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 search-free near-field source localization method with exact signal model

Most of the near-field source localization methods are developed with the approximated signal model,because the phases of the received near-field signal are highly non-linear.Nevertheless,the approximated signal model based methods suffer from model mismatch and performance degradation while the exact signal model based estimation methods usually involve parameter searching or multiple decomposition procedures.In this paper,a search-free near-field source localization method is proposed with the exact signal model.Firstly,the approximative estimates of the direction of arrival(DOA)and range are obtained by using the approximated signal model based method through parameter separation and polynomial rooting operations.Then,the approximative estimates are corrected with the exact signal model according to the exact expressions of phase difference in near-field observations.The proposed method avoids spectral searching and parameter pairing and has enhanced estimation performance.Numerical simulations are provided to demonstrate the effectiveness of the proposed method.

Recursion-transform method and potential formulae of the m×n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

Stability analysis of helical rod based on exact Cosserat model

Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff＇s kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff＇s theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler＇s angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov＇s stability of the helical equilibrium is discussed in static category. Euler＇s critical values of axial force and torque are obtained. Lyapunov＇s and Euler＇s stability conditions in the space domain are the necessary conditions of Lyapunov＇s stability of the helical rod in the time domain.

Dynamics analysis of planar armored cable motion in deep-sea ROV system

The armored cable used in a deep-sea remotely operated vehicle(ROV) may undergo large displacement motion when subjected to dynamic actions of ship heave motion and ocean current. A novel geometrically exact finite element model for two-dimensional dynamic analysis of armored cable is presented. This model accounts for the geometric nonlinearities of large displacement of the armored cable, and effects of axial load and bending stiffness. The governing equations are derived by consistent linearization and finite element discretization of the total weak form of the armored cable system, and solved by the Newmark time integration method. To make the solution procedure avoid falling into the local extreme points, a simple adaptive stepping strategy is proposed. The presented model is validated via actual measured data. Results for dynamic configurations, motion and tension of both ends of the armored cable, and resonance-zone are presented for two numerical cases, including the dynamic analysis under the case of only ship heave motion and the case of joint action of ship heave motion and ocean current. The dynamics analysis can provide important reference for the design or product selection of the armored cable in a deep-sea ROV system so as to improve the safety of its marine operation under the sea state of 4 or above.

Hierarchical closed form solutions for plates bent by localized transverse loadings

3D and 2D closed form plate models are here applied to static analysis of simply supported square isotropic plates. 2D theories are hierarchically classified on the basis of the accuracy of the displacements and stresses obtained by comparison to the 3D exact results that could be assumed by the reader as benchmark for further analyses. Attention is mainly paid on localized loading conditions, that is, piecewise constant load. Also bi-sinusoidal and uniformly distributed loadings are taken into account. All of those configurations are considered in order to investigate the behavior of the 2D models in the case of continu- ous/uncontinuous, centric or off-centric loading conditions. The ratio between the side length a and the plate thickness h has been assumed as analysis parameter. Higher order 2D models yield accurate results for any considered load condition in the case of moderately thick plates, a/h=10. In the case of thick plates, a/h=5, and continuous/uncontinuous centric loading conditions high accuracy is also obtained. For the considered off-centric load condition and thick plates good results are provided for some output quantities. A better solution could be achieved by simply increasing the polynomial approximation order of the axiomatic 2D displacement field.

Effects of electron correlation on superconductivity in the Hatsugai-Kohmoto model

Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm.We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space.The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory.The self-consistent equation for the pair potential is derived and solved.Somewhat contrary to expectation,a weak attractive U comparable to the pair potential can destroy the superconductivity,whereas for weak to intermediate repulsive U,the pair potential can be enhanced.The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation.We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors,in contrast to the uncorrelated BCS limit.

Adaptive Dual Wavelet Threshold Denoising Function Combined with Allan Variance for Tuning FOG-SINS Filter

Allan variance(AV)stochastic process identification method for inertial sensors has successfully combined the wavelet transform denoising scheme.However,the latter usually employs a traditional hard threshold or soft threshold that presents some mathematical problems.An adaptive dual threshold for discrete wavelet transform(DWT)denoising function overcomes the disadvantages of traditional approaches.Assume that two thresholds for noise and signal and special fuzzy evaluation function for the signal with range between the two thresholds assure continuity and overcome previous difficulties.On the basis of AV,an application for strap-down inertial navigation system(SINS)stochastic model extraction assures more efficient tuning of the augmented 21-state improved exact modeling Kalman filter(IEMKF)states.The experimental results show that the proposed algorithm is superior in denoising performance.Furthermore,the improved filter estimation of navigation solution is better than that of conventional Kalman filter(CKF).

Exact solution of U(5)–O(6) transitional description in interacting boson model with two-particle and two-hole configuration mixing

The exact solution of the U(5)-O(6)transitional description in the interacting boson model with twoparticle and two-hole configuration mixing is derived based on the Bethe ansatz approach.The Bethe ansatz equations are provided to determine the model’s eigenstates and corresponding eigen-energies.N=2 and N=4 cases are considered as examples to demonstrate the solution features.As an example of the application,some low-lying level energies and B(E2)ratios of 108Cd are fitted and compared with the corresponding experimental data.

Exact expression for decoherence factor in the time-dependent generalized Cini model

The present letter finds the complete set of exact solutions of the time-dependent generalized Cini model by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation and, based on this, the general explicit expression for the decoherence factor is therefore obtained. This study provides us with a useful method to consider the geometric phase and topological properties in the time-dependent quantum decoherence process.