Equivalent Excitations Research Articles

Failure diagnosis for time-modulated arrays based on compressed sensing

Time-modulated arrays (TMAs) have a high design degrees of freedom (DoFs) to improve radiation performance, while they are prone to failure due to their hardware characteristics. In this article, we propose a novel technique to diagnose impaired TMAs based on compressed sensing (CS). The TMA diagnosis problem is reformulated as a sparse signal recovery problem at the center frequency and sidebands. Then, a method based on the difference of convex sets theory and sequential convex programming (DCS-SCP) is developed to implement diagnosis for impaired TMAs. Using a small number of far-field measurements at the same position but different frequencies, the joint recovery of the equivalent excitations at the center frequency and sidebands is realized by a mixed l 0 / l 2 -norm minimization method. The numerical simulation and the successful comparison with the state-of-the-art algorithms demonstrate the superiority of the proposed methods in terms of noise robustness and diagnosis accuracy.

Experimental and analytical study on the performance of wind turbine tower attached with particle tuned mass damper

According to the global wind energy council report, a dramatic increase in the annual wind installations is needed to satisfy the goal of net-zero, which means there will be a large market for wind turbine towers. Therefore, the safety and suitability of wind turbine towers must be ensured by certain methods under wind and seismic excitations for reliable wind energy production. This paper presents a comprehensive study involving experimental, analytical, and computational approaches to study the performance of the particle tuned mass damper (PTMD) that is attached to a 1/20 scaled wind turbine tower model through a shaking table test. During the test, the overall performance of PTMD is analyzed under earthquake and equivalent wind excitations. The results indicate that PTMD can significantly mitigate the dynamic responses of the tower top and tower body. Then, a parametric study of PTMD is carried out to detail its damping mechanisms. The results show that the robustness of PTMD is good, and PTMD possesses a wider vibration control frequency band. Finally, based on the experimental test, a finite element model is built, and then a comparison of experimental and numerical results is conducted to investigate the vibration reduction effect of PTMD under coupled wind and earthquake excitations. The numerical simulation and experimental results agree well, and PTMD has good vibration reduction effectiveness under coupled wind and earthquake excitations. Besides, the numerical simulation indicates that aerodynamic damping can restrain the vibration of the wind turbine tower to a certain extent. Both the experimental and numerical results indicate that the PTMD can reduce the vibration of wind turbine towers significantly under wind and earthquake excitations.

A Response Spectrum Method for Base-Isolated Structures with Equivalent Base Excitations

Base isolation is an effective seismic design strategy that has received considerable attention in recent decades. This research is dedicated to developing a response spectrum method (RSM) for analysis of base-isolated structures under seismic excitation. A novel analytical model consisting of a linear superstructure under equivalent base excitations is proposed in the present study. To determine the response spectra corresponding to the base excitations, termed as the base response spectra, a sufficient number of samples of base excitations comprising base responses need to be obtained through time-history analysis of the nonlinear base-isolated structure in conjunction with the Monte Carlo simulation (MCS). To improve the efficiency for each sample analysis, the recently proposed explicit time-domain method (ETDM) is utilized for fast analysis of the base acceleration and velocity responses with a dimension-reduced iteration scheme. Once the base response spectra are obtained, the mean peak values (MPVs) of structural responses of the linear superstructure can be conveniently evaluated through the complete quadratic combination (CQC) rule. A 4-story nonlinear base-isolated frame structure was analyzed to validate the effectiveness of the proposed analytical model and the feasibility of the present approach for seismic response analysis of nonlinear base-isolated structures.

Joint time-frequency analysis on space-time-coding digital metasurfaces

Space-time and time-varying metastructures have attracted a lot of research interest in recent years. On the other hand, digital programmable metasurfaces have also gained great attention owing to their powerful capabilities in controlling electromagnetic (EM) fields and waves in real time, which is very suitable for implementing spatiotemporal modulations in a digital manner. Accordingly, space-time-coding (STC) digital metasurfaces have recently been proposed to realize advanced manipulations of EM wavefronts and digital information, allowing simultaneous control of propagation directions in the space domain and harmonic distributions in the frequency domain. However, their instantaneous responses and the connection between the time- and frequency-domain characteristics have not yet been fully revealed. Here, we present a joint time-frequency analysis method to revisit STC digital metasurfaces, in which the time-domain instantaneous scattering patterns and frequency-domain equivalent excitations are investigated to analyze the spatial-spectral distributions of the modulated waves. This joint time-frequency analysis method helps to better explain the basic working principle of STC digital metasurfaces and is expected to facilitate more applications in wireless communications, radar, imaging, and beamforming.

Stochastic propeller force and moment reconstruction at a shaft end based on an improved Kalman filter

Measuring the unsteady hydrodynamic excitation of a marine propeller at a shaft end accurately from multiple directions is crucial for minimizing the unwanted vibration and noise of ships. Due to the synchronous loading of high static thrust and torque, an innovative piezoelectric multicomponent balance embedded into a hollow shaft end is designed. However, complex coupling between the balance and shaft structure is formed. This leads to crosstalk disturbance and a modal dynamic amplification effect on all measuring channels. To overcome this, an improved Kalman filter algorithm based on the subspace modal identification (SMI) method is established, thus allowing us to reconstruct and locate equivalent unsteady excitations accurately in multiple directions with response-only networks. The effectiveness of proposed framework is test on a simulated nonrotating shaft end system with twelve force and three acceleration response channels. The selection of the smoothing delay parameter and whether crosstalk is considered are two main factors that influence the reconstruction accuracy.

An explicit time-domain method for non-stationary random analysis of nonlinear frame structures with plastic hinges

In this study, a novel approach for random vibration analysis of nonlinear frame structures under seismic random excitations is developed. The explicit time-domain method is improved in this approach by integrating the plastic hinge model, which can simulate the nonlinear behaviors caused by material property changes. Specifically, the hysteretic system’s equation of motion is constructed using auxiliary differential equations that govern the plastic rotational displacements and their corresponding hysteretic displacements. Additionally, by introducing the concept of equivalent excitations, an explicit iteration scheme for solving the equation of the hysteretic system is developed, in which the auxiliary differential equations are solved under the assumption that the plastic rotational velocity changes linearly with time between two adjacent time instants. Finally, by combining the Monte Carlo simulation method and the proposed explicit time-domain method, the non-stationary random responses of nonlinear frame structures can be obtained. As illustrated by numerical examples, the proposed method achieves satisfactory solution accuracy and efficiency when applied to nonlinear frame structures with plastic hinges. Moreover, the proposed iterative method resolves equations involving displacements describing the frame’s global state, plastic rotational displacements, and corresponding hysteretic parameters, introducing a novel concept for solving problems with nonlinear coupled variables of multiple types.

ANALYSIS OF CALCULATION METHODS, OBTAINING ESTIMATES AND ENSURING THE ACCURACY OF SIMULATION OF CONTROL OBJECTS

Systems of linear algebraic equations are a mathematical apparatus that is widely used in solving a significant number of problems in the practical application of mathematics and engineering. The analysis of errors in solving linear algebraic equations and the sensitivity function of nonlinear systems using the method of equivalent excitations, which, in turn, makes it possible to make informed decisions on the choice and development of methods for studying the accuracy of computing devices. Methods for constructing estimates «from below» of the distribution functions of the fatal error of the numerical solution of systems of linear algebraic equations are also presented, in particular, a posteriori estimates of the effectiveness of the methods under study are analyzed.

Performance of a Cantilever Energy Harvester under Harmonic and Random Excitations

The technique of harvesting the energy from base structural vibration through a piezoelectric transducer attached at an appropriate location on the vibrating structure is gaining popularity in recent years. Although the amount of energy harvested depends on the type and magnitude of base excitation, the energy harvest under random excitation as compared to equivalent harmonic excitations is not yet well understood and is investigated in this paper through a cantilever energy harvester. Initially, the energy harvested under harmonic excitations is numerically simulated and experimentally validated under increasing base accelerations with different load resistances. Subsequently, the performance of this energy harvester is experimentally studied under random excitations. The results demonstrate that the harvested energy (a) reaches maximum value when the base excitation matches the natural frequency of the harvester, (b) increases with the increase in base accelerations irrespective of the type of excitation, and (c) increases by 2-14 times under random excitations as compared to equivalent harmonic excitations i.e. under same energy input. It is recommended that the energy harvester be used in aerospace structures where random vibration amplitude is higher, to harvest more energy.

Efficient Pencil Beam Synthesis in 4-D Antenna Arrays Using an Iterative Convex Optimization Algorithm

A novel iterative convex optimization algorithm is proposed for the efficient synthesis of 4-D antenna arrays in this paper. A general nonconvex programming problem in terms of pencil beam synthesis at the center frequency and the suppression of multiple sidebands with different time schemes is first established. In order to decrease the nonconvexity with respect to equivalent excitations, the nonconvex programming problem is then decomposed into a convex optimization problem at the center frequency and a simplified nonconvex optimization problem at sidebands. Based on the optimized results at the center frequency, an iterative convex optimization algorithm that consists in solving a sequence of convex optimization problems is adopted to solve the nonconvex optimization problem efficiently. Because of the introduction of iterative idea and convex optimization, the proposed method achieves a good tradeoff between the optimization time and the optimality of the solution for the synthesis of 4-D antenna arrays of various scales. Numerical examples of uniformly or nonuniformly spaced 4-D antenna arrays are presented to demonstrate the excellent performance of the proposed algorithm in comparison with those of the previously reported methods.

Extraordinary Enhancement of Quadrupolar Transitions Using Nanostructured Graphene

Surface plasmons supported by metallic nanostructures interact strongly with light and confine it into subwavelength volumes, thus forcing the corresponding electric field to vary within nanoscale distances. This results in exceedingly large field gradients that can be exploited to enhance the quadrupolar transitions of quantum emitters located in the vicinity of the nanostructure. Graphene nanostructures are ideally suited for this task, since their plasmons can confine light into substantially smaller volumes than equivalent excitations sustained by conventional plasmonic nanostructures. Furthermore, in addition to their geometric tunability, graphene plasmons can also be efficiently tuned by controlling the doping level of the nanostructure, which can be accomplished either chemically or electrostatically. Here, we provide a detailed investigation of the enhancement of the field gradient in the vicinity of different graphene nanostructures. Using rigorous solutions of Maxwell’s equations, as well as an...

Primary parametric resonance–primary resonance response of stiffened plates with moving boundary conditions

An approach is presented to investigate the nonlinear vibration of stiffened plates. A stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as geometrically nonlinear Euler beams. Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to the energy of the system. Besides, the effect caused by boundary movement is transformed into equivalent excitations. The primary parametric resonance–primary resonance of the stiffened plate is studied by using homotopy analysis method. Numerical examples for stiffened plates with different thicknesses of the plates are presented to discuss the amplitude–frequency and amplitude–excitation relationship of the primary parametric resonance–primary resonance. In addition, the analysis on how the damping coefficients and the transverse excitations influence amplitude–frequency curves is also carried out. Some nonlinear vibration characteristics of stiffened plates are obtained, which are useful for engineering design.

Efficient MCS for random vibration of hysteretic systems by an explicit iteration approach

A new method is proposed for random vibration anaylsis of hysteretic systems subjected to non-stationary random excitations. With the Bouc-Wen model, motion equations of hysteretic systems are first transformed into quasi-linear equations by applying the concept of equivalent excitations and decoupling of the real and hysteretic displacements, and the derived equation system can be solved by either the precise time integration or the Newmark-<TEX>${\beta}$</TEX> integration method. Combining the numerical solution of the auxiliary differential equation for hysteretic displacements, an explicit iteration algorithm is then developed for the dynamic response analysis of hysteretic systems. Because the computational cost for a large number of deterministic analyses of hysteretic systems can be significantly reduced, Monte-Carlo simulation using the explicit iteration algorithm is now viable, and statistical characteristics of the non-stationary random responses of a hysteretic system can be obtained. Numerical examples are presented to show the accuracy and efficiency of the present approach.

Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions

An approach is presented to investigate the nonlinear vibration of stiffened plates. A stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as Euler beams. Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. Besides, the effect caused by boundary movement is transformed into equivalent excitations. The first approximation solution of the non-resonance is obtained by means of the method of multiple scales. The primary parametric resonance and primary resonance of the stiffened plate are studied by using the same method. The accuracy of the method is validated by comparing the results with those of finite element analysis via ANSYS. Numerical examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary resonance. In addition, the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried out. Some nonlinear vibration characteristics of stiffened plates are obtained, which are useful for engineering design.

Phase Modulation Technique for Four-Dimensional Arrays

A novel type of four-dimensional array based on phase modulation technique named phase-modulated arrays (PMAs) is proposed in this letter. The antenna elements of PMAs are modulated by an amplitude-phase function. During each modulation period, the antenna is successively connected with two different delay lines selected by the switch and radiates in two different phases, which would generate additional equivalent phase excitations at the center frequency. By controlling the operation sequence of the two delay lines, the static excitations can be completely replaced by the dynamic ones. Therefore, beam steering can be realized at the center frequency without phase shifters. To verify its performance, PMAs are applied to synthesize low sidelobe level beam-steering patterns without phase shifters and attenuators. Simulation results illustrate that PMAs can meet the design requirement and simplify the structure of the array greatly.

Increasing the sonoporation efficiency of targeted polydisperse microbubble populations using chirp excitation

The therapeutic use of microbubbles for targeted drug or gene delivery is a highly active area of research. Phospholipid- encapsulated microbubbles typically have a polydisperse size distribution over the 1 to 10 μm range and can be functionalized for molecular targeting and loaded with drugcarrying liposomes. Sonoporation through the generation of shear stress on the cell membrane by microbubble oscillations is one mechanism that results in pore formation in the cell membrane and can improve drug delivery. A microbubble oscillating at its resonant frequency would generate maximum shear stress on a membrane. However, because of the polydisperse nature of phospholipid microbubbles, a range of resonant frequencies would exist in a single population. In this study, the use of linear chirp excitations was compared with equivalent duration and acoustic pressure tone excitations when measuring the sonoporation efficiency of targeted microbubbles on human colorectal cancer cells. A 3 to 7 MHz chirp had the greatest sonoporation efficiency of 26.9 ± 5.6%, compared with 16.4 ± 1.1% for the 1.32 to 3.08 MHz chirp. The equivalent 2.2- and 5-MHz tone excitations have efficiencies of 12.8 ± 2.1% and 15.6 ± 1.1%, respectively, which were all above the efficiency of 4.1 ± 3.1% from the control exposure.

Random Vibrations of a Cable-Stayed Bridge under Multi-Dimensional Seismic Excitations

It is a challenging problem for scientists and engineers to calculate the random vibration responses of a large scale engineering structure, during which, the calculating efficiency and accuracy are always the main concerns. In civil engineering, there are some even more difficult cases that have to be considered, such as a large span cable-stayed bridge under multi-dimensional seismic loads consisting of evolutionary random processes. In this paper, such a problem is analyzed by using equivalent excitation method, in which the equivalent excitations are constructed by using continuous wavelet transform, and the affections of multi-dimensional seismic excitations are investigated. Simulations of a typical cable-stayed bridge show some of the plausible features of the method presented.

Research on a Building under Multi-Dimensional Seismic Excitations

For a building under multi-dimensional seismic excitations, a new random vibration analysis based on equivalent excitation method is presented, in which, a new equation of motion of the building is used to depict its dynamics and kinematics features. Since most of the earth shocks are non-stationary random processes, the input power spectral density of the seismic excitations are modulated by a time varying function, and their equivalent excitations are constructed by using continuous wavelet transform, where the continuous wavelet coefficients are calculated by using scales and the evolutionary power spectral density, while the equivalent excitations are constructed by inverse continuous wavelet transform. The random vibration analysis is carried out following the procedures of the equivalent excitation method. A simulation example is given to investigate some affection of the multi-dimensional seismic inputs, especially the rotational one.

A Pattern Synthesis Approach in Four-Dimensional Antenna Arrays with Practical Element Models

This paper introduces a novel approach for the synthesis of array patterns in four-dimensional (4-D) antenna arrays, taking into account practical element models. The approach is based on the combination of the differential evolution (DE) algorithm and full-wave simulation software HFSS. The DE algorithm is used to optimize the time sequences and static phase excitations, and then the equivalent amplitude and phase excitations are transferred to HFSS automatically by an interface program. The patterns at the center frequency and sideband frequencies are all obtained through full-wave simulation of practical antenna arrays in HFSS, thus many non-ideal effects such as mutual coupling can be taken into account. Numerical simulation results for the synthesis of low sidelobe sum-difference patterns in a 16-element printed dipole linear array and a 16-element microstrip patch conformal array are presented to demonstrate the effectiveness of the proposed approach.

Dynamic equivalence, self-equilibrated excitation and Saint-Venant’s principle for an elastic strip

The distinction between the near and far-fields for a semi-infinite, elastic strip has been exploited to derive conditions under which different dynamic excitations can be considered as equivalent. These different excitations are equivalent in the sense that they produce the same displacement field far from the excited end. It is shown that dynamically equivalent excitations degenerate to statically equivalent loads in the limit of a vanishing frequency. The no-radiation condition is derived, and its relation to self-equilibrated, dynamic and static loads is presented. Dynamically equivalent excitations are utilized to formulate a dynamic version of Saint-Venant’s principle for symmetric excitations with frequencies below the first cut-off frequency of a strip. It has been shown that the requirement of self-equilibrium of a load for the decay of end effects for static fields can be deduced from the requirement of zero average power for the dynamic fields.

Diagnostics of a crack in a load coupling of a gas turbine using the machine model and the analysis of the shaft vibrations

The diagnostics of malfunctions that can cause catastrophic failures has to be made in early stage in the industrial environment. Often flexible couplings are employed in industrial rotating machines when gearboxes and heavy thermal gradients are present. The hot and cold alignment of these couplings can be very different. Severe misalignments can generate cracks in the stub shafts, which can propagate in operating condition. Owing to the flexural flexibility of the load coupling, the shaft vibrations may be not noticeably affected by some typical symptoms that usually point out the presence of a crack, like twice per revolution harmonics in the vibration spectrum. Anyhow, suitable diagnostic strategies can detect clear fault symptoms, while model-based methods can confirm the occurrence of the shaft bow induced by the progressive yielding of a load coupling due to a crack. This paper shows as a model-based diagnostic methodology would have allowed a crack in a load coupling of a gas turbine to be identified before a serious failure happened by means of the shaft vibration analysis under operating conditions and rated speed. Finally, the vibrations caused by the shaft bow due to the propagation of a crack in the stub shaft of the coupling have been simulated using suitable equivalent excitations, the magnitude and phase of which have been estimated by means of a model-based identification method.