Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

On dynamics of elastic rod based on exact Cosserat model

The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.

A method to Estimate Dynamic Responses of VLFS Based on Multi-Floating-Module Model Connected by Elastic Hinges

Based on the elastic foundation beam theory and the multi-floating-module hydrodynamic theory,a novel method is proposed to estimate the dynamic responses of VLFS(Very Large Floating Structure).In still water,a VLFS can be simplified as an elastic foundation beam model or a multi-floating-module model connected by elastic hinges.According to equivalent displacement of the two models in static analysis,the problem of rotation stiffness of elastic hinges can be solved.Then,based on the potential flow theory,the dynamic responding analysis of multi-floatingmodule model under wave loads can be computed in ANSYS-AQWA software.By assembling the time domain analysis results of each module,the dynamic responses of the VLFS can be obtained.Validation of the method is conducted through a series of comparison calculations,which mainly includes a continuous structure and a three-part structure connected by hinges in regular waves.The results of this paper method show a satisfactory agreement with the experiment and calculation data given in relative references.

On the Elastic Vibration Model for High Length-Diameter Ratio Rocket with Attitude Control System

An elastic vibration model for high length diameter ratio spinning rocket with attitude control system which can be used for trajectory simulation is established. The basic theory of elastic dynamics and vibration dynamics were both used to set up the elastic vibration model of rocket body. In order to study the problem more conveniently, the rocket's body was simplified to be an even beam with two free ends. The model was validated by simulation results and the test data.

Dynamic Elastic Modulus of Cement Paste at Early Age based on Nondestructive Test and Multiscale Prediction Model

This paper introduced a nondestructive testing method to evaluate the dynamic elastic modulus of cement paste. Moreover, the effect of water-cement ratio and conventional admixtures on the dynamic elastic modulus of cement paste was investigated, in which three kinds of admixtures were taken into account including viscosity modifying admixture （VMA）, silica.fume （SF）, and shrinkage-reducing admixture （SRA）. The experimental results indicate that the dynamic elastic modulus of cement paste increases with decreasing water-cement ratio. The addition of SF increases the dynamic elastic modulus, however, the overdosage of VMA causes its reduction. SRA reduces the dynamic elastic modulus at early age without affecting it in later period. Finally, a multiscale micromechanics approach coupled with a hydration model CEMHYD3D and percolation theory is utilized to predict the elastic modulus of cement paste, and the predictive results by the model are in accordance with the experimental data.

Elastic Constants of Superconducting MgB2 from Molecular Dynamics Simulations with Shell Model

The elastic constants of superconducting MgB2 are calculated using a molecular dynamics method (MD)with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperature, and bulk modulus of MgB2 are obtained. Meanwhile, the dependence of the bulk modulus B, the lattice parameters a and c, and the unit cell volume V on the applied pressure are presented. It is demonstrated that the method introduced here can well reproduce the experimental results with a reasonable accuracy.

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre- ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion- deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.

Dynamic analysis of new type elastic screen surface with multi degree of freedom and experimental validation

A feasible method was proposed to improve the vibration intensity of screen surface via application of a new type elastic screen surface with multi degree of freedom(NTESSMDF). In the NTESSMDF, the primary robs were coupled to the main screen structure with ends embedded into the elastomers, and the secondary robs were attached to adjacent two primary robs with elastic bands. The dynamic model of vibrating screen with NTESSMDF was established based on Lagrange's equation and the equivalent stiffnesses of the elastomer and elastic band were calculated. According to numerical simulation using the 4th order Runge-Kutta method, the vibration intensity of screen surface can be enhanced substantially with an averaged acceleration amplitude increasing ratio of 72.36%. The primary robs and secondary robs vibrate inversely in steady state, which would result in the friability of materials and avoid stoppage. The experimental results validate the dynamic characteristics with acceleration amplitude rising by62.93% on average, which demonstrates the feasibility of NTESSMDF.

Transverse Vibration Analysis of Single-Walled Carbon Nanotubes Embedded in an Elastic Medium Using Bernoulli-Fourier Method

Based on the Timoshenko beam theory and Bernoulli-Fourier method, a single-elastic beam model is developed for transverse vibrations of single-walled carbon nanotubes under additional axial load, which includes the effects of the elastic medium around them. Explicit expressions are derived for the natural frequencies and transversal responses of simply supported single-walled carbon nanotubes. The influence of addition axial load and the properties of elastic medium on the vibrations are discussed. The results showed that the effects of addition axial load on the lower natural frequencies of single-walled carbon nanotubes are sensitive to the lower vibration modes and the stiff elastic medium. The lower natural frequencies depend on the axial load;they become smaller with increasing axial load and vary with the vibration modes. In addition, except for the first mode, the effects of the axial load on the stiff elastic medium are considerably greater than those on the flexible one. However, the constants of the elastic medium have little effect on the first mode. The critical axial buckling stress and strain for simply-supported single-walled carbon nanotubes are also obtained.

Dynamic analysis of elastic screen surface with multiple attached substructures and experimental validation

A feasible method to improve the reliability and processing efficiency of large vibrating screen via the application of an elastic screen surface with multiple attached substructures(ESSMAS) was proposed.In the ESSMAS,every screen rod,with ends embedded into elastomer,is coupled to the main screen structure in a relatively flexible manner.The theoretical analysis was conducted,which consists of establishing dynamic model promoted from the fuzzy structure theory as well as calculating for the equivalent stiffness of each attached structure.According to the numerical simulation using the NEWMARK-β integration method,this assembling pattern significantly leads to the screen surface/rod having larger vibration intensity than that of the corresponding position on screen structure,which specifically,with an averaged acceleration amplitude increasing ratio of 11.37% in theoretical analysis and 20.27% in experimental test.The experimental results,within a tolerant error,also confirm the established model and demonstrate the feasibility of ESSMAS.

Dynamic behaviors of water contained in calcium-silicate-hydrate gel at different temperatures studied by quasi-elastic neutron scattering spectroscopy

The dynamic behaviors of water contained in calcium-silicate-hydrate（C-S-H） gel with different water content values from 10%to 30%（by weight）,are studied by using an empirical diffusion model（EDM） to analyze the experimental data of quasi-elastic neutron scattering（QENS） spectra at measured temperatures ranging from 230 K to 280 K.In the study,the experimental QENS spectra with the whole Q-range are considered.Several important parameters including the bound/immobile water elastic coefficient A,the bound water index BWI,the Lorentzian with a half-width at half-maximum（HWHM） Γ;（Q） and Γ;（Q）,the self-diffusion coefficients D;and D;of water molecules,the average residence times τ;and τ;,and the proton mean squared displacement（MSD）(u;) are obtained.The results show that the QENS spectra can be fitted very well not only for small Q（≤1 A;） but also for large Q.The bound/immobile water fraction in a C-S-H gel sample can be shown by the fitted BWI.The distinction between bound/immobile and mobile water,which includes confined water and ultra-confined water,can be seen by the fitted MSD.All the MSD tend to be the smallest value below 0.25 A;（the MSD of bound/immobile water） as the Q increases to 1.9 A;no matter what the temperature and water content are.Furthermore,by the abrupt changes of the fitted values of D;,τ;,and Γ;（Q）,a crossover temperature at 250 K,namely the liquid-to-crystal-like transition temperature,can be identified for confined water in large gel pores（LGPs） and/or small gel pores（SGPs） contained in the C-S-H gel sample with 30% water content.

DYNAMIC BUCKLING MODE OF AN ELASTIC BAR

The conception of buckling relative initial imperfection is presented in this paper. According to Bornoulli-Euler beam equation, the dynamic buckling mode of an elastic bar under the homogeneous boundary conditions can be derived by applying the preferred mode analytical method. As an example, the dynamic buckling mode of an elastic bar clamped at both ends is discussed.

Vertical vibrations of elastic foundation resting on saturated half-space

This paper is mainly concerned with the dynamic response of an elastic foundation of finite height bounded to the surface of a saturated half-space. The foundation is subjected to time-harmonic vertical loadings. First, the transform solutions for the governing equations of the saturated media are obtained. Then, based on the assumption that the contact between the foundation and the half-space is fully relaxed and the halfspace is completely pervious or impervious, this dynamic mixed boundary-value problem can lead to dual integral equations, which can be further reduced to the Predhohn integral equations of the second kind and solved by numerical procedures. In the numerical extortples, the dynamic colnpliances, displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system. In most of the cases, the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.

DYNAMIC RESPONSE OF SHAPE MEMORY ALLOY SYSTEM AND ITS VIBRATION CONTROL

A hysteric model is represented to describe the dependence of restoring force on deformation of pseudoelastic SMA.The dynamic response of the system is investigated by means of mathematical models.The result shows that this kind of vibration absorbing system can suppress vibration with large amplitude effectively.Furthermore,the vibration absorbing system can work in optimum state by adjusting temperature and using piezoelectric sensors and actuators.

First-principles calculations on the elastic and thermodynamic properties of NbN

The elastic and thermodynamic properties of NbN at high pressures and high temperatures are investigated by the plane-wave pseudopotential density functional theory （DFT）. The generalized gradient approximation （GGA） with the Perdew-Burke Ernzerhof （PBE） method is used to describe the exchange-correlation energy in the present work. The calculated equilibrium lattice constant a0, bulk modulus B0, and the pressure derivative of bulk modulus B~ of NbN with rocksalt structure are in good agreement with numerous experimental and theoretical data. The elastic properties over a range of pressures from 0 to 80.4 GPa are obtained. Isotropic wave velocities and anisotropic elasticity of NbN are studied in detail. It is indicated that NbN is highly anisotropic in both longitudinal and shear-wave velocities. According to the quasi-harmonic Debye model, in which the phononic effect is considered, the relations of （V - Vo）/Vo to the temperature and the pressure, and the relations of the heat capacity Cv and the thermal expansion coefficient α to temperature are discussed in a pressure range from 0 to 80.4 GPa and a temperature range from 0 to 2500 K. At low temperature, Cv is proportional to T3 and tends to the Dulong Petit limit at higher temperature. We predict that the thermal expansion coefficient α of NbN is about 4.20 × 10-6/K at 300 K and 0 GPa.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

Prediction of high-speed train induced ground vibration based on train-track-ground system model

The development of analysis on train-induced ground vibration is briefly summarized. A train-track- ground integrated dynamic model is introduced in the paper to predict the ground vibration induced by high-speed trains. Representative dynamic responses of the train-track-ground system predicted by the model are presented. Some major results measured from two field tests on the ground vibration induced by two high-speed trains are reported. Numerical prediction with the proposed train-track-ground model is validated by the high-speed train running experiments. Research results show that the wheel/rail dynamic interaction caused by track irregularities has a significant influence on the ground acceleration and little influence on the ground displacement. The main frequencies of the ground vibration induced by high-speed trains are usually below 80 Hz. Compared with the ballasted track, the ballastless track structure can produce much larger train-induced ground vibration at frequencies above 40 Hz. The vertical ground vibration is much larger than the lateral and longitudinal components.