Flapwise Bending Vibration Analysis of Rotating Tapered Rayleigh Beams for the Application of Offshore Wind Turbine Blades

The flapwise bending vibrational equations of tapered Rayleigh beam are derived based on Hamilton’s principle.The corresponding vibrational characteristics of rotating tapered Rayleigh beams are investigated via variational iteration method(VIM).Natural frequencies and corresponding mode shapes are examined under various rotation speed,taper ratio and slenderness ratio focusing on two types of tapered beam.The convergence of VIM is examined as part of the paper.Validation of VIM solution is made by referring to results available in other literature and corresponding results show that VIM is capable of yielding precise results in a very efficient way.

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.

Study on adhesively-bonded surface of tapered double cantilever specimen made of aluminum foam affected with shear force

Aluminum foam is widely used in diverse areas to minimize the weight and maximize the absorption of shock energy in lightweight structures and various bio-materials.It presents a number of advantages,such as low density,incombustibility,non-rigidity,excellent energy absorptivity,sound absorptivity and low heat conductivity.The aluminum foam with an air cell structure was placed under the TDCB Mode II tensile load by using Landmark equipment manufactured by MTS to examine the shear failure behavior.The angle of the tapered adhesively-bonded surfaces of specimens was designated as a variable,and three models were developed with the inclined angles differing from one another at 6°,8° and 10°.The specimens with the inclined angles of 6°,8° and 10° have the maximum reaction forces of 168 N,194 N when the forced displacements are 6,5 and 4.2 mm respectively.There are three specimens with the inclined angles of 10°,8° and 6° in the order of maximum reaction force.As the analysis result,the maximum equivalent stresses of 0.813 MPa and 0.895 MPa happened when the forced displacements of 6 mm and 5 mm proceeded at the models of 6° and 8°,respectively.A simulation was carried out on the basis of finite element method and the experimental design.The results of the experiment and the simulation analysis are shown not different from each other significantly.Thus,only a simulation could be confirmed to be performed in substitution of an experiment,which is costly and time-consuming in order to determine the shearing properties of materials made of aluminum foam with artificial data.

Dynamic analysis of wind turbine tower structures in complex ocean environment

Studying and analyzing the dynamic behavior of offshore wind turbines are of great importance to ensure the safety and improve the efficiency of such expensive equipments.In this work,a tapered beam model is proposed to investigate the dynamic response of an offshore wind turbine tower on the monopile foundation assembled with rotating blades in the complex ocean environment.Several environment factors like wind,wave,current,and soil resistance are taken into account.The proposed model is ana-lytically solved with the Galerkin method.Based on the numerical results,the effects of various structure parameters including the taper angle,the height and thickness of the tower,the depth,and the diameter and the cement filler of the monopile on the funda-mental natural frequency of the wind turbine tower system are investigated in detail.It is found that the fundamental natural frequency decreases with the increase in the taper angle and the height and thickness of the tower,and increases with the increase in the diameter of the monopile.Moreover,filling cement into the monopile can effectively im-prove the fundamental natural frequency of the wind turbine tower system,but there is a critical value of the amount of cement maximizing the property of the monopile.This research may be helpful in the design and safety evaluation of offshore wind turbines.

Curve Optimization of Tapered Cantilever Beams Under Tip Loads

The study adopts the variational method for analyzing the cantilever tapered beams under a tip load as well as a definite end displacement,and further determining the optimized shapes and materials that can minimize the weights.Two types of beams are taken into account,i.e.,the Euler-Bernoulli beam without considering shear deformation and the Timoshenko beam with shear deformation.By using the energy theorem and the reference of isoperimetric problem,the width variation curves and the corresponding minimum masses are derived for both beam types.The optimized curve of beam width for the Euler-Bernoulli beam is found to be a linear function,but nonlinear for the Timoshenko beam.It is also found that the optimized curve in the Timoshenko beam case starts from non-zero at the tip end,but its tendency gradually approaches the one of the Euler-Bernoulli beam.The results indicate that with the increase of the Poisson’s ratio,the required minimum mass of the beam will increase no matter how the material changes,suggesting that the optimized mass for the case of Euler-Bernoulli beam is the lower boundary limit which the Timoshenko case cannot go beyond.Furthermore,the ratio r/E(density against Elastic Modulus)of the material should be as small as possible,while the ratio h2/L4 of the beam should be as large as possible in order to minimize the mass for the case of Euler-Bernoulli beam,of which the conclusion is extended to be applicable for the case of Timoshenko beam.In addition,the optimized curves for Euler-Bernoulli beam types are all found to be power functions of length for both tip point load cases and uniform load cases.

Buckling Analysis of Axially Functionally Graded and Non-Uniform Beams Based on Timoshenko Theory

In this paper,the buckling behaviors of axially functionally graded and non-uniform Timoshenko beams were investigated.Based on the auxiliary function and power series,the coupled governing equations were converted into a system of linear algebraic equations.With various end conditions,the characteristic polynomial equations in the buckling loads were obtained for axially inhomogeneous beams.The lower and higher-order eigenvalues were calculated simultaneously from the multi-roots due to the fact that the derived characteristic equation was a polynomial one.The computed results were in good agreement with those analytical and numerical ones in literature.

Effect of Scanning Beam Profile to Fabricate Fused Fiber Tapers by CO_2 Laser Irradiation Method

Beam uniformity is a crucial building block of CO2 experiments aimed at fusing and stretching optical fibers in a lossless manner. When the irradiation beam is expanded through a galvanometer mirror, ways to achieve beam uniformity are investigated.

Performance enhancement of cantilever piezoelectric energy harvesters by sizing analysis

This paper presents the results of the performance of piezoelectric cantilever beams in relation to their size.The total produced power represents the main indicator of performance of a piezoelectric harvesting system while the area of the beams stays constant.Lightweight design is an important aspect in any industry,mainly in the aerospace.In this study,the effects of non-uniformity on the efficiency and power output are studied.Finite element method(FEM)with the application of superconvergent element(SCE)is adopted here to solve the equations.It is observed that the trapezoidal geometry(converging beam)provides a higher output power while the efficiency decreases.Moreover,in order to prove that the power enhancement is achievable while the amount of piezoelectric material consumed is constant the new configuration is proposed.In the configuration,an array of uniform beams connected in series is used instead of one single rectangular beam.The proposed setting generates an output power of 1.817mWat a resonant frequency of 284.6 Hz when excited by an input acceleration of 1 g.The only challenge is the fundamental frequency difference which ismet with the application of proof mass and thinner substrate and piezoelectric layers.

Model-driven path planning for robotic plasma cutting of branch pipe with single Y-groove based on pipe-rotating scheme

The automatic cutting of intersecting pipes is a challenging task in manufacturing.For improved automation and accuracy,this paper proposes a model-driven path planning approach for the robotic plasma cutting of a branch pipe with a single Y-groove.Firstly,it summarizes the intersection forms and introduces a dual-pipe intersection model.Based on this model,the moving three-plane structure(a description unit of the geometric characteristics of the intersecting curve)is constructed,and a geometric model of the branch pipe with a single Y-groove is defined.Secondly,a novel mathematical model for plasma radius and taper compensation is established.Then,the compensation model and groove model are integrated by establishing movable frames.Thirdly,to prevent collisions between the plasma torch and workpiece,the torch height is planned and a branch pipe-rotating scheme is proposed.Through the established models and moving frames,the planned path description of cutting robot is provided in this novel scheme.The accuracy of the proposed method is verified by simulations and robotic cutting experiments.