Dynamic Equations Of Motion Research Articles

Fluid Structure Interaction Using Modal Superposition and Lagrangian CFD

This study investigates the impact of fluid loads on the elastic deformation and dynamic response of linear structures. A weakly coupled modal solver is presented, which involves the solution of a dynamic equation of motion with external loads. The mode superposition method is used to find the dynamic response, utilizing predetermined mode shapes and natural frequencies associated with the structure. These essential parameters are pre-calculated and provided as input for the simulation. Integration of the weakly coupled modal solver is accomplished with the Lagrangian Differencing Dynamics (LDD) method. This method can directly use surface mesh as boundary conditions, so it is much more convenient than other meshless CFD methods. It employs Lagrangian finite differences, utilizing a strong formulation of the Navier–Stokes equations to model an incompressible free-surface flow. The elastic deformation of the structure, induced by fluid forces obtained from the flow solver, is computed within the modal coupling algorithm through direct numerical integration. Subsequently, this deformation is introduced into the flow solver to account for changes in geometry, resulting in updated flow pressure and velocity fields. The flow particles and vertices of the structure are advected in Lagrangian coordinates, resulting in Lagrangian–Lagrangian coupling in spaces with weak or explicit coupling in time. The two-way coupling between fluid and structure is successfully validated through various FSI benchmark cases. The efficiency of the LDD method is highlighted as it operates directly on surface meshes, streamlining the simulation setup. Direct coupling of structural deformation eliminates the conventional step of mapping fluid results onto the structural mesh and vice versa.

A dynamic study of a bead sliding on a wire in fractal space with the non-perturbative technique

Drawing on the principles of fractal properties and nonlinear vibration analysis, this paper delves into the investigation of a moving bead on a vertically rotated parabola. The dynamical nonlinear equation of motion, incorporating fractal derivatives, transforms traditional derivatives within continuous space. Consequently, the equation of motion takes the form of the Duffing-Van der Pol oscillator. Utilizing a non-perturbative approach, the nonlinear oscillator is systematically transformed into a linear one, boasting an exact solution. The analytical solution yields two valid formulas governing the frequency-amplitude relationships. Numerical solutions affirm that these proposed formulas offer highly satisfactory approximations to the analytical solution. Leveraging fractal properties through Galerkin’s method, the paper successfully determines the fractalness parameter of the medium, shedding light on the intricate dynamics of the system.

Genetically Tuned Linear Quadratic Regulator for Trajectory Tracking of a Quadrotor

In this paper, a linear quadratic regulator (LQR) controller operating according to the genetically tuned inner-outer loop structure is proposed for trajectory tracking of a quadrotor. Setting the parameters of a linear controller operating according to the inner-outer loop structure is a matter that requires profound expertise. Optimization algorithms are used to cope with the solution of this problem. First, the dynamic equations of motion of the quadrotor are obtained and modelled in state-space form. The LQR controller, which will operate according to the inner-outer loop structure in the MATLAB/Simulink environment, has been developed separately for 6 degrees of freedom (DOF) of the quadrotor. Since adjusting these parameters will take a long time, a genetic algorithm has been used at this point. The LQR controller with optimized coefficients and a proposed LQR controller-based study in the literature are evaluated according to their success in following the reference trajectory and their responses to specific control inputs. According to the results obtained, it was observed that the genetically adjusted LQR controller produced more successful outcomes.

Orbital motion of gold heterodimer driven by optical force of circularly polarized light and reactive drag of medium

Abstract This theoretical study explores the two-dimensional orbital motion of an optically bound heterodimer consisting of two gold nanoparticles (NPs) of different sizes, driven by circularly polarized (CP) light. Although a CP light possesses only spin angular momentum without orbital angular momentum, it can still induce orbital revolution in the plasmonic heterodimer. This phenomenon arises from the interaction between the optical force and torque generated by the CP light and the reactive drag force and torque from the surrounding medium. We calculate the optical forces acting on each NP by analyzing the Maxwell stress tensor at their surfaces, and we account for the reactive drag force using Stokes’ law. These forces are used to simulate the trajectories of the NPs through dynamic equations of motion. Our results demonstrate that, regardless of the initial conditions of the two NPs, they will become optically bound together, exhibiting rigid-body translation and rotation. Notably, the center of mass of the heterodimer undergoes an orbital revolution around a fixed point eventually. The CP light-manipulated heterodimer behaves like a boomerang, acting as a spinning rotor on a circular path. The heterodimer's orbital radius and direction of revolution are influenced by the size disparity between the two NPs. Additionally, each NP experiences spin motion, with the spin direction determined by the handedness of the CP light. The optically bound gold heterodimer functions as a light-driven microrotor, with potential applications in microfluidic channels. These findings offer valuable insights into the optomechanical manipulation of non-monodisperse NP clusters using CP light.

Coalescence-Induced Droplet Jumping for Electro-Thermal Sensing.

Jumping droplet condensation, whereby microdroplets (ca. 1-100 μm) coalescing on suitably designed superhydrophobic surfaces jump away from the surface, has recently been shown to have a 10× heat transfer enhancement compared to filmwise condensing surfaces. However, accurate measurements of the condensation heat flux remain a challenge due to the need for low supersaturations (<1.1) to avoid flooding. The low corresponding heat fluxes (<5 W/cm2) can result in temperature noise that exceeds the resolution of the measurement devices. Furthermore, difficulties in electro-thermal measurements such as droplet and surface electrostatic charge arise in applications where direct access to the condensing surface, such as in isolated chambers and small integrated devices, is not possible. Here, we present an optical technique that can determine the experimental electro-thermal parameters of the jumping droplet condensation process with high fidelity through the analysis of jumping droplet trajectories. To measure the heat flux, we observed the experimental trajectories of condensate droplets on superhydrophobic nanostructures and simultaneously matched them in space and time with simulated trajectories using the droplet dynamic equations of motion. Two independent approaches yielded mean heat fluxes of approximately 0.13 W/cm2 with standard deviations ranging from 0.047 to 0.095 W/cm2, a 79% reduction in error when compared with classical energy balance-based heat flux measurements. In addition, we analyzed the trajectories of electrostatically interacting droplets during flight and fitted the simulated and experimental results to achieve spatial and temporal agreement. The effect of image charges on a jumping droplet as it approaches the surface was analyzed, and the observed acceleration has been numerically quantified. Our work presents a sensing methodology of electro-thermal parameters governing jumping droplet condensation.

Ensemble fluid simulations on quantum computers

We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to its linearity, such an equation is in principle more amenable to quantum computing than the dynamic equations of fluid motion. After suitable marginalization and associated closure, the Liouville approach is shown to require several hundreds of logical qubits, hence calling for a major thrust in current noise correction and mitigation techniques.

Local control of magnetic microbubble behavior by magnetic field and pulsed ultrasound

The localization of magnetic microbubbles (MMBs) to a target site has been shown to be essential to their efficacy in therapeutic applications such as targeted drug delivery and gene therapy. In this work, the MMBs’ dynamic equations of vibration, horizontal and vertical motion in a fluid-filled tube, subject to a magneto-acoustic complex field, are established by Lagrange method. The responses and capture efficiency under three ultrasonic pulses waveform in a magnetic field are numerically analyzed. The regulation effects of the external field are observed by experiments. The results show that the transport behavior is influenced by bubble size, original position, liquid flow rate, tube diameter, parameters of acoustic and magnetic field. For the same acoustic parameters, square wave pulse can make stronger vibrate compared with cosine wave and sawtooth wave, which pushes MMBs closer to the magnet. In addition, high frequency and large amplitude pulse are benefit to translation, and increasing the cycle number in a single pulse can also promote translation. In practical applications, variable parameters such as bubble speed and magnet length can be used to improve the capture efficiency. The observations of high-speed camera are consistent with the prediction of theoretical model, which indicates the model is mostly correct.

Influence of the Manipulator Configuration on Vibration Effects

Abstract Vibration analysis of industrial robots is one of the key issues in the context of robotisation of machining processes. Low-frequency vibrations result from flexibility in manipulator joints. Within the scope of the article, a model of a two-link robot manipulator was built. Dynamic equations of motion were formulated to study the influence of the robot arm configuration on vibration effects. Based on numerical simulations, the frequency spectrum of vibrations of the robot’s links was determined, and tests were carried out in a number of configurations, obtaining a map of resonant frequencies depending on the configuration of the manipulator. Experimental studies were then carried out, which confirmed the conclusions from the simulation studies. The results obtained confirm that the positioning of the manipulator’s links has a significant effect on vibration effects. Tests conducted using a vision system with a motion amplification application made it easier to interpret the results. The formulated mathematical model of the manipulator generates results that coincide with the results of experimental studies.

Quasi discreteness analysis of a 2-dimensional Heisenberg ferromagnetic spin system with biquadratic interactions

The dynamical theory of soliton excitations in two-dimensional ferromagnets is studied by introducing a Hamiltonian that includes biquadratic interaction along with uniaxial anisotropy. To obtain a dynamical equation of motion, we use the Dyson-Maleev transformation and the coherent state ansatz. We obtain a Nonlinear Schrdinger equation by applying the multiple-scale and quasi-discreteness methods. For the more general nonintegrable case, we perform a multiple scale perturbation analysis to determine the discreteness effect on the soliton excitations. Finally, we examine modulational instability (MI) under the influence of small perturbations.

Reduced-order model of geometrically nonlinear flexible structures for fluid–structure interaction applications

This paper deals with the numerical computation, via a reduced order models (ROM), of the vibrations of geometrically nonlinear structures triggered by the aeroelastic coupling with a fluid flow. The formulation of the ROM proposed in this paper is based on the projection on a basis of reduced dimension enhanced with dual modes. An explicit expression of the projected nonlinear forces is computed in a non-intrusive way based on the Implicit Condensation method. The resulting ROM is an improvement of the classical ICE method since the effects of membrane stretching are taken into account in the resolution of the dynamic equation of motion. Such a ROM aims to be adapted to follower aerodynamic unsteady loads. The construction of the ROM is first detailed and validated under several load cases on a Euler–Bernoulli beam with von Kármán hypothesis. Then a fluid–structure partitioned coupling on a two-dimensional example involving vortex-induced vibrations is considered to demonstrate the capability of such ROM to replace a nonlinear FE solver. In this paper, the limitations of the ICE method are highlighted in the examples treated, while the ROM proposed overcomes such limitations and captures accurately the dynamics.

Mathematical modelling of the dynamic response of an implantable enhanced capacitive glaucoma pressure sensor

Glaucoma as an eye disease influences the optic nerve, resulting in progressive vision loss and, thus, blindness. For this disease, the most important risk factor is high intraocular pressure. Therefore, it is important to accurately measure the intraocular pressure. The present work aimes to present a mathematical description of a capacitive pressure sensor based on a Micro-Electro-Mechanical-Systems (MEMS) to measure intraocular pressure (IOP). The relatively high working bias voltage of MEMS capacitive pressure sensors restricts their potential applications as implantable sensors. Hence, Polydimethylsiloxane (PDMS) is employed as a porous elastomeric substance between the deformable and fixed electrodes of the capacitor. With a low young modulus and a higher dielectric constant, it reduces the sensor's working bias voltage. The PDMS's permittivity and young modulus are a function of the porosity volume fraction based on displacement in terms of a power law with fractional power constant. The dynamic equation of the microplate's transversal motion is used in the developed model, taking mid-plane stre-tching into account along with the generated force owing to the PDMS film squeezing. To decompose the governing nonlinear equation, a weak formulation is used with appropriate basis functions, thus integrating the attained ordinary differential equations over time. The sensor response to static pressure and step-wise alteration of the applied pressure is examined by dynamic and static analysis. The results of pull-in voltage reveal that using the PDMS as a dielectric causes a considerable reduction. Additionally, the effect of the PDMS elasticity on the capacitance and displacement was assessed along with the effects of the geometrical parameters on the sensor response.

Sound radiation of a vibrating circular plate set in a hemispherical enclosure

This study rigorously addresses the Neumann–Robin problem of sound radiation from a vibrating flexible disk embedded into a hemispherical enclosure. The enclosure is acoustically soft on its inside surface and hard on its outside surface. The method of superimposed solutions, expressed in terms of Dini series and spherical harmonics, has been applied for this purpose. The presented solution is applicable to any vibration velocity profile on the radiator, with an elastically supported thin plate excited asymmetrically used as an example. The results presented here can be valuable for modeling vibroacoustic responses of various speakers, sensors, and microphones with edges either clamped to the enclosure or nearly free. Achieving this involves modifying the values of the boundary stiffness for resisting transverse displacement and the rotation of the plate’s edge. Additionally, when applying these results to model the responses of alarm or signaling transducers, high-amplitude responses are expected for selected resonant frequencies. In such cases, the boundary stiffness values can be set to ensure multiple strong and wide resonant maxima in the frequency characteristics. In addition, the results presented in this study include solving the dynamic equation of motion for the plate or rigid piston with external excitation. This equation is coupled with the wave equation inside and outside the hemispherical enclosure, allowing the inclusion of the enclosure’s effect on the plate-enclosure system’s responses. This approach can be useful for modeling and improving the acoustic responses of spherical speakers. In such cases, the boundary stiffness values should be relatively small to emulate a soft suspension of the plate. The impedance of the enclosure’s internal surface can be arbitrarily selected, ranging from acoustically hard to acoustically soft. In this study, the impedance of mineral wool has been applied. Numerical analysis is presented for frequencies below 4kHz, with errors smaller than 0.2%. The results have been validated using the finite element method.

Study on the Dynamic Stability and Spectral Characteristics of a Toppling Dangerous Rock Mass under Seismic Excitation

To evaluate the dynamic stability of dangerous rock masses under seismic excitation more reasonably, a mass viscoelasticity model was adopted to simulate the two main controlling surfaces of a toppling dangerous rock mass. Based on the principles of structural dynamics, a dynamic response analysis model and motion equations were established for toppling dangerous rock masses. The Newmark-β method was utilized to establish a calculation method for the dynamic stability coefficient of a toppling dangerous rock mass. This method was applied to the WY2 dangerous rock mass developed in a steep cliff zone in Luoyi Village, and the dynamic stability coefficient time history was calculated. Subsequently, the acceleration response signals of the dangerous rock mass in different directions were analyzed using wavelet packet transform. The results show that the sum of the energy proportions of the first to third frequency bands in the n1 and s2 directions exceeded 95%. This suggests that the n1 and s2 directions of the WY2 dangerous rock mass suffered the initial damage under bidirectional seismic actions. Finally, the marginal spectra variations of the acceleration response signals in different directions were analyzed based on the HHT. The results show that the seismic energy in the n1 and s2 directions of the dangerous rock mass was found to be the most significant under seismic loading, indicating that the rock mass experienced the most severe damage along these two directions. This reveals that the failure mode of the dangerous rock mass is inclined toppling, consistent with the results of wavelet packet analysis.

Design and optimization of roof-top fire water tanks as compliant deep tank dampers-inerter for seismic protection of multi-storeyed buildings

Water tanks are installed on the roofs of high-rise buildings for services and to fight fire outbreaks. These tanks are often considered unsuitable for design as tuned liquid dampers (TLDs) and have higher depth ratios than that required in conventional TLDs due to practical constraints in dimensioning the tank as per the tuning requirement. The present work aims at alleviating these hindrances and utilizing deep water storage tanks as effective passive damping devices for the host building. In this paper, a water storage tank for firefighting, situated on the roof of a building, is designed as a compliant deep tank damper inerter (CDTDI) in controlling the response of the host building subjected to seismic excitations. The tank is flexibly connected to the building through spring and damping elements to act as a compliant damper system. Further, the tuning effect, mass, and damping enhancement potential of an inerter element are employed to improve the volumetric efficiency of the compliant damper system. Two example buildings, 10- and 20-storey, are taken up and modeled as multi-degree-of-freedom (MDOF) systems whose masses are lumped at storey levels. The coupled dynamic equations of motion of the CDTDI-MDOF structural system are formed and solved in the time domain using the Newmark-β method. An external excitation-dependent, multi-objective Grey Wolf optimization is performed to estimate the optimum CDTDI parameters by subjecting the buildings to 100 recorded seismic ground excitations. The average values of the peak roof displacement, the maximum inter-storey drift ratio, and the peak floor acceleration are considered objective functions of the optimization. The results reveal the proficiency of the CDTDI in controlling the multiple modes of the structure. Further, the optimally designed CDTDI provides significant damping and stability to the structure, which is evident from the energy plots.

Optimal mode movement of the robot manipulator on an elastic base according to the criterion of the mean square value of the acceleration of the drive torque

Previous studies of the optimization of the manipulator motion mode on an elastic base based on the criteria of the rms value of the drive torque and the rate of change of the rms value of the drive torque established that the use of optimal manipulator motion modes, which are created on the basis of higher derivatives of the characteristics of the change of the drive torque, allow to obtain more smooth movements of the boom system of the manipulator, thereby reducing its oscillations on the elastic support. At the same time, the obtained optimal modes of movement didn't completely eliminate the boom system oscillations during the change of departure. By observing the oscillations of the elastic link of the manipulator, the quality of the obtained optimal modes of movement was evaluate and the presence of residual oscillations was shown.&#x0D; This work considers the possibility of optimizing the manipulator's motion mode based on the criterion of the mean square value of the acceleration of the drive torque change. For this purpose, the second derivative of the driving torque function of the manipulator boom system drive was determined first. Such a criterion for optimizing the motion mode is an integral functional, the minimization of which is carry out by the methods of variational calculus. The regularity of the change of the driving torque it was find from the dynamic equation of motion.&#x0D; The search for the optimal motion mode of the manipulator realized through the solution of the Poisson boundary nonlinear differential equation of the fourth order.&#x0D; The results of the conducted research made it possible to clarify much better the nature of the vibrations of the manipulator boom system and, as a result, to develop a drive control system that allows the realization of the obtained optimal mode of movement.

Thermoelastic free vibration analysis of functionally graded conical shell based on trigonometric higher-order shear deformation theory

The fundamental frequency of a rotating cantilevered porous functionally graded (FG) twisted conical shell with varying thickness along the longitudinal direction is calculated using a trigonometric higher-order shear deformation theory under thermal loading. Finite element method is employed for this purpose. The shell is discretized using eight-noded isoparametric shell elements with seven degrees of freedom per node. Using a simple power law across the transverse direction, the temperature-dependent material properties of the FG shell are determined. The nonlinear temperature distribution across the thickness direction is calculated using the one-dimensional Fourier heat conduction equation. The dynamic equation of motion is derived using Lagrange's equation. Finally, a parametric investigation of the effects of taper ratio, porosity, pretwist angle, temperature, and rotational speed on the fundamental frequency of the porous FG rotating conical shell is performed. It is also discussed how such characteristics affect mode shapes.

Experimental analysis of a planing monohull model during forward acceleration: part II – evaluation of an indirect method for applying thrust angle in the experiments

ABSTRACT Most towing tank model tests conducted on planing hulls are not performed under self-propulsion conditions, and it is often not feasible to directly apply towing force at the corresponding point of action and along the thrust of the full-scale vessel. Therefore, it is essential to establish a well-defined method for accurately applying the thrust line in bare hull model tests using alternative loading solutions, such as CG shift, and understand how any deviation affects the model’s running attitude and performance. This article presents an analysis of the dynamic equilibrium equations of motion for the model, considering various variables that can be used to adjust the thrust line in towing tank tests. The proposed formalism can aid in determining the external loading requirements in resistance tests. Finally, the article discusses the challenges and provides an error estimation for a simplified method of applying a constant thrust angle in the accelerated tests.

Dynamic Responses of Train-Symmetry-Bridge System Considering Concrete Creep and the Creep-Induced Track Irregularity

This work considers the influence of concrete creep on track irregularities and establishes the dynamic motion equation of the train-track-bridge coupling system. The track irregularity is obtained by superposition of the initial geometric irregularity and additional geometric irregularity of the steel rail caused by creep. When high-speed railway trains pass through bridges; the vertical acceleration and vertical displacement of continuous beam bridges are related to the train’s operating speed, and the influence of creep camber is relatively small. At the same time, considering the randomness of track irregularities, the dynamic responses of the train track bridge coupling system under the action of random track irregularities are analyzed, and the dynamic responses of trains at different operating speeds are obtained. The deterministic and uncertain dynamic responses of the train track bridge system were compared and analyzed to verify the accuracy of the Karhunen Loéve expansion (KLE)-Point estimate method (PEM) calculation results. The results indicate that the random characteristics of track irregularities have a significant impact on train dynamic response. Based on the random system vibration analysis and considering the safety and comfort indicators of high-speed railway trains, the creep deformation limit of a continuous beam bridge with a length of 48 m + 80 m + 48 m is obtained to be 19 mm. This is the first time that the dynamic responses of train-symmetry-bridge system are calculated by considering concrete creep and the creep-induced track irregularity, which has certain significance for understanding the dynamics of train -bridge system. In addition, the proposed creep threshold is also of great significance to ensure the safety of traveling.

A Comparative Analysis of the Response-Tracking Techniques in Aerospace Dynamic Systems Using Modal Participation Factors

Mechanical structural systems are subject to multiple dynamic disturbances during service. While several possible scenarios can be examined to determine their design loading conditions, only a relatively small set of such scenarios is considered critical. Therefore, only such particular deterministic set of critical load cases is commonly employed for the structural design and optimization. Nevertheless, during the design and optimization stages, the mass and stiffness distributions of such assemblies vary, and, in consequence, their dynamic response also varies. Thus, it is important to consider the variations in the dynamic loading conditions during the design-and-optimization cycles. This paper studies the modal participation factors at length and proposes an alternative to the current point-wise treatment of the dynamic equations of motion of flexible bodies during design optimization. First, the most relevant-to-structural-dynamics definitions available in the literature are reviewed in depth. Second, the analysis of those definitions that have the potential to be adopted as point-wise constraint equations during structural optimization is extended. Finally, a proof of concept is presented to demonstrate the usability of each definition, followed by a case study in which the potential advantages of the proposed extended analysis are shown.

Vibration response of viscoelastic nanobeams including cutouts under moving load

This manuscript presents a mathematical model and numerical solution to predict vibration responses of nonlocal strain gradient (NLS) perforated viscoelastic nanobeam under dynamic moving loads. The microstructure and size length scales are considered in the frame of NLS theory. The viscoelastic damping of the structure is considered by linear Kelvin Voigt viscoelastic model. Timoshenko and Euler Bernoulli beam theories are developed to consider both thin and thick structure response. The moving load is portrayed by point load and harmonic type. The dynamic equations of motion incorporating viscoelasticity and size dependency effects is derived by using Hamilton principle. A differential quadrature method (DQM) with Chebyshev–Gauss–Lobatto formula is used to discretize the space domain and solve the model numerically. The obtained results are validated and compared with available literature. Numerical studies are conducted to show the influence of the material viscosity parameter, perforation parameters, shear deformation effect, nonlocal strain gradient, moving load velocity, and beams slenderness ratio on the dynamic behavior of viscoelastic perforated nanobeams under moving load. The material viscosity parameter can effectively control the magnitude and stability of the magnification factor profiles. Higher filling ratios result in larger values of the dynamic magnification factor, whereas larger numbers of hole rows lead to smaller values. The proposed procedure is supportive in the analysis and design of perforated viscoelastic NEMS structures under moving load.