Dynamic Equations Research Articles

A frequency-domain hydroelastic analysis of a membrane-based offshore floating photovoltaic platform in regular waves

This study presents an approach for analyzing the hydroelastic response of membrane-based floating photovoltaic (PV) platforms. The structural deformation of the platform’s main components, including a floater and a membrane, is further described through a comprehensive set of in-plane and out-of-plane modes. This analysis employs potential flow theory and 3D hydroelasticity theory to evaluate the hydrodynamic loads. Additionally, the Morison equation is utilized to express the drag term associated with the floater’s in-plane motion. Addressing the connection between the floater and the membrane is achieved through the Lagrange multiplier method. Ultimately, this study establishes a frequency-domain coupled dynamic equation for the platform. The response results provide modal amplitudes and displacement data for test points, revealing that under low-frequency conditions, the flexible floater and the membrane conform to wave profiles. As the frequency increases, the impact of the floater’s stiffness becomes prominent, resulting in a substantial three-dimensional interaction effect. In addition, this study examines various structural parameters, specifically the membrane pretension, elastic modulus, and the bending stiffness of the floater, to illustrate their influence on the motion and deformation of the platform. This work contributes to a deeper comprehension of membrane-based floating PV systems and their practical applications.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

Redundant Non-Serial Implicit Manipulator Kinematics and Dynamics

Abstract Redundant non-serial manipulators that include a spectrum of parallel and non-parallel heavy load bearing construction and material handling equipment are treated, using foundations of differential geometry. Kinematics of this category of manipulator are defined in manipulator configuration space by algebraic equations in input and output coordinates that cannot be explicitly solved for either as a function of the other. New sets called assembly components of manipulator configuration space are defined that partition the space into maximal, path-connected, disjoint, topological components. All configurations within an assembly component can be connected by one or more continuous paths within that component, but configurations in different assembly components cannot be connected by continuous paths. Forward and inverse kinematically singular configurations are characterized by criteria that partition each assembly component into path-connected, singularity-free assembly components in which equations of kinematics and dynamics are well behaved. It is shown that a generalized inverse velocity-based kinematic formulation that is problematic for serial manipulators is likewise plagued with problems for non-serial implicit manipulators that can be avoided using the methods presented. Singularity-free differentiable manipulator configuration space components are defined and parameterized by both input and operational coordinates, leading to well-posed ordinary differential equations of manipulator dynamics in both input and operational coordinates. Three typical applications and associated model problems are studied throughout the paper to illustrate the methods and results presented.

The Influence of Nonlinear High-Intensity Dynamic Processes on the Standing Wave Precession of a Non-Ideal Hemispherical Resonator.

The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks with large angular velocities and angular accelerations, this paper investigates the standing wave precession of a non-ideal hemispherical resonator under nonlinear high-intensity dynamic conditions. Based on the thin shell theory of elasticity, a dynamic model of a hemispherical resonator is established by using Lagrange's second kind equation. Then, the dynamic model is equivalently transformed into a simple harmonic vibration model of a point mass in two-dimensional space, which is analyzed using a method of averaging that separates the slow variables from the fast variables. The results reveal that taking the nonlinear terms about the square of the angular velocity and the angular acceleration in the dynamic equation into account can weaken the influence of the 4th harmonic component of a mass defect on standing wave drift, and the extent of this weakening effect varies with the dimensions of the mass defects, which is very important for steering the development of the high-precision hemispherical resonator gyroscope.

Breather Transitions and Their Mechanisms of a (2+1)-Dimensional Sine-Gordon Equation and a Modified Boussinesq Equation in Nonlinear Dynamics

Breather Transitions and Their Mechanisms of a (2+1)-Dimensional Sine-Gordon Equation and a Modified Boussinesq Equation in Nonlinear Dynamics

Large eddy simulation of a turbulent channel flow using dynamic Smagorinsky subgrid scale model and differential equation wall model

A large eddy simulation (LES) is conducted in a plane channel flow which is turbulent. For understanding the mechanism of the turbulent motion more efficiently, the present study is an attempt to conduct the LES using a Dynamic Smagorinsky Model (DSM) and a Differential Equation Wall Model (DEWM). DSM is a subgrid-scale model and DEWM is for approximating the near wall layer. The simulation is performed in a domain of 2 π δ × 2 δ × π δwhich is discretized by 32 × 20 × 32grid points where δ is the channel half width. The discretization techniques have been used in the simulation, are the 3rd order low storage R-K method in time and 2nd order finite difference formulation in space. To assess the performance of the LES with DSM and DEWM, the simulation results are compared with direct numerical simulation (DNS) data and LES data using Standard Smagorinsky Model (SSM). Comparing the results in the essential turbulence statistical field it has been found that DSM performs better than SSM in most of the cases and shows better agreement with the DNS results. Flow structures in the turbulent flow field are compared in isosurfaces and contour plots, and found that tube-like vortical structures are randomly distributed over the entire flow field, and the number of the vortical structures are more for the DSM case than that of SSM.

Revised Enskog equation for hard rods

We point out that Percus’s collision integral for one-dimensional hard rods (Percus 1969 Phys. Fluids 12 1560–3) does not preserve the thermal equilibrium state in an external trapping potential. We derive a revised Enskog equation for hard rods and show that it preserves this thermal state exactly. In contrast to recent proposed kinetic equations for dynamics in integrability-breaking traps, both our kinetic equation and its thermal states are explicitly nonlocal in space. Our equation differs from earlier proposals at third order in spatial derivatives and we attribute this discrepancy to the choice of collision integral underlying our approach.

Nonlinear transient response of magneto-electro-elastic cylindrical shells with initial geometric imperfection

Exploring the nonlinear mechanical behaviors of structures under external excitation is significant. This article, for the first time, attempts to demonstrate the transient response of imperfect magneto-electro-elastic (MEE) cylindrical shells under pulse load in thermal environment by time history curves and phase trajectories. Using Love's thin shell theory and Maxwell's equations, expressions for displacement-, electric-, and magnetic- fields are obtained. Combining Hamiltonian principle and Galerkin method, the nonlinear dynamic equations of cylindrical shells are derived, and Runge-Kutta method is employed to solve the whole problem. Subsequently, the transient responses under various parameters including BaTiO3 vol fraction, geometric imperfection, electrical potential, magnetic potential, prestress, viscoelastic foundation, positive phase duration, damping coefficient, maximum blast load, geometrical parameter, temperature variation and various pulse loads are presented in numerical analysis in the forms of time history curves and phase trajectories. Finally, the conclusion advocates that the BaTiO3 vol fraction, geometric imperfection and dimensions of cylindrical shells have significant impacts on the transient response.

The Dynamical Equations of the Restricted Three-Body Problem with Poynting-Robertson Drag Force and Variable Masses

The restricted three-body problem (R3BP) is a formulation which defines the motion of a passively gravitating test particle having infinitesimal mass and moving in the gravitational environment of two bodies, called primaries. The R3BP is still an exciting and active research field that has been getting attention of scientists and astronomers because of its applications in dynamics of the solar and stellar systems, lunar theory, and artificial satellites. The equations of motion are usually the starting point in the investigations of the dynamical predictions of the infinitesimal mass. Therefore, in this paper, we examine the derivations of the dynamical equations of the R3BP with Poynting-Robertson (P-R) Drag force and variable masses. In this model formulation, both primaries are assumed to vary their masses under the combined Mestschersky law (CML) and they move in the frame of the GyldenMestschersky equation (GME). Further, the bigger primary is assumed to be emitting radiation force, which is a component of the radiation pressure and the P-R drag. The non- autonomous dynamical equations of the model are derived and converted into the autonomized equations with constant coefficients using the Mestschersky transformation (MT), the CML, the particular solutions of the GMP, and a transformation for the time dependent velocity of light. We observed that the P-R drag of the bigger primary depends on the mass parameter, radiation pressure, velocity of light and the mass variation constant . The derived systems of equations with variable and constant coefficients can be used to model the long-term motion of satellites and planets in binary systems.

The inertia of anger and sadness among adolescents and adults: The role of self-efficacy in regulating negative emotions

Emotional inertia (i.e., the resistance to change of emotional states) is an index of regulatory deficit linked to psychological maladjustment. Using ecological momentary assessment, we explored the role of Self-efficacy in Regulating Negative Affect (SRN), as a baseline measure, to buffer sadness and anger inertia, measured three times a day over 28 days in two samples from the UK: (1) adults ( n = 166 adults; Mage = 35.71, SD = 12.96; 73% women) and (2) adolescents ( n = 82 adolescents; Mage 14.88, SD = 1.34; 72% girls). Dynamic Structural Equation Modeling showed that both sadness and anger had significant levels of inertia. Importantly, the inertia of sadness was weakened by high levels of SRN among both adults and adolescents ( β = −.211, 95% CI [−.303, −.112]; and β = −.485, 95% CI [−.707, −.162], respectively). No buffering effect of SRN was found for the inertia of anger. These findings suggest the importance of strengthening adults’ and adolescents’ SRN to manage their sadness in everyday life.

Experimental and numerical study on the blast performance of the corrugated double steel plate concrete composite wallboard under blast loads

The corrugated double steel plate concrete composite wallboard (CDSCW) exhibits superior axial compressive load-bearing capacity, lateral flexural stiffness, impact resistance, and seismic performance compared to the traditional reinforced concrete wallboard and plane double steel plate concrete composite wallboard (PDSCW). Therefore, it has great potential application in offshore engineering and military engineering. This study designs and fabricates two types of CDSCW specimens. Firstly, a comparative analysis is conducted to examine the damage patterns and dynamic responses of the two specimens under near-field explosion experiments. Secondly, the damage mechanisms and explosion response of CDSCW and PDSCW subjected to close-in explosions are numerically investigated by using ANSYS/LS-DYNA, and the results are then compared with experimental findings. Parameter analysis is performed to assess the influence of concrete thickness, steel plate thickness, and explosive charge on the blast resistance of CDSCWs. Furthermore, a nonlinear resistance equation and an equivalent single degree of freedom (ESDOF) theoretical model for simply supported beams is established to predict the dynamic response of CDSCWs under near-blast loads. This theoretical model considers the constitutive model of bilinear materials and the effect of plastic hinges. The reliability of the proposed theoretical model is verified by comparing the residual deflection of CDSCWs obtained from explosion tests with validated numerical simulation results. The results demonstrate that the CDSCWs, with the same concrete and component dimensions (length, width), exhibit greater flexural stiffness and superior energy dissipation capacity subjected to close-in explosion. Moreover, their blast resistance significantly surpasses that of PDSCWs. In particular, an increase in corrugation depth effectively improves the blast resistance of CDSCWs. The dynamic response equations, based on the established elastic-plastic model and primarily considering bending deformation of the components, precisely predict the dynamic response of simply supported CDSCWs under near-blast loads. consequently, these findings can provide a robust foundation for further research and the design of blast-resistant structures.

New oscillation criteria of nonlinear second order delay dynamic equations with sublinear neutral term

New oscillation criteria of nonlinear second order delay dynamic equations with sublinear neutral term

The motion of Brownian particles suspended in a non-uniform fluid flow

The effect of the type of fluid flow velocity profile on the motion of a Brownian particle in a circular tube has been studied using a Monte Carlo technique to simulate particle trajectories. Three types of fluid flow were studied: uniform (UF), parabolic (PF), and an initial uniform flow which evolves and may eventually attain the parabolic velocity profile, i.e. transient flow (TF). For UF and PF, radial and axial particle diffusion were simultaneously considered in some cases; for TF, where fluid dynamics equations had to be solved in addition to the Monte Carlo simulations, axial diffusion was neglected for fluid and particles, so that calculations had to be restricted to tube aspect ratios (radius/length) smaller than 0.1, a common scenario in most practical aerosol applications. A first series of simulations were performed to determine the overall particle penetration through the tube. For fixed tube geometry and particle diffusion coefficient, penetration in TF lied between those in PF (highest) and UF (lowest), in such a manner that, for a given value of the diffusion coefficient, the larger the degree of flow development (i.e., the smaller the values of the tube aspect ratio and the Reynolds number), the larger the penetration. These findings are coherent with those found in a former investigation dealing with the particle residence time in the tube. In a second series of simulation runs, calculations were done for selected initial locations of the particle within the tube entrance cross section, to examine the effect that the proximity of the particle starting position to the tube wall or to the tube axis has on variables such as penetration, mean first hitting time and length, mean first exit time, and mean axial velocity of lost and survived particles. When the fluid flow is not uniform but varies from place to place, the mean particle axial velocity is larger than that of the fluid. This counterintuitive fundamental result allows interpretation of the trends observed in penetration and residence time.

Weakly nonlinear models of stochastic wave propagation in two-layer hydrodynamic systems

The paper discusses three-dimensional models of the propagation of stochastic internal waves in hydrodynamic systems: ’half-space - half-space’, ’half-space - layer with rigid lid’, and ’layer with solid bottom - layer with rigid lid’. In constructing the models, the layers are considered to be ideal fluids separated by a contact surface. The main objective of the modeling is to obtain a dynamic equation for the stochastic amplitude of surface waves. A comparative analysis of the obtained results has been conducted. In order to control the contribution of nonlinear terms, a dimensionless non-numerical parameter has been introduced. The models are distinguished by boundary conditions that determine the general form of solutions. As a result, a dynamic equation for the stochastic amplitude of internal waves has been derived. After ensemble averaging of the amplitudes, the dynamic equation is formulated in integral form using Fourier-Stieltjes integrals. The dynamic equation reveals two-wave and three-wave interactions, as well as the contribution of dispersion to wave dynamics. An investigation of the boundary case of the transition of internal waves in the ’half-space - half-space’ system to surface waves in the absence of an upper liquid layer confirms the validity of the results.

Finite element model updating and damage detection using strain-based modal data in the Bayesian framework

This paper proposes a novel methodology for Bayesian model updating and damage detection of a structural system using strain-based modal data. The strain-based modal data are assumed to consist of the posterior statistics of natural frequencies and strain mode shapes corresponding to measured strains from a classically damped system. The dynamic strain-based equation of the motion is formulated utilizing the energy functional of the structural system and the strain displacement relation. The state variables in the considered strain-based formulation consist of the strains and the elemental rigid body displacements. The methodology is developed by incorporating strain-based formulation into the Bayesian framework for Finite Element (FE) model updating. Besides, additional uncertain parameters in the form of system strain-based modal parameters are introduced in the eigenvalue equation to avoid mode-matching. The model reduction technique is utilized to eliminate the rigid body displacements and the strains that are not measured. Metropolis-Hastings (MH) within Gibbs sampling is proposed to simulate samples from the posterior Probability Density Function (PDF) of the model parameters of the FE model. The effectiveness of the proposed methodology is demonstrated using simulated examples. An experimental study is also conducted to validate the proposed methodology.

Simultaneous thermal zoning and demand control ventilation

Heating, Ventilation, and Air Conditioning systems play a crucial role in controlling indoor air conditions, including temperature, humidity, and CO₂ concentration, to ensure human comfort and safety. Thermal zoning and demand-controlled ventilation have demonstrated enhancements in comfort and energy efficiency. This study aims to develop a mathematical model for a Heating, Ventilation, and Air Conditioning system employing an estimated state-feedback control algorithm to optimize indoor comfort and energy savings while minimizing sensor requirements. The model encompasses dynamic equations governing CO₂ concentration and temperature in a five-room building. Temperature regulation is achieved by adjusting the airflow from a cooling unit with dampers, while CO₂ levels are managed by controlling the proportion of fresh air intake. To showcase the advantages of the proposed control approach, comparisons were made with alternative methods based on response performance, energy consumption, and sensor requirements. The estimated state-feedback control outperformed other approaches, requiring only one temperature and one CO₂ sensor at the mixed return. Additional occupancy sensors in each room are not necessary if an Extended Kalman filter is utilized. This technique exhibits scalability, adaptable to varying output variables and room configurations, and holds promise for broader implementation in the HVAC industry. By optimizing energy consumption and maintaining indoor air quality, this approach aligns with established sustainability metrics, promoting environmental responsibility. Compliance with health and safety audit standards ensures the fulfillment of social targets, while adherence to regulations and laws ensures governance targets are met.

Permeability estimation for deformable porous media with convolutional neural network

Purpose Accurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis. Design/methodology/approach A convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN. Findings The proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R2) is 0.93 for the validation set, and the R2 for the test set A and test set B are 0.93 and 0.94, respectively. Originality/value This study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications.

Dynamic equation for evaporative cooling of trapped atoms in microgravity

Dynamic equation for evaporative cooling of trapped atoms in microgravity

Parameter optimization of vibration control system for adjacent building structures based on negative stiffness inerter damper

Building structures are subjected to strong earthquakes, which result in lateral collisions between them. Such collisions often cause severe structural damage and exacerbate the seismic hazard risk of building structures during earthquake events. This paper discusses the application of vibration control devices based on negative stiffness inerter damper in single-story adjacent building structures. The dynamic equations of the vibration control system containing different types of negative stiffness inerter damper under seismic excitation are established as a unified model. The H2 norm theory and Monte Carlo pattern search method are used to optimize the design parameters to improve the vibration control performance of the system, and the dynamic characteristics of the system are investigated. The results demonstrate that attaching negative stiffness inerter damper to adjacent building structures can effectively improve the overall seismic capacity reserve of the building and reduce the risk of collision of adjacent building structures; improve the robustness and stability of the system, and better reduce the displacement response of the building structure under seismic excitation. In addition, the potential of NSID-based vibration control devices to convert seismic energy into usable electricity has been investigated.

Implementation of additional spectral wave field exchanges in a three-dimensional wave–current coupled WAVEWATCH-III (version 6.07) and CROCO (version 1.2) configuration: assessment of their implications for macro-tidal coastal hydrodynamics

Abstract. An advanced coupling between a three-dimensional ocean circulation model (CROCO) and a spectral wave model (WAVEWATCH-III) is presented to better represent the interactions of macro-tidal currents with winds and waves. In the previous implementation of the coupled interface between these two models, some of the wave-induced terms in the ocean dynamic equations were computed from their monochromatic approximations (e.g. Stokes drift, Bernoulli head, near-bottom wave orbital velocity, wave-to-ocean energy flux). In the present study, the exchanges of these fields computed from the spectral wave model are implemented and evaluated. A set of numerical experiments for a coastal configuration of the macro-tidal circulation off the Bay of Somme (France) is designed. The impact of the spectral versus monochromatic computation of wave-induced terms has a notable effect on the macro-tidal hydrodynamics, particularly in scenarios involving storm waves and opposing winds to tidal flows. This effect manifests as a reduction in the wave-induced deceleration of the vertical profile of tidal currents. The new implementation provides current magnitudes closer to measurements than those predicted using monochromatic formulations, particularly at the free surface. The spectral-surface Stokes drift and the near-bottom wave orbital velocity are found to be the spectral fields with the most impact, respectively increasing advection towards the free surface and shifting the profile close to the seabed. In the particular case of the Bay of Somme, the approximation of these spectral terms with their monochromatic counterparts ultimately results in an underestimation of ocean surface currents. Our model developments thus provide a better description of the competing effects of tides, winds, and waves on the circulation off macro-tidal bays, with implications for the study of air–sea interactions and sediment transport processes.