size and low frequency. First, the dynamic equation for the space solar power station with an Abacus configuration’s attitude-vibration coupling is developed. Additionally, the PBSID approach is used to build the relevant parameter matrix, and singular value decomposition (SVD) is chosen to evaluate the system’s structural frequency parameters. The right input signals are created via numerical simulation, and the best sensor placement technique yields the associated vibration response signals. The computing results then demonstrate that the modal frequency characteristics of the space solar power station may be successfully identified by the PBSID method, which is based on SVD. Additionally, the findings demonstrate the superior noise immunity capabilities of the PBSID algorithm when compared to the standard modal parameter identification approaches.

Coupled vibration analysis of the spacecraft with the flexible shaft and solar panels assembly

Dynamical characteristics of the spacecraft with flexible components are investigated in this paper. The component consists of a flexible shaft and solar panels, where solar panels are completely fixed on the shaft. A novel power series multiplier polynomial method is proposed to describe the connecting condition between the shaft and solar panels. The deformation and force matching conditions between the one dimensional shaft and two dimensional panels are established, which is the major contribution about the multidimensional combined structure of this study. According to constraining boundary conditions of the shaft and solar panels, the bending-torsion coupled deformation of the component is expressed. The attitude maneuvering of the central platform and the elastic vibration of the component cause the rigid-flexible coupled effect. Then the discrete dynamical equation of the spacecraft is obtained by using the rigid-flexible coupled modal shapes. The correctness of the proposed method is verified by comparing the natural characteristics with that of the finite element model. The relative error of the higher order frequency is not more than 4%. Numerical results show that the degree of the bending angle polynomial should be at least quadratic to ensure the accuracy of the calculation. The proposed power series multiplier polynomial breaks through the barriers that the traditional Lagrange multiplier cannot express the continuous constraint. It is an effective method to fit the constrained boundary by the polynomial rather than by the discrete multipoint method.

A nonlinear low frequency quasi zero stiffness vibration isolator using double-arc flexible beams

There is an increasing demand for integrated small vibration isolators in precision sensing instruments and medical equipment. Therefore, a quasi-zero stiffness (QZS) vibration isolator with double-arc flexible beams (D-AFB) is proposed. The QZS isolator consists of D-AFB units, the base, platform, fixture, guide rail, and linear bearing. The static performance of D-AFB is analyzed using the FEA method, and the QZS condition is obtained. The harmonic balance method (HBM) and the pseudo arc length method (PALM) are used to solve the dynamic equations of the nonlinear system, and the analytical solutions of displacement transmissibility and Force transmissibility are derived. In theory, the initial frequency is 77.6 % lower than that of the equivalent linear system. The QZS characteristic of D-AFB is verified by static experiment, and the low-frequency isolation performance of the QZS isolator is verified by dynamic experiment under constant amplitude and constant acceleration excitation. The D-AFB has a simple structure and can easily satisfy QZS conditions. So the D-AFB can be customized according to load requirements. Multiple vibration isolation loads can be obtained by adjusting the assembly of the D-AFB. The QZS isolator can adapt to load changes within 10 % and has an isolation effect on vibrations above 4 Hz. The idea of designing a QZS isolator with D-AFB as an array unit has a good research prospect and great application value in meeting the requirements of miniaturization and integration.

Dynamic analysis and performance evaluation of inerter fractional nonlinear quasi-zero stiffness isolator on a multi-span bridge under moving load

In this paper we propose a new vibration isolator system, which combines the advantages of a quasi-zero stiffness (QZS) isolator, a damper exhibiting fractional properties and an inerter, to reduce the vibrations of a multi-span continuous beam bridge excited by moving loads. The inerter produces a fictitious mass amplification effect to improve the controller performance and the fractional order takes into account the previous state of the viscoelastic material. After formulating the dynamics equation using beam theory, the amplitude response is determined analytically using the averaging method. The results obtained from the analytical study are validated using the direct numerical simulation method (Newton–Leipnik method). By comparing the isolation performance of the FQZS (fractional quasi-zero stiffness) isolator and the IFQZS (inerter fractional quasi-zero stiffness) isolator, it is shown that the addition of inertance can significantly suppress the tendency of the curve to slope to the right, allowing us to have a wider isolation frequency range on force transmissibility while improving the efficiency of the isolator. One also shows that increasing the fractional parameter contributes to a decrease in the vibration amplitude of the structure, the amplitude of the force transmitted and the area in which unstable solutions appear. However, beyond a certain value of the fractional parameter, we observe an increase in the latter. In order to further extend the study, bifurcation diagram, phase portrait, time history and power spectral density are explored.

A lemma on C 0-semigroups on time scales and approximate controllability of the heat dynamic equation

In this paper, we present a lemma that allows us to characterize a broad class of C 0-semigroups on time scales, which can be applied to prove existence and uniqueness of solutions of systems of partial differential equations where the time domain is a time scale. The result obtained is applied to study the controllability of the heat equation on time scales. The lemma presented in this paper can be seen as a unification of the one proved by H. Leiva in [28], for semigroups in [0,∞).

A multiscale hydro-elastoplastic model for large floating structures in two-dimension

A novel fluid–structural model was presented considering hydro-elastoplastic behavior, which coupled multiple hydro-structural-material scales. A large floating sandwich structure (LFSS) comprising upper and lower high-strength panels and a low-weight core was considered as an illustration. The mesoscale characteristics of materials and elastoplastic parameters of the low-weight perforated components were coupled by utilizing the representative volume element (RVE) method. Through the parameterized relations from RVE analysis, the flexure dynamics model for the floating sandwich structure with an equivalent homogenized core was deduced. With the flexure dynamic equation, yield criterion, and potential flow model, a multiscale hydro-elastoplasticity theoretical model was established, which combined the wave action, hierarchical component, material configuration, and structural behavior. The dynamic responses of the large floating structure under fluid–structure interaction were calculated, and the internal deformation (i.e., core strain) was set as the determining variable for the plastic region. The initially intact floating structure became hinged multi-modules after plastic cracking, and the high-strength layers at the cracking positions behaved as flexible hinges, which was defined as a hydro-elastoplastic process. The elastoplastic state evolutions of the LFSSs with different structural parameters and material configurations were solved for practical optimization. The results indicated that the multiscale coupled calculation model can provide great scientific guidance for designing large floating structures.

The Inverse of Exact Renormalization Group Flows as Statistical Inference.

We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information-theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one-parameter family of probability distributions solving an integro-differential equation derived from Bayes' law. In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation, which we dub Bayesian Diffusion. By identifying the features that define Bayesian Diffusion and mapping them onto the features that define the ERG, we obtain a dictionary outlining how renormalization can be understood as the inverse of statistical inference.