Command filtered integrated estimation guidance and control for strapdown missiles with circular field of view

In this paper,an integrated estimation guidance and control(IEGC)system is designed based on the command filtered backstepping approach for circular field-of-view(FOV)strapdown missiles.The threedimensional integrated estimation guidance and control nonlinear model with limited actuator deflection angle is established considering the seeker's FOV constraint.The boundary time-varying integral barrier Lyapunov function(IBLF)is employed in backstepping design to constrain the body line-of-sight(BLOS)in IEGC system to fit a circular FOV.Then,the nonlinear adaptive controller is designed to estimate the changing aerodynamic parameters.The generalized extended state observer(GESO)is designed to estimate the acceleration of the maneuvering targets and the unmatched time-varying disturbances for improving tracking accuracy.Furthermore,the command filters are used to solve the"differential expansion"problem during the backstepping design.The Lyapunov theory is used to prove the stability of the overall closed-loop IEGC system.Finally,the simulation results validate the integrated system's effectiveness,achieving high accuracy strikes against maneuvering targets.

The quantum spectra analysis of the circular billiards in wells

We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier- transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classlcal method provides a bridge between quantum and classical mechanics.

ANALYSIS OF THE DYNAMIC STABILITY OF ELECTRICAL GRADED PIEZOELECTRIC CIRCULAR CYLINDRICAL SHELLS

A system of Mathieu–Hill equations have been obtained for the dynamic stability analysis of electrical graded piezoelectric circular cylindrical shells subjected to the combined loading of periodic axial compression and radial pressure and electric ?eld. Bolotin’s method is then employed to obtain the dynamic instability regions. It is revealed that the piezoelectric e?ect, the piezoelectric graded e?ect and the electric ?eld only have minor e?ect on the unstable region. In contrast, the geometric parameters, the rigidity of constituent materials and the external loading play a dominant role in determining the unstable region.

Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

The natural dynamic characteristics of a circular cylindrical tube made of three-directional(3 D)functional graded material(FGM)based on the Timoshenko beam theory are investigated.Hamilton’s principle is utilized to derive the novel motion equations of the tube,considering the interactions among the longitudinal,transverse,and rotation deformations.By dint of the differential quadrature method(DQM),the governing equations are discretized to conduct the analysis of natural dynamic characteristics.The Ritz method,in conjunction with the finite element method(FEM),is introduced to verify the present results.It is found that the asymmetric modes in the tube are controlled by the 3 D FGM,which exhibit more complicated shapes compared with the unidirectional(1 D)and bi-directional(2 D)FGM cases.Numerical examples illustrate the effects of the axial,radial,and circumferential FGM indexes as well as the supported edges on the natural dynamic characteristics in detail.It is notable that the obtained results are beneficial for accurate design of smart structures composed from multi-directional FGM.

Investigation of the Free Vibrations of Radial Functionally Graded Circular Cylindrical Beams Based on Differential Quadrature Method

In the current research,an effective differential quadrature method(DQM)has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient.Based on the high-order theory of transverse vibration of circular cross-section beams,lateral displacement equation was reconstructed neglecting circumferential shear stress.Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue.Then,differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation into a set of algebraic equation eigenvalue problems.Natural frequencies of the free vibrations of cylindrical beams with circular cross-sections were calculated at one time,and corresponding modal functions were solved together.The obtained numerical results indicated that the natural frequencies of functionally graded(FG)circular cylindrical beams obtained using differential quadrature method agreed with the results reported in related literatures.In addition,influences of varying gradient parameters on the modal shapes of circular cylindrical beams were found to be strongly consistent with previous studies.Numerical results further validated the feasibility and accuracy of the developed differential quadrature method in solving the transverse vibration of FG circular cross-section beams.

Thermal buckling and postbuckling of FGM circular plates with in-plane elastic restraints

Based on von Karman＇s plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material （FGM） circular plates with in- plane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail.

Statics of FGM circular plate with magneto-electro-elastic coupling:axisymmetric solutions and their relations with those for corresponding rectangular beam

This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic（MEE） materials under tension and bending.The analysis is directly based on the three-dimensional governing equations for magnetoelectro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately（in the Saint Venant sense）. The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material（FGM） with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic（FGMEE） circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.

CHAOTIC MOTION OF AN ELASTIC CIRCULAR PLATE

The chaotic motion of a harmonically forced circular plate is studied in the paper. The virtual displacement principle is used to derive the dynamic equation of motion, with the effect of large deflection of plate taken into account. By means of Garlerkin approach and Melnikov function method, the critical condition for chaotic motion is obtained. A demonstrative example is discussed through the Poincare mapping, phase portrait and time history.

AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.

Zeroes of the Bergman Kernels on Some New Hartogs Domains

We obtain the Bergman kernel for a new type of Hartogs domain.The corresponding LU Qi-Keng's problem is considered.

DYNAMIC BEHAVIORS OF CONDUCTIVE CIRCULAR PLATE IN TIME-VARYING MAGNETIC FIELDS

In this study, we proposed an analytical solution for eddy currents as well as electromagnetic forces of a conductive circular plate in a time varying magnetic field. Specifically, an analytical series solution for eddy currents in a circular plate subjected to an axisymmetrie time varying magnetic field has been proposed based on the T-method that has been widely used in the eddy current analysis of conductive and superconductive structures. Accordingly, the dynamic response, the dynamic instability and the magnetic damping of a circular plate in a transverse transient magnetic field as well as a stationary in-plane magnetic field have also been obtained. The analytical series solution proposed in this work as well as the subsequent numerical analysis not only confirmed the emergence of dynamic instability of a circular plate in a strong transverse magnetic field, but also demonstrated the existence of magneto-damping of a circular conductive plate in an in-plane magnetic field. The method developed in this paper provides a potential new possible way by which the analysis of the electromagnetic coupling problems of conductive structures can be simplified.

Pure bending of simply supported circular plate of transversely isotropic functionally graded material

This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).

Biological roles and potential clinical values of circular RNAs in gastrointestinal malignancies

Circular RNAs(circ RNAs),a class of endogenous RNA molecules,are produced by alternative splicing of precursor RNA and are covalently linked at the 5′and 3′ends.Recent studies have revealed that dysregulated circ RNAs are closely related to the occurrence and progression of gastrointestinal malignancies.Accumulating evidence indicates that circ RNAs,including circ PVT1,circ LARP4,circ-SFMBT2,cir-ITCH,circ RNA_100782,circ_100395,circ-DONSON,hsa_circ_0001368,circ NRIP1,circ FAT1(e2),circ CCDC66,circ SMARCA5,circ-ZNF652,and circ_0030235 play important roles in the proliferation,differentiation,invasion,and metastasis of cancer cells through a variety of mechanisms,such as acting as micro RNA sponges,interacting with RNA-binding proteins,regulating gene transcription and alternative splicing,and being translated into proteins.With the characteristics of high abundance,high stability,extensive functions,and certain tissue-,time-and diseasespecific expressions,circ RNAs are expected to provide novel perspectives for the diagnoses and treatments of gastrointestinal malignancies.

Analysis of steady heat conduction for 3D axisymmetric functionally graded circular plate

The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary distribution functions of the thickness. A temperature function that satisfies thermal boundary conditions at the edges and the variable separation method were used to reduce equation governing the steady state heat conduction to an ordinary differential equation （ODE） in the thickness coordinate which was solved analytically. Next, resulting variable coefficients ODE due to arbitrary distribution of material properties along thickness coordinate was also solved by the Peano-Baker series. Some numerical examples were given to demonstrate the accuracy, efficiency of the present model, mad to investigate the influence of different distributions of material properties on the temperature field. The numerical results confirm that the influence of different material distributions, gradient indices and thickness of plate to temperature field in plate can not be ignored.

Cubic Spline Solutions of Nonlinear Bending and Buckling of Circular Plates with Arbitrarily Variable Thickness

The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.

AN ANALYTICAL METHOD FOR A MIXED BOUNDARY VALUE PROBLEM OF CIRCULAR PLATES UNDER ARBITRARY LATERAL LOADS

In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.

Advancements in our understanding of circular and long non-coding RNAs in spinal cord injury

Spinal cord injury(SCI),either from trauma or degenerative changes,can res ult in severe disability and impaired quality of life.Understanding the cellular processes and molecular mechanisms that underlie SCI is imperative to identifying molecular targets for potential therapy.Recent studies have shown that non-coding RNAs,including both long non-coding RNAs(lncRNAs)and circular RNAs(circRNAs),regulate various cellular processes in SCI.In this review,we will describe the changes in lncRNA and circRNA expression that occur after SCI and how these changes may be related to SCI progression.Current evidence for the roles of lncRNAs and circRNAs in neuronal cell death and glial cell activation will also be reviewed.Finally,the possibility that lncRNAs and circRNAs are novel modulato rs of SCI pathogenesis will be discussed.

Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion

The problem of a transversely isotropic functionally graded material （FGM） plate welded with a circular inclusion is considered. The analysis starts with the general- ized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional （3D） general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.

Bending and free vibrational analysis of bi-directional functionally graded beams with circular cross-section

The bending and free vibrational behaviors of functionally graded(FG)cylindrical beams with radially and axially varying material inhomogeneities are investigated.Based on a high-order cylindrical beam model,where the shear deformation and rotary inertia are both considered,the two coupled governing differential motion equations for the deflection and rotation are established.The analytical bending solutions for various boundary conditions are derived.In the vibrational analysis of FG cylindrical beams,the two governing equations are firstly changed to a single equation by means of an auxiliary function,and then the vibration mode is expanded into shifted Chebyshev polynomials.Numerical examples are given to investigate the effects of the material gradient indices on the deflections,the stress distributions,and the eigenfrequencies of the cylindrical beams,respectively.By comparing the obtained numerical results with those obtained by the three-dimensional(3D)elasticity theory and the Timoshenko beam theory,the effectiveness of the present approach is verified.

Identification of the Potential Function of circRNA in Hypertrophic Cardiomyopathy Based on Mutual RNA-RNA and RNA-RBP Relationships Shown by Microarray Data

The pathogenesis of hypertrophic cardiomyopathy(HCM)is very complicated,particularly regarding the role of circular RNA(circRNA).This research pays special attention to the relationships of the circRNA-mediated network,including RNA-RNA relationships and RNA-RNA binding protein(RNA-RBP)relationships.We use the parameter framework technology proposed in this paper to screen differentially expressed circRNA,messenger RNA(mRNA),and microRNA(miRNA)from the expression profile of samples related to HCM.And 31 pairs of circRNA and mRNA relationship pairs were extracted,combined with the miRNA targeting database;145 miRNA-mRNA relationship pairs were extracted;268 circRNA-mRNA-miRNA triads were established through the common mRNA in the 2 types of relationship pairs.Thus,268 circRNA-miRNA regulatory relationships were deduced and 30 circRNARBP relationship pairs were analyzed at the protein level.On this basis,a circRNA-mediated regulatory network corresponding to the two levels of RNA-RNA and RNA-RBP was established.And then the roles of circRNA in HCM were analyzed through circRNA-mRNA,circRNA-miRNA,and circRNA-RBP,and the possible role in disease development mas inferred.