Analytical Design Formulas Research Articles

Ultra-Wideband Vertical Transition in Coplanar Stripline for Ultra-High-Speed Digital Interfaces.

A design method for an ultra-wideband coplanar-stripline-based vertical transition that can be used for ultra-high-speed digital interfaces is proposed. A conventional via structure, based on a differential line (DL), inherently possesses performance limitations (<10 GHz) due to difficulties in maintaining constant line impedance and smooth electric field transformation, in addition to the effects of signal skews, FR4 fiber weave, and unbalanced EM interferences. DL-based digital interfaces may not meet the demands of ultra-high-speed digital data transmission required for the upcoming 6G communications. The use of a coplanar stripline (CPS), a type of planar balanced line (BL), for the vertical transition, along with the ultra-wideband DL-to-CPS transition, mostly removes the inherent and unfavorable issues of the DL and enables ultra-high-speed digital data transmission. The design process of the transition is simplified using the analytical design formulas, derived using the conformal mapping method, of the transition. The characteristic line impedances of the transition are calculated and found to be in close agreement with the results obtained from EM simulations. Utilizing these results, the CPS-based vertical transition, maintaining the characteristic line impedance of 100 Ω, is designed and fabricated. The measured results confirm its ultra-wideband characteristics, with a maximum of 1.6 dB insertion loss and more than 10 dB return loss in the frequency range of DC to 30 GHz. Therefore, the proposed CPS-based vertical transition offers a significantly wider frequency bandwidth, i.e., more than three times that of conventional DL-based via structures.

The Influence of the Flexibility of a Polymeric Adhesive Layer on the Mechanical Response of a Composite Reinforced Concrete Slab and a Reinforced Concrete Beam Girder.

This study addresses the challenges of modeling flexible connections in composite structures employing a polymeric adhesive layer. These types of connections provide a more uniform stress distribution compared to conventional rigid connectors. However, they lack standardized design rules and still require much research to sufficiently comprehend their properties. The novelty of this research lies in proposing an analytical solution to address these issues. Its aim is to investigate the influence of the stiffness of the polymer adhesive on the girder's deflection and on the maximum stresses in both the adhesive and concrete. The analyzed composite structure consists of a reinforced concrete (RC) slab and an RC beam connected with a layer of flexible polyurethane (FPU) adhesive. Analytical and numerical approaches for the description of the mechanical response of a composite bridge girder are presented. Another objective is to validate the analytical design formulas using 3D nonlinear numerical analysis, both in the case of uncracked and cracked concrete. Seven types of FPUs are tested in the uniaxial tension test, each examined at five strain rates. The obtained data is used to predict the mechanical response of the considered girder using finite element analysis (FEA) as well as with a simplified one-dimensional composite beam theory. Fair agreement is found between the FEA results and theoretical predictions. A comparison of the results obtained for these two models is performed, and the similarities and discrepancies are highlighted and discussed.

Pole-Placement-Based Calibration of an Electromagnetically Realizable Inerter-Based Vibration Absorber (IDVA) for Rotating Wind Turbine Blades

This paper deals with edgewise vibration mitigation of rotating wind turbine blades by means of inerter-based vibration absorber (IDVA), which can be realized both mechanically and electromagnetically. Introducing the electromagnetically-realizable IDVA to the blade forms a 3-degree-of-freedom (3-DOF) blade-IDVA system consisting of the rotating blade, an absorber, and a series inerter-dashpot-spring subsystem. Analytical optimal design formulas of the rotating blade-installed IDVA are then derived using a pole-placement method where the equal-modal-damping-ratio principle and the triple-root-bifurcation condition are applied. The analytical formulas show that the optimal parameters for the blade-IDVA system merely depend on the spinning speed of the rotor given the IDVA location and the absorber mass. Numerical results of the NREL 5 MW wind turbine with optimal IDVA show that optimal IDVA leads to superior performance than optimal TMD in mitigating the blade edgewise vibration and behaves nearly as same as optimal RIDTMD, along with slightly optimal damper parameters variation. This means that the inerter-dashpot-spring system can be deployed flexibly for damping edgewise vibrations of rotating blades.

Global and Local Geometrical Imperfections of Pultruded GFRP Profiles Based on a Modal Approach

The ultimate capacity of pultruded glass fibre reinforced polymer (pGFRP) profiles depends significantly on geometrical imperfections (GIs), given their sensitivity to buckling phenomena arising from both thin walls and low elastic moduli. However, GIs are not yet comprehensively addressed in design guidance. This paper proposes a new approach to characterize the initial GIs of pGFRP profiles based on a modal approach. Given the lack of comprehensive knowledge in this area, this study presents a highly accurate and robust methodology to measure GIs and dimensional deviations (DDs) in pGFRP profiles using a 3D contact coordinate measurement machine (CMM). The modal approach encompasses the measurement of dimensional parameters and a point cloud transformation that enables the assessment of GIs associated with pure buckling modes of pGFRP profiles. This procedure allows the quantification of three types of global GIs associated to (i) minor-axis (weak axis), (ii) major-axis (strong axis) bending, and (iii) twist. Additionally, the procedure also includes the assessment of local GIs, considering the wall (plate-like) imperfections. The separation of GIs into these four types (shape and amplitude) is of major relevance as its paves the way to the development of analytical design formulas for the strength prediction of pGFRP members. The approach described in this paper also serves two important purposes: (i) the statistical analysis of DDs and GIs of pGFRP members, and (ii) the identification of distinct shapes and amplitudes of GIs that form the basis for reliable design considerations of pGFRP members.

Equivalent Static Wind Load for Structures with Inerter-Based Vibration Absorbers

Equivalent Static Wind Loads (ESWL) are desired in structural design to consider peak dynamic wind effects. Conventional ESWLs are for structures without control. For flexible structures with vibration control devices, the investigation of ESWL is required. Inerter-based Vibration Absorbers (IVAs), due to the light weight and high performance, gained much research attention recently. This paper established a generic analytical framework of ESWL for structures with IVAs. The analytical optimal design formulas for IVAs with different configurations and installation locations are provided. Subsequently, the solutions to uncontrolled and controlled wind-induced responses are derived based on the filter approach. Finally, the ESWL for controlled structures are presented with a gust response factor approach. The ESWL estimation for a tall chimney controlled by IVAs is illustrated, and the results revealed a significant ESWL reduction effect of the IVAs, particularly for the cross-wind vortex resonance. In the presented framework, the conventional uncontrolled ESWL can be converted to the controlled one with a control ratio. The closed form solution of the control ratio is provided, which enables a quick estimation of ESWL for controlled structures particularly in the preliminary design stage. The presented approach has the potential to be extended to more complex structures and vibration control devices.

Designing three-level cluster randomized trials to assess treatment effect heterogeneity.

Cluster randomized trials often exhibit a three-level structure with participants nested in subclusters such as health care providers, and subclusters nested in clusters such as clinics. While the average treatment effect has been the primary focus in planning three-level randomized trials, interest is growing in understanding whether the treatment effect varies among prespecified patient subpopulations, such as those defined by demographics or baseline clinical characteristics. In this article, we derive novel analytical design formulas based on the asymptotic covariance matrix for powering confirmatory analyses of treatment effect heterogeneity in three-level trials, that are broadly applicable to the evaluation of cluster-level, subcluster-level, and participant-level effect modifiers and to designs where randomization can be carried out at any level. We characterize a nested exchangeable correlation structure for both the effect modifier and the outcome conditional on the effect modifier, and generate new insights from a study design perspective for conducting analyses of treatment effect heterogeneity based on a linear mixed analysis of covariance model. A simulation study is conducted to validate our new methods and two real-world trial examples are used for illustrations.

A Compact Symmetrical Single-Cell Bidirectional Absorption Common-Mode Filter

A novel circuit with two mirror symmetry planes is proposed to synthesize bidirectional absorption common-mode filters (A-CMFs). In contrast to the literature, this proposed circuit first realizes bidirectional A-CMFs in only one stage (also called a single cell) featuring a compact size. Based on the symmetry property, bidirectional common-mode (CM) noise absorption can be achieved in the proposed single-cell circuit. Analytical design formulas have been found; thus, all circuit parameters can be straightforwardly determined. To validate the proposed circuit, two configurations are developed for CM noise absorption in the 2.4-GHz industrial, scientific, and medical (ISM) band. One uses a meander differential pair with a slotline, and the other applies a straight differential pair with a meander asymmetrical coplanar strip (MACPS). To obtain a better differential-mode (DM) signal integrity and 43&#x0025; size reduction, the latter one, MACPS-type A-CMF, is fabricated and measured. The measurement results show that <inline-formula> <tex-math notation="LaTeX">$\vert S_{\text {cc21}}\vert $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\vert S_{\text {cc12}}\vert $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\vert S_{\text {cc11}}\vert $ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\vert S_{\text {cc22}}\vert $ </tex-math></inline-formula> are less than &#x2212;10 dB from 2.37 to 2.76 GHz to have the bidirectional CM absorption efficiency of more than 80&#x0025;, and the &#x2212;3-dB bandwidth of DM insertion loss reaches 7.83 GHz. In the time domain, the measured eye diagram of the proposed A-CMF is identical to that of a reference board for data rates up to 20 Gb/s. Above all, having a cost advantage, a compact size of <inline-formula> <tex-math notation="LaTeX">$0.0317\lambda _{\text {g}}^{{2}}$ </tex-math></inline-formula> in a two-layer printed circuit board (PCB) is presented.

Targeted modal response control of structures using inerter systems based on master oscillator principle

Although the first modal response generally dominates in structural vibration control, higher-order mode control or multiple-mode control should also be taken into account when higher-order modes are excited. An effective way to accomplish multiple-mode control is to resort to inertial vibration absorbers, wherein the inerter serves as a two-terminal device with dynamic mass amplification and damping enhancement effects. Although previously published studies focused on inerter-based multiple-mode control, analytical design formulae have not been proposed owing to the peculiar mechanism of the inerter. Inspired by the two-terminal, relative-acceleration-related characteristics of the inerter, this study proposes a closed-form design formulation to identify the parameters of inerter systems to achieve targeted multiple-mode control. In this method, the relative deformation at the installation location is considered as the master degree-of-freedom, and the shape of the targeted control mode is considered as a structural deformation shape. In this way, by transforming the complex original structure into a master oscillator with the inerter, the parameters needed for the targeted-mode control can be easily determined based on the use of closed-form design formulae. The proposed targeted control method is applied to a benchmark 10-story building to illustrate how the parameters of inerter systems are designed by the proposed demand-oriented, targeted control method. The comparative analyses between the proposed and previous methods are conducted to demonstrate its superiority. The reductions of the designed inertances compared with alternative methods exceed 90%. Results show that the designed inerter systems can accurately and efficiently realize the targeted control of specific, multiple modal responses. The proposed method is proved to yield a high-precision, targeted-mode control effect, and requires relatively low computational effort. Therefore, it can be easily implemented in an inerter-based, multiple-mode control system.

Load transfer mechanism of an unwelded, unbolted, grouted connection for prefabricated square tubular columns under axial loads

This study develops a novel unwelded, unbolted, ultrahigh-performance fibre-reinforced concrete (UHPFRC) grouted connection for prefabricated square tubular composite columns. Herein, eight full-scale columns with UHPFRC grouted connections are tested to investigate their ultimate tensile and compressive resistance. The test results show that the novel connections exhibit good tensile and compressive resistance and structural stiffness. The primary failure modes are punching shear of the end plate, welding fracture at the inner tube, tube yielding and local buckling of the steel tube. The test specimens are simulated using finite element (FE) analysis in ABAQUS. The experimental and simulated results are in good agreement, indicating that the FE simulations can capture the observed failure modes and ultimate tensile and compressive resistance. Thereafter, existing analytical design formulas are evaluated to assess their suitability to predict the compressive and tensile resistance of prefabricated tubes with/without the novel grouted connections. A good agreement between the formula predictions and the test results are observed. These analytical formulas have the potential to be used in the design of the novel unwelded, unbolted, UHPFRC grouted connections for prefabricated steel, reinforced concrete and steel–concrete composite columns.

Development of a WCLL DEMO First Wall design module in the SYCOMORE system code interfaced with the neutronic one

The pre-conceptual design of the DEMOnstration reactors has already started and several tokamak configurations have to be tested to find the best design by exploring different design parameters. Fast simulations involving the different components behavior must be performed. Within the European framework, SYCOMORE (SYstem COde for MOdelling tokamak REactor) is developed by CEA for this purpose. The Breeding Blanket (BB) facing the plasma is a key component in DEMO ensuring tritium self-sufficiency, shielding against neutrons and heat extraction for electricity production. Several BB concepts are being studied, among which the Water Cooled Lithium Lead (WCLL) one. SYCOMORE includes several specific modules in Python linked together, one of which has been developed to define a suitable design of the WCLL Breeding Blanket and is presented in this paper.The method to define automatically the WCLL First Wall (FW) design using analytical design formulae starting from thermo-hydraulic and thermo-mechanical considerations as well as design criteria coming from Codes & Standards (C&S) is presented. Furthermore WCLL FW design obtained with SYCOMORE is compared to Finite Elements (FE) analyses of the DEMO WCLL BB.Finally, a coupling between thermo-mechanics and neutronics is implemented, several iterations are necessary to obtain a converged design. Neutronic block evaluates the radial build, the BB tritium production, and the nuclear heating in the FW and the Breeding Zone (used by thermo-mechanical block). Thermo-mechanical module gives the design data (FW thickness, compositions, etc.) to the neutronic block.

Optimal design based on analytical solution for storage tank with inerter isolation system

An optimal design method based on closed-form analytical solutions is proposed for a liquid storage tank with inerter isolation system. The storage tank is modeled accounting for the flexibility of the tank wall, and isolated by the inerter isolation system composed of an inerter, a damping element, and a spring element connected between the same two terminals in parallel. The stochastic response of the storage tank with inerter isolation system, in terms of sloshing height and isolation displacement, is derived in closed form under the assumption of white-noise excitation. These analytical results are then used in an extensive parametric analysis to investigate the response variation pattern with respect to changes in the parameters of inerter system. In the extremum condition that represents the most efficient parameter set of inertance-mass ratio and damping ratio for response mitigation, an optimal design method is developed by exploiting a performance-demand-oriented design philosophy. The optimal design formulae of the inerter system are derived on the basis of target sloshing height mitigation ratio in analytical form. Moreover, a series of examples are provided to verify the proposed analytical design formulae and design criterion. Based on results from response history analysis under both artificial and natural ground motion records, the design method proves to be effective to meet the desired demand of sloshing height response, while simultaneously reducing base shear force and isolation displacement. The derived analytical design formulae are practical and convenient for preliminary design purposes and substantially explain the mechanism of inerter system for vibration control of liquid storage tank.

Development of helium coolant DEMO first wall model for SYCOMORE system code based on HCLL concept

The conceptual design of the demonstration fusion power reactor, known as DEMO, is ongoing and several reactor configurations have to be investigated by exploring different design parameters. For these reasons, within the European framework, systems codes like SYCOMORE (SYstem COde for MOdelling tokamak REactor) have been developed. SYCOMORE includes several specific modules, one of which is aimed to define a suitable design of the helium breeding blanket. The research activity has been devoted to improve the method to define automatically the First Wall design starting from thermal-hydraulic and thermo-mechanical considerations, using analytical design formulae and, also, taking into account the design criteria coming from Codes&Standards. Thanks to these considerations, it has been possible to derive the first dimensions of the First Wall channels from which all the other characteristics are deducted. Afterwards, it has been assessed the thermal and mechanical field using a theoretical approach. Therefore, in order to compare and validate the results, a 3D geometric model has been created and FEM analyses have been carried out finding out very satisfying results with maximum error of 6.06% for the thermal analysis while a maximum error of 20% for primary and secondary stresses.

Tunable Wilkinson Power Divider Utilizing Parallel-Coupled-Line-Based Phase Shifters

A tunable Wilkinson power divider (WPD) utilizing parallel-coupled-line-based phase shifters (PSs) is designed in this letter. With the derived analytical design formulas, the adopted 90°-PS possesses tunable center frequency and controllable impedance by adjusting the two embedded varactors and features 0.5–1.3 GHz tuning range (88.9% tunability). Taking advantage of the two tunable PSs in replace of the two quarter-wave transformers among the conventional WPD, the divider can be realized with satisfactory tunability. The measured results validate the feasibility of the design approach.

Analytical model and design formulae of circular CFSTs under axial tension

A circular concrete-filled steel tube (CCFST) component is subjected to tension in certain practical engineering projects. Several past experimental programs have stressed that the apparent strength and stiffness enhancement phenomena observed in tensile circular steel tubes can be attributable to the filled concrete. In this study, an analytical model for describing the strength and stiffness enhancement of the circular steel tubes is developed. The interface performance between the steel tube and filled concrete is considered in the model. Based on the proposed analytical model, simplified design formulae for strength and stiffness enhancement coefficients are proposed. These design formulae indicate that the confining and fibre-reinforcing effects lead to the strength improvement, while the confining effect, fibre-reinforcing effect, and tension-stiffening effects all contribute to the stiffness enhancement. Then, a design procedure for determining the axial tensile strength and stiffness of CCFSTs is provided, and a design example is also demonstrated. The accuracy of both the proposed analytical model and design formulae are validated by the results of two groups of axial tension tests, which demonstrates that the full-process load-strain behaviour can be accurately captured by a bilinear model based on the proposed analytical formulae. Finally, analytical solutions for the longitudinal stress distributions of the steel tube and filled concrete are provided for a better understanding of the tension-stiffening effect. In addition, the contributions of different effects to strength and stiffness enhancements are quantitatively evaluated for all the test specimens.

Research on analytical model and design formulas of permanent magnetic bearings based on Halbach array with arbitrary segmented magnetized angle

The bearing capacity of permanent magnetic bearings can be improved efficiently by using the Halbach array magnetization. However, the research on analytical model of Halbach array PMBs with arbitrary segmented magnetized angle has not been developed. The application of Halbach array PMBs has been limited by the absence of the analytical model and design formulas. In this research, the Halbach array PMBs with arbitrary segmented magnetized angle has been studied. The magnetization model of bearings is established. The magnetic field distribution model of the permanent magnet array is established by using the scalar magnetic potential model. On the basis of this, the bearing force model and the bearing stiffness model of the PMBs are established based on the virtual displacement method. The influence of the pair of magnetic rings in one cycle and the structure parameters of PMBs on the maximal bearing capacity and support stiffness characteristics are studied. The reference factors for the design process of PMBs have been given. Finally, the theoretical model and the conclusions are verified by the finite element analysis.

Perfect magnetic mirror and simple perfect absorber in the visible spectrum

Known experimental artificial magnetic conductors for terahertz and optical frequencies are formed by arrays of nanoparticles of various shapes. In this paper, we show that artificial magnetic conductors for the visible spectrum can be realized as simple, effectively quasistatic resonating structures, where the effective inductance is due to the magnetic flux inside a uniform metal substrate, and the effective capacitance is due to electric polarization of a thin uniform dielectric cover. To illustrate the main potential application of artificial magnetic conductors, we concentrate on the perfect-absorption regime, achieved by adjusting the loss factor of the artificial magnetic conductor to match its real input impedance to free space. We provide approximate analytical design formulas and introduce a simple equivalent circuit to explain the physical mechanism of emulation of magnetic response and perfect absorption of light. A prototype of a nearly perfect absorber for optical (from green to ultraviolet) frequencies is designed and experimentally tested. The results confirm the theoretical predictions and show polarization insensitivity and angular independence of response in a wide range of incidence angles.

PROPAGATION AND RADIATION CHARACTERISTICS OF MULTILAYER COUPLED-LINE BANDPASS FILTERS USING CONDUCTOR-BACKED COPLANAR TRANSMISSION LINES

This paper presents the analytical design formulas for the bandpass filters which are built on the asymmetrically coupled-line conductor-backed coplanar transmission lines (CBCTLs) in multilayer configuration. The full-wave simulation is employed to characterize the far-field patterns of space-wave and surface-wave radiations as well as the frequency-dependent conductor, dielectric, and radiation losses. Good agreement among the results of full-wave simulation, transmission-line model, and measurement justifies the design procedure and validates the analytical design formulas. By properly placing the dielectric materials in multilayer configuration, a bandpass filter for minimizing the radiated power loss and improving the stopband characteristic can be achieved.

A Critical Investigation of Coupled Inductors SEPIC Design Issues

This paper discusses design issues of single-ended primary-inductor converter (SEPIC) with coupled inductors (CIs). The main investigation is focused on the correlation existing among the size of coupling capacitor, the magnetic coupling factor of CIs, the voltage conversion ratio, and the amplitude of peak-to-peak (pk-pk) ripple current in the input and output ports of the CIs. It is shown how the above elements must be properly correlated to prevent large input and output ripple currents, particularly if tightly coupled inductors are used. Analytical design formulas for the coupling capacitor are applied to the design of a low-power SEPIC. Simulations and experimental measurements prove the validity of the model predictions and the reliability of related design rules.

Optical isolation via unidirectional resonant photon tunneling

We show that tri-layer structures combining epsilon-negative and magneto-optical material layers can exhibit unidirectional resonant photon tunneling phenomena that can discriminate between circularly polarized (CP) waves of given handedness impinging from opposite directions, or between CP waves with different handedness impinging from the same direction. This physical principle, which can also be interpreted in terms of a Fabry-Perot-type resonance, may be utilized to design compact optical isolators for CP waves. Within this framework, we derive simple analytical conditions and design formulae, and quantitatively assess the isolation performance, also taking into account the unavoidable imperfections and nonidealities.

Ungrounded composite right-/left-handed metamaterials: design, synthesis and applications

The design of ungrounded meander line inductors (UMIs) and ungrounded interdigital capacitors (UICs) employed in the practical realisation of a planar ungrounded composite right-/left-handed (UCRLH) metamaterial is presented. Accurate lumped-element circuit models are proposed based on partial element theory and conformal mapping method. New and accurate analytical design formulas, for both the UMI and the UIC at very high frequency and ultra high frequency bands are derived and successfully validated through a proper comparison with the existing measurement data and the results obtained with the full wave method of moments. Further insight is sought through the investigation of the resonance mechanism of a printed dipole antenna loaded with UCRLH metamaterial cells. A prototype of the loaded dipole is fabricated to confirm and validate the theoretical calculations. The experimental results are found to be in good agreement with the theoretical calculations.