Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect

Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work.With the reservation of the axial nonlinear strain,there are more coupling terms for axial and transverse deformations.The discretized dynamic governing equations are obtained by using the finite element method and Lagrange’s equations of the second kind.Time responses are conducted to compare the proposed model with other previous models.The stretching deformation due to rotating motion is observed and calculated by special formulations under dynamic equilibrium.The stretching deformation and the change of the associated equilibrium position are taken into account to analyze the free vibration and frequency response of the rotating beams.Analytical and numerical comparisons show that the proposed model can provide reliable results,while the previous models may lead to imprecise results,especially in high-speed conditions.

Novel Method for Spatial Angle Measurement Based on Rotating Planar Laser Beams

Spatial angle measurement, especially the measurement of horizontal and vertical angle, is a basic method used for industrial large-scale coordinate measurement. As main equipments in use, both theodolites and laser trackers can provide very high accuracy for spatial angle measurement. However, their industrial applications are limited by low level of automation and poor parallelism. For the purpose of improving measurement efficiency, a lot of studies have been conducted and several alternative methods have been proposed. Unfortunately, all these means are either low precision or too expensive. In this paper, a novel method of spatial angle measurement based on two rotating planar laser beams is proposed and demonstrated. Photoelectric receivers placed on measured points are used to receive the rotating planner laser signals transmitted by laser transmitters. The scanning time intervals of laser planes were measured, and then measured point＇s horizontal/vertical angles can be calculated. Laser plane＇s angle parameters are utilized to establish the abstract geometric model of transmitter. Calculating formulas of receiver＇s horizontal/vertical angles have been derived. Measurement equations＇ solvability conditions and judgment method of imaginary solutions are also presented after analyzing. Proposed method for spatial angle measurement is experimentally verified through a platform consisting of one laser transmitter and one optical receiver. The transmitters used in new method are only responsible for providing rotating light plane signals carrying angle information. Receivers automatically measure scanning time of laser planes and upload data to the workstation to calculate horizontal angle and vertical angle. Simultaneous measurement of multiple receivers can be realized since there is no human intervention in measurement process .Spatial angle measurement result indicates that the repeatable accuracy of new method is better than 10＂. Proposed method can improve measurement＇s automation degree and speed while ensuring measurement accuracy.

Modeling and Free Vibration Behavior of Rotating Composite Thin-walled Closed-section Beams with SMA Fibers

Smart structure with active materials embedded in a rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with piezoelectric actuation. The free vibration of the rotating composite thin-walled beams with shape memory alloy（SMA） fiber actuation is studied. SMA fiber actuators are embedded into the walls of the composite beam. The equations of motion are derived based on Hamilton＇s principle and the asymptotically correct constitutive relation of single-cell cross-section accounting for SMA fiber actuation. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin＇s method. The formulation for free vibration analysis includes anisotropy, pitch and precone angle, centrifugal force and SMA actuation effect. Numerical results of natural frequency are obtained for two configuration composite beams. It is shown that natural frequencies of the composite thin-walled beam decrease as SMA fiber volume and initial strain increase and the decrease in natural frequency becomes more significant as SMA fiber volume increases. The actuation performance of SMA fibers is found to be closely related to the rotational speeds and ply-angle. In addition, the effect of the pitch angle appears to be more significant for the lower-bending mode ones. Finally, in all cases, the precone angle appears to have marginal effect on free vibration frequencies. The developed model can be capable of describing natural vibration behaviors of rotating composite thin-walled beam with active SMA fiber actuation. The present work extends the previous analysis done for modeling passive rotating composite thin-walled beam.

Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method

The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.

A node-based smoothed point interpolation method for dynamic analysis of rotating flexible beams

We proposed a mesh-free method, the called node-based smoothed point interpolation method(NS-PIM),for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence of the displacement functions are further weakened. In static problems, the beams with three types of boundary conditions are analyzed, and the results are compared with the exact solution, which shows the effectiveness of this method and can provide an upper bound solution for the deflection.This means that the NS-PIM makes the system soften. The NS-PIM is then further extended for solving a rigid-flexible coupled system dynamics problem, considering a rotating flexible cantilever beam. In this case, the rotating flexible cantilever beam considers not only the transverse deformations,but also the longitudinal deformations. The rigid-flexible coupled dynamic equations of the system are derived via employing Lagrange’s equations of the second type. Simulation results of the NS-PIM are compared with those obtained using finite element method(FEM) and assumed mode method. It is found that compared with FEM, the NS-PIM has anti-ill solving ability under the same calculation conditions.

Flutter analysis of rotating beams with elastic restraints

The aeroelastic stability of rotating beams with elastic restraints is investigated.The coupled bending-torsional Euler-Bernoulli beam and Timoshenko beam models are adopted for the structural modeling.The Greenberg aerodynamic model is used to describe the unsteady aerodynamic forces.The additional centrifugal stiffness effect and elastic boundary conditions are considered in the form of potential energy.A modified Fourier series method is used to assume the displacement field function and solve the governing equation.The convergence and accuracy of the method are verified by comparison of numerical results.Then,the flutter analysis of the rotating beam structure is carried out,and the critical rotational velocity of the flutter is predicted.The results show that the elastic boundary reduces the critical flutter velocity of the rotating beam,and the elastic range of torsional spring is larger than the elastic range of linear spring.

Propagation of rotating elliptical Gaussian beams from right-handed material to left-handed material

By applying the ABCD matrix method, we report the propagating properties of the rotating elliptical Gaussian beams（REGBs） from the right-handed material（RHM） to the left-handed material（LHM）. Based on the propagation equation, we obtain the intensity distributions of the REGBs during the propagation. It is found that the rotating direction of the REGBs is opposite in the RHM and the LHM, and the rotation angles tend to be π /2 as the propagation distance is long enough.Then we analyze the relationship between the refractive index and the rotating velocity. Furthermore, the energy flow and the angular momentum（AM） of the REGBs which can rotate are also obtained.

MODELING AND BIFURCATION ANALYSIS OF THE CENTRE RIGID-BODY MOUNTED ON AN EXTERNAL TIMOSHENKO BEAM

For the system of the centre rigid_body mounted on an external cantilever beam, the equilibrium solution of the steadily rotating beam is stable if the effect of its shearing stress (i.e. the beam belongs to the Euler_Bernoulli type) is not considered. But for the deep beam, it is necessary to consider the effect of the shearing stress (i.e. the beam belongs to the Timoshenko type). In this case, the tension buckling of the equilibrium solution of the steadily rotating beam may occur. In the present work, using the general Hamilton Variation Principle, a nonlinear dynamic model of the rigid_flexible system with a centre rigid_body mounted on an external Timoshenko beam is established. The bifurcation regular of the steadily rotating Timoshenko beam is investigated by using numerical methods. Furthermore, the critical rotating velocity is also obtained.

Wave propagation analysis of rotating thermoelastically-actuated nanobeams based on nonlocal strain gradient theory

This paper is concerned with the wave propagation behavior of rotating functionally graded（FG）temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform,linear and nonlinear temperature distributions across the thickness are investigated.Thermo-elastic properties of FG beam change gradually according to the Mori–Tanaka distribution model in the spatial coordinate.The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function.The governing equations are derived by Hamilton’s principle as a function of axial force due to centrifugal stiffening and displacement.The solution of these equations is provided employing a Galerkin-based approach which has the potential to capture various boundary conditions.By applying an analytical solution and solving an eigenvalue problem,the dispersion relations of rotating FG nanobeam are obtained.Numerical results illustrate that various parameters including temperature change,angular velocity,nonlocality parameter,wave number and gradient index have significant effects on the wave dispersion characteristics of the nanobeam under study.The outcome of this study can provide beneficial information for the next-generation research and the exact design of nano-machines including nanoscale molecular bearings,nanogears,etc.

The Computer Analysis of the Excimer Laser Beam Intensity Uniformization by Rotational Lens Array

The excimer laser has important applications in many fields. Because of its non-uniform intensity distribution there are some limits in applications. This paper introduces rotational lens array to improve intensity distributions. The intensity variation is reduced to 1 percent by computer simulation.

On-chip silicon polarization and mode handling devices

Mode-and polarization-division multiplexing are new promising options to increase the transmission capacity of optical communications.On-chip silicon polarization and mode handling devices are key components in integrated mode-and polarization-division multi-plexed photonic circuits.In this paper,we review our recent progresses on silicon-based polarization beam splitters,polarization splitters and rotators,mode（de）multiplexers,and mode and polarization selective switches.Silicon polarization beam splitters and rotators are demonstrated with high extinction ratio,compact footprint and high fabrication tolerance.For on-chip mode multiplexing,we introduce a low loss and fabrication tolerant three-mode（de）multiplexer employing sub-wavelength grating structure.In analogy to a conventional wavelength selective switch in wavelength-division multi-plexing,we demonstrate a selective switch that can route mode-and polarization-multiplexed signals.