Multi-beam Structures Research Articles

Electrostatic chuck having compliant multi-beam structures with rotatable bipolar pad-shaped electrodes

The demand for the manipulation of flexible film-like objects and those with non-planar surfaces, which cannot be handled using current technologies, has increased considerably. A bipolar electrostatic chuck (ESC) is a device that clamps target objects using a uniform electrostatic force. Traditional ESCs cannot satisfy these demands because of their planar surfaces. Bipolar ESCs with a compliant multi-beam assembly have been proposed to manipulate such objects while leveraging the uniform force distribution of ESCs. Although the proposed compliant ESCs have the potential for such manipulations, increasing the attractive force remains a critical technical issue. This study aims to develop a compliant ESC with pad-shaped bipolar electrodes connected to beam tips with rotational degrees of freedom (RDOFs). Four ESC models with pad-shaped electrodes with different RDOFs between zero and three and one without a pad-shaped electrode are fabricated via 3D printing. The experimental comparison of the five models indicates that an increase in the RDOFs significantly improves the attractive force of each electrode. The high potential of compliant ESCs with three RDOFs at the beam tips is illustrated using three different demonstrations: picking and placing dielectric films, a rigid object with a plane surface, and a rigid object with a curved surface. The results provide insights into the development of industrial electrostatic grippers.

Optimisation of a forced multi-beam piezoelectric energy harvester

A high-power multi-beam piezoelectric energy harvesting device is designed to meet the demands of the emerging technologies in Body Sensors Networks (BSNs), Wireless Sensors Networks (WSNs), the Internet of Things (IoT) and the Industrial Internet of Things (IIoTs). The proposed device utilises a plucking mechanism to excite the beams, organised in a comb-like structure. The harvester is presented in different length configurations and its performance is optimised to deliver the highest power under a given set of parameter values, constraints, and excitation characteristics. The unique feature of the device is that it can be tuned to any given frequency, although it demonstrates its superior performance in the frequency range of 2–50 Hz, delivering hundreds of mW. The device optimisation is conducted using a harmonic excitation, a harmonic excitation with random phase modulations, experimental vibration data collected using an internal combustion engine, and numerical data from simulations of out-of-plane oscillations of wind turbine blades. The paper proposes solutions to a number of challenges specific for multi-beam structures that have never been addressed before. It is demonstrated for the first time that the proposed harvester is able to meet the demands of relevant sensing applications.

A 340 GHz High-Power Multi-Beam Overmoded Flat-Roofed Sine Waveguide Traveling Wave Tube

A phase shift that is caused by the machining errors of independent circuits would greatly affect the efficiency of the power combination in traditional multi-beam structures. In this paper, to reduce the influence of the phase shift and improve the output power, a multi-beam shunted coupling sine waveguide slow wave structure (MBSC-SWG-SWS) has been proposed, and a multi-beam overmoded flat-roofed SWG traveling wave tube (TWT) based on the MBSC-SWG-SWS was designed and analyzed. A TE10-TE30 mode convertor was designed as the input/output coupler in this TWT. The results of the 3D particle-in-cell (PIC) simulation with CST software show that more than a 50 W output power can be produced at 342 GHz, and the 3 dB bandwidth is about 13 GHz. Furthermore, the comparison between the single-beam sine waveguide (SWG) TWT and the multi-beam overmoded SWG TWT indicates that the saturated output power of the multi-beam overmoded SWG TWT is three times more than that of the single beam SWG TWT.

Nonlinear dynamics of a Z-shaped structure with validated global analytical mode shapes

The nonlinear partial differential governing equations of the planar motion of a Z-shaped structure are derived using Hamilton's principle. The 1:2 internally resonant global analytical mode shapes are validated by figure contrast and the modal assurance criterion (MAC). The partial differential governing equations are truncated into a two-degree-of-freedom ordinary differential system with the validated resonant global analytical mode shapes, and they are further investigated for internal and simultaneous primary resonances. The steady-state responses are studied, and numerical simulations of the system are performed. Complex nonlinear phenomena in the system, such as jumps, bifurcations, quasiperiodic motion and chaos, are observed under specific parameters. The parametric rule of these phenomena obviously depends on the accuracy of mode shapes. This work proposes a nonlinear analysis based on the quantitative validation of mode shapes, which may provide new insights into the optimal design of the parameters and the precise control of the motions of Z-shaped or other multibeam structures in engineering.

Optimization of EH Multi-beam Structures for Freight Car Vibration

Autonomous sensors (AS) became a suitable alternative to the constant monitoring of mechanical systems, preventing unexpected failure of the components and resulting in significant savings in maintenance costs and time. Regarding railroad transportation, these autonomous sensors can provide useful information of the freight cars’ conditions, preventing damage and even derailments. However, many freight cars equipped with pneumatic control valves do not have an electric power source to keep the AS running. Energy harvesting (EH) appears to be a viable alternative to powering the AS by converting the vibration energy naturally present in the freight cars into electricity by means of piezoelectrics. This study searched for and found an optimized configuration of a piezoelectric multi-beam structure adequate for freight cars’ vibrational frequencies, resulting in an output power of 13 mW, which is enough to power a conventional vertical accelerometer.

Global bifurcations and chaotic motions of a flexible multi-beam structure

Global bifurcations and multi-pulse chaotic motions of flexible multi-beam structures derived from an L-shaped beam resting on a vibrating base are investigated considering one to two internal resonance and principal resonance. Base on the exact modal functions and the orthogonality conditions of global modes, the PDEs of the structure including both nonlinear coupling and nonlinear inertia are discretized into a set of coupled autoparametric ODEs by using Galerkin’s technique. The method of multiple scales is applied to yield a set of autonomous equations of the first order approximations to the response of the dynamical system. A generalized Melnikov method is used to study global dynamics for the “resonance case”. The present analysis indicates multi-pulse chaotic motions result from the existence of Šilnikov’s type of homoclinic orbits and the critical parameter surface under which the system may exhibit chaos in the sense of Smale horseshoes are obtained. The global results are finally interpreted in terms of the physical motion of such flexible multi-beam structure and the dynamical mechanism on chaotic pattern conversion between the localized mode and the coupled mode are revealed.

Nonlinear Dynamics of Flexible L-Shaped Beam Based on Exact Modes Truncation

Nonlinear dynamics of flexible multibeam structures modeled as an L-shaped beam are investigated systematically considering the modal interactions. Taking into account nonlinear coupling and nonlinear inertia, Hamilton’s principle is employed to derive the partial differential governing equations of the structure. Exact mode functions are obtained by the coupled linear equations governing the horizontal and vertical beams and the results are verified by the finite element method. Then the exact modes are adopted to truncate the partial differential governing equations into two coupled nonlinear ordinary differential equations by using Galerkin method. The undamped free oscillations are studied in terms of Jacobi elliptic functions and results indicate that the energy exchanges are continual between the two modes. The saturation and jumping phenomena are then observed for the forced damped multibeam structure. Further, a higher-dimensional, Melnikov-type perturbation method is used to explore the physical mechanism leading to chaotic behaviors for such an autoparametric system. Numerical simulations are performed to validate the theoretical predictions.

Generalized Solutions of Piezoelectric Vibration-Based Energy Harvesting Structures Using an Electromechanical Transfer Matrix Method

Piezoelectric vibration-based energy harvesting (pVEH) offers much potential as renewable energy structures. Within the literature, often geometry-specific models are developed, making designs of new structures difficult. In this work, a generalized linear algebraic method is developed. The method incorporates the transfer matrix method (TMM) into the well-accepted distributed parameter electromechanical model for a composite-piezoelectric, Euler–Bernoulli beam. The result is an electromechanical TMM which is highly accurate at predicting both structural and energy harvesting performances for a wide variety of designs which have chainlike topologies. A simplification is made within the method to model structures which operate solely within bending modes, reducing the computation to analyses of only four-by-four state transition matrices, regardless of structural complexity. As many applications aim to optimize the large bending mode piezoelectric effect, this simplification does not limit the versatility of the method. To demonstrate the validity of this statement, comparisons were performed to evaluate the accuracy of the method's predictions for six piezoelectric topologies, including a unimorph without a tip mass, a bimorph with a tip mass, several partial-length bimorphs without a tip mass, and three different multibeam bimorph structures with inline and folded-back designs. The results show differences no greater than 2.24% for the first and second natural frequencies of the structures. Likewise, the method yields excellent predictions for the mode shapes, their slopes, and the voltage frequency responses, especially within the ±10% bounds of the natural frequencies. Thus, the future design of new structures is shown to be simplified using this generalizable method.

Aerodynamic studies of typical multi-beam structures

The dependence of the aerodynamic characteristics of typical multi-beam structures of bridge spans on the angle of attack, the incident flow turbulence, the number of beams, and the distance between them has been studied. For the model of three beams bridge span, the characteristic vortex structures were obtained, the thermo-anemometer probing of the near wake was performed, and the diagrams of the distribution of the averaged pressure were plotted.

Dynamic Analysis of Multi-Beam MEMS Structures for the Extraction of the Stress-Strain Response of Thin Films

Freestanding MEMS structures made of two long connected beams from different materials are fabricated and released in order to extract the stress-strain properties of thin films. The first material, named actuator, contains a high internal tensile stress component and, when released, pulls on the other beam. The strain in the beams is calculated based on the measurement of the displacement with respect to the reference configuration using scanning electron microscopy. The stress is estimated using two different methods. The first method, already reported, is based on the displacement of the actuator and the knowledge of its internal stress. The method which constitutes the novelty of the present study is based on the dynamic analysis of the multi-beam structures, and the determination of the stress value that corresponds to the measured resonance frequencies. The dynamic analysis is performed via two different methods: (i) the modified Rayleigh–Ritz technique and (ii) the Euler–Bernoulli beam dynamics. Results are provided for palladium thin films which deform plastically and for monocrystalline silicon thin films, exhibiting a purely elastic behavior. The results show the higher accuracy of the dynamic measurements for the estimation of the stress compared to the static method. The dynamic measurements also show that the Rayleigh–Ritz technique tends to give a higher bound for the resonance frequencies compared to the Euler–Bernoulli technique. This dynamic method extends the potential of this on-chip material testing technique which can also be adapted to stress controlled sensors applications.

Vibration analysis for elastic multi‐beam structures by the C0‐continuous time‐stepping finite element method

AbstractSome C0‐continuous time‐stepping finite element method is proposed for investigating vibration analysis of elastic multi‐beam structures. In the time direction, the C0‐continuous Galerkin method is used to discretize the generalized displacement field. In the space directions, the longitudinal displacements and rotational angles on beams are discretized using conforming linear elements, while the transverse displacements on beams are discretized by the Hermite elements of third order. The error of the method in the energy norm is proved to be O(h+k3), where h and k denote the mesh sizes of the subdivisions in the space and time directions, respectively. The finite difference analysis in time is developed to discuss the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low‐frequency regime. The method has also been extended to study some nonlinear problems. A number of numerical tests are included to illustrate the computational performance of the method. Copyright © 2008 John Wiley & Sons, Ltd.

Equilibrium and modal analyses of rotating multibeam structures employing multiple reference frames

A single reference frame is frequently employed to derive equations of motion in structural dynamic analysis. For simple structures like a single beam and a single plate, the method of employing a single reference frame usually provides well converged and accurate results for equilibrium and modal analyses. However, for structures having more general configurations such as multibeam structures, use of a single reference frame often results in slow convergence and even erroneous analysis results. In the present study, a modeling method employing multiple reference frames for dynamic equilibrium and modal analyses of rotating structures is presented. The superiority of the proposed modeling method over the single reference frame modeling method is verified with numerical examples.

A reduced-order analytical model for the nonlinear dynamics of a class of flexible multi-beam structures

Nonlinearities in the differential equations of motion of dynamical systems can play, under certain conditions, such a dominant role that the motion described by linearized differential equations bears no resemblance to the actual motion exhibited by the systems. For a structure, nonlinearities are due to material behavior and to deformation. The latter are called “geometric nonlinearities” and, even for linear (i.e., Hookean) materials and small deformations, their effect can be dramatic. To investigate the nonlinear behavior of a dynamical system by making use of analytical techniques, one must start the analysis by formulating a set of mathematically consistent differential equations of motion for the system. Furthermore, the equations must be cast in a form that makes them amenable to the application of known analytical methods, such as perturbation techniques, to investigate the motion. The work presented in this paper addresses the formulation of such equations for a class of multi-beam structures. Each beam in the structure may have arbitrary cross section variation along its span, but behaves as inextensional. The structure may have any number of beams and supports, and may carry any number of lumped masses along its span.

Geotail observations of ion velocity distributions with multi‐beam structures in the post‐plasmoid current sheet

Two unusual ion velocity distributions were observed by the Geotail LEP instrument in the distant current sheet just after the passage of plasmoids. These ion distributions are particular in that in each case there are two or three well‐ordered, cold and dense beams embedded in a hot, tenuous component. The beams are roughly aligned in the convection direction and flow duskward and tailward with large velocities. When those distributions were observed, the spacecraft was very close to the middle plane of the current sheet, where the Bx and Bz components of the magnetic field were quite small and at the same time Bx was the dominant component. The present observations reveal much more complicated pattern of the ion velocity distributions in the current sheet during the course of substorm than as expected.

Asymptotic stability of the Euler-Bernoulli beam with boundary control

We show that under appropriate conditions a Euler-Bernoulli beam, clamped at one end, with boundary controls at the other end, can be made uniformly, exponentially stable. The method can also be applied to multibeam structures with controls either at the end or somewhere along the structure.

Optical branching effect in Ti:LiNbO_3 waveguides: near-field pattern studies

The paper presents a detailed study of a single optical beam splitting into several beams (the branching effect) in photorefractive sensitive Ti:LiNbO3 optical slab waveguides. The near-field patterns of the multibeam structures are presented for different values of optical power coupled into TE guided modes of different orders. The process of partial recovery of the optically damaged waveguide (the partial shrinking of the multibeam bundle created) is also described.