Bending Coupling Research Articles

Optimal Control of Pretwisted Rotating Thin-Walled Beams via Piezoelectrically Induced Couplings

Problems related to mathematical modeling and optimal active control of pretwisted adaptive blade are considered. The blade is modeled as a rotating thin-walled composite beam embedded with anisotropic piezo-composite layers accounting for nonclassical effects, such as transverse shear and warping inhibitions. The linear-quadratic-regulator feedback control strategy is adopted to study the tailoring of piezo-actuators on vibration suppression. Control authority of piezoelectrically induced transverse shear and bending coupling is highlighted. Tailoring studies using the present model reveal that piezoelectrically induced transverse shear plays an important role on control effectiveness. In addition, the relations between the control authority and the elastic couplings, piezoelectrically induced actuation couplings, pretwist angle, and size and position of piezo-actuators are investigated.

Bending analysis of functionally graded beam with porosities resting on elastic foundation based on neutral surface position

In this paper, the Timoshenko beam theory is developed for bending analysis of functionally graded beams having porosities. Material properties are assumed to vary through the height of the beam according to a power law. Due to unsymmetrical material variation along the height of functionally graded beam, the neutral surface concept is proposed to remove the stretching and bending coupling effect to obtain an analytical solution. The equilibrium equations are derived using the principle of minimum total potential energy and the physical neutral surface concept. Navier-type analytical solution is obtained for functionally graded beam subjected to transverse load for simply supported boundary conditions. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. The influences of material parameters (porosity distributions, porosity coefficient, and power-law index), span-to-depth ratio and foundation parameter are investigated through numerical results.
 Keywords: functionally graded beam; bending analysis; porosity; elastic foundation; bending; neutral surface.
 Received 10 December 2018, Revised 28 December 2018, Accepted 24 January 2019

Buckling of beams with finite prebuckling deformation

The prebuckling deformation of structures is usually very small in conventional concepts, and is always neglected in the conventional buckling theory (CBT) and numerical method (CNM). In this paper, we find a class of structures from the emerging field of stretchable electronics, of which the prebuckling deformation becomes large and essential for determining the critical buckling load. Although great progress has been made for the buckling theory in the past hundred years, it is still challenging to analyze the buckling problems with finite prebuckling deformation (FPD buckling) straightforwardly. Here, the experimental stretch of a series of serpentine interconnects was firstly conducted as a representative example to show the FPD buckling behaviors and inapplicability of the CBT and CNM. The CNM can yield a huge error of 50% on the critical buckling load for the case with thickness-to-width ratio of the cross section h/b = 0.6. Most importantly, a systematic and straightforward theory (FPD buckling theory) is developed to analyze the FPD buckling behaviors of beams with the coupling of bending, twist and stretch/compression. As a comparison, various theoretical and numerical methods are applied to three classic problems, including lateral buckling of a three-point-bending beam, lateral buckling of a pure bending beam and Euler buckling. Our FPD buckling theory for beams is able to give a good prediction, while the CBT (by Timoshenko et al.) and CNM (by commercial program packages) yield unacceptable results (with 70% error for a three-point-bending beam with h/b = 0.8, for example). Discussion on the FPD buckling of bulk structures is deferred to a following paper.

Flexural Analysis Along the Sunda Trench: Bending, Buckling and Plate Coupling

AbstractThe bathymetry and free‐air gravity data offshore Sunda trench are used here to analyze the flexural forebulge and bending moment variations along the Southeast Asian subduction zone. The observed bathymetry is corrected for various effects such as the sediment loading, lithosphere age, and the gravity‐derived isostatically compensated topography, which gave rise to the flexural deformation surface of the subducting Indo‐Australian plate. From this, 28 across‐trench sections were constructed to model the plate flexural bending along the Sunda trench. We observed that except in the northern Sumatra trench, rest of the Sunda trench is in agreement with the flexural model explained by the bending moment applied by the slab. In the northern Sumatra part of the trench, additional horizontal stresses of ~30–40 MPa are required for better match of the flexural forebulge thereby increasing the coupling with the upper plate. The outcome of this analysis in comparison with the slab depth variation, which abruptly reduces from ~600 km in Java to ~200 km toward northern Sumatra, suggests that very large bending moment and horizontal stresses are anticorrelated with the slab depth. The shorter slab in Sumatra does not effectively pull the incoming plate in the mantle, and therefore, plate convergence is accommodated at shallow depth, increasing the coupling with the upper plate. We propose that horizontal stresses are the result of the lateral propagation of the stronger slab pull from the neighboring deeper southeastern Java slab.

Small-size planar printed loop antenna for octa-band WWAN/LTE smartphone application

In this letter, a planar printed loop antenna which can cover eight bands of LTE (LTE2300/2500), WWAN (GSM850/900/DCS1800/PCS1900/UMTS2100) and LTE (LTE3500) in 5G communication is proposed for smartphone application. The antenna adopts the principle of coupled-fed, and its structure consists of a T-shaped feeding strip, a coupling bending shorted strip and a tuning line. To further attain good impedance matching for WWAN/LTE bands, a tuning line is used. In addition, the proposed antenna is very simple and compact, only occupying a size of 15 × 27 mm2, and the proposed antenna is very easy to be fabricated. Finally, from the measurement results, it shows over 40% of good antenna efficiencies in LTE/WWAN communication bands of 824MHz-960MHz, 1710MHz-2690MHz and 3300MHz-3600MHz.

Modelling process induced deformations in 0/90 non-crimp fabrics at the meso-scale

The manufacture of non-crimp fabric composites typically requires the forming and consolidation of the reinforcement material. During this process the material is subjected to complex loading where the coupling of tensile, bending, shear and compressive forces result in deformations to the internal architecture of the textile. To determine the extent of these deformations a numerical modelling method has been developed to capture the kinematic behaviour of non-crimp fabric textiles. This method focuses on capturing the interactions between the fibrous tows and the stitch yarns which bind the tows together. Through modelling at a level of detail in which the meso-scale interactions are explicitly present, the macro-scale behaviour of the material proceeds naturally within the model, negating any requirement for detailed characterisation of the physical material. This also enables a detailed description of the internal architecture of the deformed fabric to be extracted for analysis or further modelling. The present study explores the method's ability to capture both local and global deformations which occur in non-crimp fabrics, specifically to capture the onset of deformations that appear due to tow-stitch interactions and the forming and compaction of multiple layers. Comparison with experimental results show good agreement for both meso-scale deformations, resulting from multi-layer compaction, and global in-plane shear deformations induced through forming over complex tooling.

System modeling and instability control of wind turbine blade based on hydraulic pitch system and radial basic function neural network proportional–integral–derivative controller

System modeling and aeroservoelastic control for divergent instability of stall-induced composite wind turbine blade modeled as thin-walled symmetric layup beam analysis have been investigated based on hydraulic pitch system and radial basic function neural network control. The blade is modeled as single-cell thin-walled beam structure with the circumferentially asymmetric stiffness design, exhibiting flap/lead-lag bending coupling deformation. The stall flutter and aeroservoelastic control of composite blade are investigated based on dynamic stall Beddoes–Leishman aerodynamic model and radial basic function neural network proportional–integral–derivative controller, with pitch actuator performed by hydraulic system. The system motion equations consist of the aeroelastic equations and the six-order pitch equation. The nonlinear aeroelastic responses, including both flap/lead-lag responses and pitch angle responses under different parameters, are solved by Galerkin method and the nonlinear time integration scheme with nonlinear residual analysis. To verify the effectiveness of the control scheme and realize visualized display of large thin-walled blade in the laboratory, experimental platform based on hardware-in-the-loop simulation is built to realize real-time control and virtual simulation. The platform structure consists of PLC hardware, monitoring interface in configuration software, and simulation environment that is connected by the OPC server with PLC system. The platform lays the foundation for vibrational behavior research on visualization of large wind turbine blade under divergent stall situation and verifies the real-time feasibility of the control algorithm proposed.

3-D Multilayer S-Bend Silicon Waveguide Optical Interconnect

A 3-D S-bend silicon waveguide optical interconnect on silicon on insulator is proposed to connect optical circuits in a multilayered photonic-integrated circuit (PIC). Critical parameters like bending loss, axial shift, and coupling loss are calculated for efficient implementation in the dense wavelength division multiplexing wavelength spectrum (1.46-1.62 μm). The critical parameters for tight bends are kept in control by optimizing geometrical parameters for application in miniaturized optical circuits in multilayered PIC. Possibility of fabrication of proposed complex interconnect is also explored.

Application of fiber model considering the shear effect in the analysis of nonlinear RC shear wall

Because of the good performance of the fiber model in the simulation of axial and bending coupling, the new fiber model considering the axial, bending and shear effects is established to analysis the nonlinear properties of RC shear wall. The way of the shear fiber distribution in the cross section consistent with the axial fiber and each shear fiber current state of stiffness get from the independent shear hysteretic rules, then establish tangent element stiffness matrix containing the axial, bending and shear deformation under complex loading paths. Two different cross-section fiber models is compared. Compiling corresponding calculation program to simulate a shear wall’s nonlinear performance under monotonic load and compare with the laboratory RC shear wall test results to verify the validity of the model.

Coupled bending and torsional vibrations of non-uniform thin-walled beams by the transfer differential transform method and experiments

This paper describes a new methodology capable of analyzing coupled bending and torsional vibrations in non-uniform thin-walled beams. The transfer matrix method (TMM) and the differential transform method (DTM) are combined to create the proposed transfer differential transform method (TDTM) for solving equations coupling bending and torsional vibrations in non-uniform beams. Compared with the finite element method (FEM), the TDTM utilizes a type of changeable mode shape functions so that the number of meshed elements can be reduced greatly when the beam's geometric size is uniform. The equations of motion of the non-uniform thin-walled beams are established using Hamilton's principle. The method considers both the warping and rotary effects of the beam section. The natural frequencies and mode shapes of the bending and torsional components are obtained using the TDTM. The accuracy of solutions can be controlled by the mesh density and the series expansion order of the mode shape whose ranges are also discussed. For illustrative purposes, the natural frequencies and the frequency response curves of a uniform beam and a non-uniform beam are studied respectively and are validated by experiments. The effects of warping and the distance between the centroid of a given section and the corresponding shear center on the vibration properties of the beam are also investigated.

An L-shaped ultrasonic linear piezoelectric motor with two second-order bending coupling modes

ABSTRACTIn order to simplify the motor structure, reduce the difficulty of modal coupling and obtain a wide driving frequency range, a new piezoelectric motor which works on the two second bending vibration coupling modes was designed in this study. Based on the bonded-type structure, it consists of four pieces of piezoelectric ceramics, a copper substrate and one driving tip. The finite element method (FEM) was used for optimizing the design and further analysis, and a prototype was designed, fabricated and experimentally researched in this study for verifying its mechanical properties. Experimental results show that the working frequency is 89 kHz, and the maximum value of the movement velocity of a certain direction is 53 mm/s, at 680 Vpp(voltage, peak to peak value),while the maximum movement velocity of reverse direction is 44 mm/s at the same voltage.

Simplified and Accurate Stiffness of a Prismatic Anisotropic Thin-Walled Box

Background:Beam models have been proven effective in the preliminary analysis and design of aerospace structures. Accurate cross sectional stiffness constants are however needed, especially when dealing with bending, torsion and bend-twist coupling deformations. Several models have been proposed in the literature, even recently, but a lack of precision may be found when dealing with a high level of anisotropy and different lay-ups.Objective:A simplified analytical model is proposed to evaluate bending and torsional stiffness of a prismatic, anisotropic, thin-walled box. The proposed model is an extension of the model proposed by Lemanski and Weaver for the evaluation of the bend-twist coupling constant.Methods:Bending and torsional stiffness are derived analytically by using physical reasoning and by applying bending and torsional stiffness mathematic definition. Unitary deformations have been applied when evaluation forces and moments arising on the cross section.Results:Good accuracy has been obtained for structures with different geometries and lay-ups. The model has been validated with respect to finite element analysis. Numerical results are commented upon and compared with other models presented in literature.Conclusion:For cross sections with a high level of anisotropy, the accuracy of the proposed formulation is within 2% for bending stiffness and 6% for torsional stiffness. The percentage of error is further reduced for more realistic geometries and lay-ups.The proposed formulation gives accurate results for different dimensions and length rations of horizontal and vertical walls.

Compliant structures based on stiffness asymmetry

ABSTRACTOne of the key problems in the development of morphing aircraft is the morphing structure, which should be able to carry loads and change its geometry simultaneously. This paper investigates a compliant structure, which has the potential to change the dihedral angle of morphing wing-tip devices. The compliant structure is able to induce deformation by unsymmetrical stiffness allocation and carry aerodynamic loads if the total stiffness of the structure is sufficient.The concept has been introduced by building a simplified model of the structure and deriving the analytical equations. However, a properly designed stiffness asymmetry, which is optimised, can help to achieve the same deformation with a reduced actuation force.In this paper, round corrugated panels are used in the compliant structure and the stiffness asymmetry is introduced by changing the geometry of the corrugation panel. A new equivalent model of the round corrugated panel is developed, which takes the axial and bending coupling of the corrugated panel into account. The stiffness matrix of the corrugated panel is obtained using the equivalent model, and then the deflections of the compliant structure can be calculated. The results are compared to those from detailed finite element models built in the commercial software Abaqus. Samples with different geometries were manufactured for experimental tests.After verifying the equivalent model, optimisation is performed to find the optimum geometries of the compliant structures. The actuation force of a single compliant structure is first optimised, and then the optimisation is performed for a compliant structure consisting of multiple units. A case study is used to show the performance improvement obtained.

Modal Analysis of Laminated “CAS” and “CUS” Box-Beams

Abstract In the paper, the authors discuss the numerical and experimental modal analysis of the cantilever thin-walled beams made of a carbon-epoxy laminate. Two types of beams were considered: circumferentially asymmetric stiffness (i.e., CAS) and circumferentially uniform stiffness (i.e., CUS) beams. The layer-up configurations of the laminate were chosen to get a vibration mode coupling effect in both analysed cases. The aim of the paper was to perform the numerical and experimental modal analysis of the composite structures, when a flapwise bending with torsion coupling effect or flapwise-chordwise bending coupling effect took place. Firstly, numerical studies by the finite element method was performed. The numerical simulations were carried out by the Lanczos method in the Abaqus software package. The natural frequencies and the corresponding free vibration modes were determined. Next, the experimental modal analyses of the CAS and CUS beams were performed. The test stand was consisted of a special grip, two beams with an adhered holder, the LMS Scadas III system with a modal hammer and an acceleration sensor. Finally, the results of both methods were compared.

Data-driven reduced-order model of microtubule mechanics.

A beam element is constructed for microtubules based upon data reduction of the results from atomistic simulation of the carbon backbone chain of αβ-tubulin dimers. The database of mechanical responses to various types of loads from atomistic simulation is reduced to dominant modes. The dominant modes are subsequently used to construct the stiffness matrix of a beam element that captures the anisotropic behavior and deformation mode coupling that arises from a microtubule's spiral structure. In contrast to standard Euler-Bernoulli or Timoshenko beam elements, the link between forces and node displacements results not from hypothesized deformation behavior, but directly from the data obtained by molecular scale simulation. Differences between the resulting microtubule data-driven beam model (MTDDBM) and standard beam elements are presented, with a focus on coupling of bending, stretch, shear deformations. The MTDDBM is just as economical to use as a standard beam element, and allows accurate reconstruction of the mechanical behavior of structures within a cell as exemplified in a simple model of a component element of the mitotic spindle.

Improved one-dimensional beam model for unbalanced composite single-lap joint

An analytical nonlinear solution was provided for unbalanced composite single-lap joint (CSLJ) using an improved one-dimensional beam model, which incorporated the effect of bending–tension coupling. The bending–tension coupling stiffness was introduced to characterize the coupling bending and tension behavior induced by the un-symmetric stacking sequence of composite laminates. The governing differential equations captured the bending–tension coupling behavior and the geometrically nonlinear features were constructed based on the displacement compatibility conditions of flexible interface. The transverse deformation in overlap region, edge moment factors and adhesive stress distributions for the unbalanced CSLJ with inflexible, intermediate flexibility and flexible adhesive can be determined by the present one-dimensional beam model. The accuracy of the present model was validated by the comparison with nonlinear finite element model. The effect of bending–tension coupling on edge moment factors and peak values of adhesive stresses was shed light on with the present model.

A coupled-field model of a rotating composite beam with an integrated nonlinear piezoelectric active element

The dynamics of a system consisting of a rotating rigid hub and a thin-walled composite beam with embedded active element is presented. The beam comprises of a generally orthotropic host made of an arbitrary laminate and an additional layer of a transversely isotropic piezoceramic material. The higher-order constitutive relations for piezoelectric are used to properly model its electromechanical structural behaviour when operated in near resonance conditions or subjected to strong electric fields. In the mathematical formulation of the problem, the full two-way coupling piezoelectric effect is considered by adopting the assumption of a spanwise electric field variation. To enhance the generality of the formulation, the model considers also the hub mass moment of inertia and a non-constant rotating speed case. A general nonlinear system of mutually coupled partial differential equations is derived using the Hamilton principle, and the Galerkin method is applied to reduce these governing equations to the ordinary differential ones. A specific case of CAS lamination scheme that exhibits flapwise bending and twist mode elastic coupling is discussed in detail. Numerical results for system free vibrations are obtained to investigate the natural mode shapes and electrical field spatial distribution depending on the system rotation speed and laminae fibre orientation angle. Next, a forced vibration case is studied by applying to the hub a periodic driving torque with zero mean value. Nonlinear frequency response curves for the combined beam–hub system together with time series plots are prepared for different driving torque scenarios.

A Real-Time Vibration Suppression Strategy in Electric Vehicles

In electric vehicles (EVs), the source of noise, vibration, and harshness (NVH) involves various components inside/outside of the vehicle. Besides the vibration from each NVH source, the resonances between multiple sources contribute even more significant vibrations. This paper proposes a generalized real-time suppression strategy to mitigate the coupling vibration during vehicle idling and cruising. Using a high-performance field-oriented-controlled electric motor drive, a relatively small amount of rotation velocity offset can be added to the traction motor to significantly reduce the resonant vibration with negligible impact to vehicular speed. In this paper, torsional and bending coupling vibrations between traction motor and driveline are investigated because these two are the most common forced vibrations due to resonances. The system is simulated using MATLAB/Simulink, and the results of the vibration suppression are presented. The strategy proposed in this paper presents a simple and robust way to suppress the coupling vibration in EVs with no additional hardware requirement.

10.32: Experimental study on high temperature elastic modulus of China made high strength structural steel

ABSTRACTHigh strength structural steel (HSSS) has better economic and environmental benefits than mild structural steel, and becomes more popular in the building construction projects. The current codes for fire safety design of steel structures is mainly developed based on the test data from mild structural steel and might be not applicable to the high strength structural steel. This paper reports an experimental study on the high temperature elastic modulus of China made high strength structural steel. Both static and dynamic test methods were used to determine the elastic modulus of Q550, Q690 and Q890 China grade steel at temperatures ranging from 20 °C to 800 °C. Suspended coupling bending resonance method was used to measure the dynamic elastic modulus. The reduction factors of elastic modulus from test data were compared with the reduction factors determined by current codes, including the Chinese code CECS200, the Eurocode 3, the American code AISC and the Austrian code AS4100, and by other researchers. The study found that unlike the static reduction factors (reduction factors determined by the static method) the dynamic reduction factors are not sensitive to the steel grade. The static elastic modulus is greater than the dynamic elastic modulus at low temperatures and is less than the dynamic modulus at high temperatures. Both the static and dynamic reduction factors of HSSS are greater than the elastic modulus reduction factors employed by the current codes. Design equation for dynamic elastic modulus of HSSS was derived from curve‐fitting of the test data.

Parallel misalignment modeling and coupling bending stiffness measurement of a rotor-bearing system

This paper sheds the light on vibration modeling and diagnosis of misalignment beyond traditional approaches. Firstly, the paper presents a detailed finite element and dynamic simulation model of a vibration test rig. The model includes the construction of mass, stiffness and damping matrices of a test rig and the inclusion of a time invariant, nonlinear rolling element bearing model, a misalignment model and residual unbalance force excitation. Secondly, a detailed measurement setup and signal processing methodology to characterize the coupling bending stiffness and misalignment forces as a function of the rotation angle and amount of parallel misalignment is developed and presented. Thirdly, equations of motions of the model were formulated and solved using a variable step solver. The displacements at the motor and rotor sides of the coupling were used along with the interpolated coupling stiffness values to calculate the misalignment forces, which were then fed to the system as excitation forces. The stiffness of the coupling was interpolated as a function of the shaft rotational speed and the level of misalignment. Finally experimental and simulated results are presented and discussed. Results from simulated data were compared to those measured experimentally. Both simulated and experimental results exhibited similar behavior. An increase of lower and higher harmonics of the shaft speed of the acceleration vibration signal was observed with smearing noticed at higher orders. A low-frequency modulation was reported in the measured signal with similar behavior captured in the simulated signal. Further investigation still needs to be carried out to provide a solid understanding of this interaction.