Contribution Of Modes Research Articles

Evaluation of recursive Bayesian filters for modal contribution estimation in high-tech compliant mechanisms

This study evaluates three recursive Bayesian input and state estimation algorithms, as introduced in the field of Structural Health Monitoring, for estimating modal contributions for high-tech compliant mechanisms. The aim of estimating modal contributions is the use for active vibration control. High-tech compliant motion stages allow for different sensor configurations, making new and interesting performance evaluations of these filters possible. The algorithms used, namely, the Augmented Kalman Filter (AKF), Dual Kalman Filter (DKF) and Gilijns de Moor Filter (GDF) are implemented on a compliant motion stage for guidance flexure deformation estimation. Our results show the GDF performs overall best, with good estimation performance and real-world tuning capability.

Qualitative Considerations on the Influence of the Gases Water Vapor and Carbon Dioxide on the Global Environmental Temperature from the Point of View of Textbook Knowledge

The solar radiation that hits the Earth conditions the dynamic equilibrium that prevails on our planet. Consideration of basic physical-chemical knowledge shows that this equilibrium can be changed only by additional energy input or prolongation of the interaction time solar radiation—Earth matter. The contribution of H2O(g) and CO2 to the protection of the earth against excessive warming is experimentally and by basic laws of nature secured. For a greenhouse effect, a part of the earth radiation must be radiated back to the earth and then into space. If one understands the earth radiation as radiation of a black body with the average global environmental temperature, from all vibrations normal modes of the gases H2O(g) and CO2 only the bending mode of CO2 with 4% of the solar constant can contribute beside the rotational modes of the water to the greenhouse effect. The contributions of the normal modes of H2O(g) and CO2 to the heat capacity of the atmosphere are negligible. Therefore, in agreement with studies by K. Ångström, CO2 contributes only to the stabilization of the global environmental temperature. Whether the use of renewable energies can actually at least mitigate the increase of the environmental temperature is by no means certain but must be examined for each individual case. With certainty, this goal can only be achieved by reducing the energy consumption of mankind.

Radiative heat exchange driven by acoustic modes between two solids at the atomic scale

In the near field (for separation distances smaller than the thermal wavelength, of the order of some microns at ambient temperature), the radiative heat flow between two solids at different temperatures can exceed the blackbody limit by several orders of magnitude. Furthermore, at the atomic scale, close to contact, the vibrational modes of the crystal lattice are expected to play an important role in the heat exchange. While the contribution of acoustic phonons tunnel-ing due to Van der Waals forces and electrostatic interactions near the surface has been investigated [1–5], the radiative contribution of the acoustic modes has been neglected so far. Under the local assumption (wavevector k ≈ 0), optical modes are independent from the acoustic modes, and are the sole responsible for the thermal radiation for distances larger than a few nanometers. However at subnanometer distances, the electromagnetic response of solids is nonlocal (k ≠ 0) and both acoustic and optical modes are coupled, contributing together to the radiative heat exchange. In order to demonstrate the role of this contribu-tion, we calculate [6] the nonlocal dielectric permittivity of magnesium oxide (MgO) using molecular dynamics. In conjunction with fluctuational electrody-namics calculations, we are able to highlight the role of radiation between two polar crystals produced by acoustic modes compared to the expected results from the local theory. We show that this additional contribution can become the dominant channel for radiative heat exchanges at atomic scale in the cryo-genic regime (below 100 K). Since the acoustic vibration modes can be excited with the help of piezoelectric transducers, our work opens the possibility to the control of radiative heat exchanges at atomic scale using external mechanical actuation.

Tensile strain and finite size modulation of low lattice thermal conductivity in monolayer TMDCs (HfSe2 and ZrS2) from first-principles: a comparative study.

With excellent physical and chemical properties, 2D TMDC materials have been widely used in engineering applications, but they inevitably suffer from the dual effects of strain and device size. As typical 2D TMDCs, HfSe2 and ZrS2 are reported to have excellent thermoelectric properties. Thermal transport properties have great significance for exerting the performance of materials, ensuring device lifetime and stable operation, but current research is not detailed enough. Here, first-principles combined with the phonon Boltzmann transport equation are used to study the phonon transport inside monolayer HfSe2 and ZrS2 under tensile strain and finite size, and explore the band structure properties. Our research shows that they have similar phonon dispersion curve structures, and the band gap of HfSe2 increases monotonically with the increase of tensile strain, while the bandgap of ZrS2 increases and then decreases with the increase of tensile strain. Thermal conductivity has obvious strain dependence: with the increase of tensile strain, the thermal conductivity of HfSe2 gradually decreases, while that of ZrS2 increases slightly, and then gradually decreases. Reducing the system size can limit the contribution of phonons with a long mean free path, significantly decreasing thermal conductivity through the controlling effect of tensile strain. The mode contribution of thermal conductivity is systematically investigated, and anharmonic properties including mode and frequency-level scattering rates, group velocity and Grüneisen parameters are used to explain the associated mechanism. Phonon scattering processes and channels in various cases are discussed in detail. Our research provides a detailed understanding of the phonon transport and electronic structural properties of low thermal conductivity monolayers of HfSe2 and ZrS2, and further completes the study of thermal transport of the two materials under strain and size tuning, which will provide a foundation for further popularization and application.

Practical Suggestions for Specifications for the Vibration Serviceability of Footbridges Based on Two Recent Long-Span Footbridges

Human-induced vibration serviceability often governs the dynamic design of modern footbridges. Many design specifications have been issued, applying different load models, response calculation strategies and comfort limits (three key aspects), which may inevitably cause inconsistent evaluation results for the same structure. It requires the comparison of specifications, and better practical suggestions proposed, to guide the vibration serviceability of footbridges. This article performs the most comprehensive evaluation of specification performance. It includes six current specifications: the UK NA, the HiVoSS guidelines, the Sétra guidelines, the ISO standard, the American guide and the Chinese standard. After comparison of the three key aspects, practical suggestions are proposed. Evaluations are made based on two recent long-span footbridges in China. The footbridges are found to be low in damping ratios and there exist low and close natural frequencies, even closely-spaced modes. Vibration serviceability assessments show obviously inconsistent results owing to differences in the three key aspects. Furthermore, owing to contributions of closely-space modes, the total structural responses are significantly larger than the single dominating mode (often applied in response calculations according to the specifications). Thus, the article suggests considering the contributions of multiple modes in designing for the vibration serviceability of long-span footbridges. Finally, considering large vibrations, mitigation measures are applied. Instead of applying external dampers, e.g. tuned mass dampers (which may add to the economic costs of the structure), effective vibration mitigation measures are suggested by changing structural parameters. Except for the traditionally applied wind-resistant cables, a steel box girder with infilled concrete is applied to the main girder, replacing the original design. As a result, vibration amplitudes are significantly reduced. Footbridges are also made less sensitive to human-induced excitation.

Two-point function of a quantum scalar field in the interior region of a Kerr black hole

Quantum field effects on a classical background spacetime may be obtained from the semiclassical equations of General Relativity with the expectation value of the stress-energy tensor of the quantum field as a source. This expectation value can be calculated from Hadamard's elementary two-point function, which in practice is given in terms of sums of products of field modes evaluated at two spacetime points. We derive expressions for the two-point function for a massless scalar field in the Unruh state on a Kerr black hole spacetime. Our main result in this paper is a novel expression valid when the two points lie inside the black hole; we also (re-)derive, using a new method, the known expression valid when the two points lie outside the black hole. We achieve these expressions by finding relationships between Unruh modes, defined in terms of the retarded Kruskal coordinate, and Eddington modes, defined in terms of the Eddington coordinates. While our starting expression for the two-point function is written in terms of the Unruh modes, we give our final expression in terms of the Eddington modes, which have the computational advantage that they decompose into factors that obey ordinary differential equations. In an appendix we also derive expressions for the bare mode contributions to the flux components of the stress-energy tensor for a minimally-coupled massless scalar field inside the black hole. Our results thus lay the groundwork for future calculations of quantum effects inside a Kerr black hole.

Effects of circular plates on forced vibration of orthogonally stiffened cylindrical shell in wavenumber-frequency domain

A modified variational method for orthogonally stiffened cylindrical shell coupled with multiple circular plates is proposed in this paper. A unified variational modelling procedure is developed to accommodate three dimensional deformation restrains between the shell and substructures, including circular plates, ring and axial stiffeners. The vibration displacements are analytically expanded with Fourier series in the circumferential direction. The input energies due to external loads and the responses of the shell in circumferential wavenumber domain can be naturally obtained, which significantly facilitate the effect analysis of substructures. Close orthogonal independent polynomials are employed for the displacements in the axial direction to achieve satisfactory solutions. The convergence and accuracy of the present method are validated by comparing the analytical and numerical results. The effects of circular plates on vibration responses under different external forces are investigated. The contributions of different circumferential modes to the forced responses are analyzed, and reasons for the effects of the circular plates are then revealed in the circumferential wavenumber-frequency domain. The results indicate that the circular plates not only lead to frequency shift, but also coupling of the circumferential modes of the shell, which will respectively account for frequency shifts and increase of the resonance peaks.

Prediction of the Influence of Higher Modes on the Dynamic Response of High-Rise Buildings Subjected to Narrow-Banded Ground Motions

This paper presents the results of a study aimed at assessing the effects of higher modes of vibration on the nonlinear dynamic response of tall framed-buildings subjected to narrow-banded motions. For this purpose, analytical models of a 20-story building were developed under the consideration of two types of hysteretic behavior and subjected to 20 seismic excitations having a dominant period of motion of 1[Formula: see text]s. While the fundamental period of vibration of the building equals 2.7[Formula: see text]s, its second period is close to 1[Formula: see text]s; as a result, the selected seismic excitations over-stimulate the participation of the second mode in the overall dynamic response of the building. The circumstances under which the contribution of higher modes gives place to an excessive response of the upper stories are identified, and quantitative measures are presented. From an engineering point of view, parameters that predict an excessive response of higher-level floors are proposed.

Automatic Generation of Local Vibrational Mode Parameters: From Small to Large Molecules and QM/MM Systems.

LModeAGen, a new protocol for the automatic determination of a nonredundant, complete set of local vibrational modes is reported, which is based on chemical graph concepts. Whereas local mode properties can be calculated for a selection of parameters targeting specific local modes of interest, a complete set of nonredundant local mode parameters is requested for the adiabatic connection scheme (ACS), relating each local vibrational mode with a normal mode counterpart, and for the decomposition of normal modes (CNM) in terms of local mode contributions, a unique way to analyze vibrational spectra. So far, nonredundant parameter sets have been generated manually following chemical intuition or from a set of redundant parameters in a trial-and-error fashion, which has hampered the study of larger systems with hundreds of parameters. LModeAGen was successfully applied for a test set of 11 systems, ranging from small molecules to the large QM (>100 atoms) subsystem of carbomonoxy-neuroglobin protein, described with a hybrid QM/MM method. The ωB97X-D/aug-cc-pVDZ, M06L/def2-TZVP, and QM/MM ωB97X-D/6-31G(d,p)/AMBER model chemistries were adopted for the description of the molecules in the test set. Our new protocol is an important step forward for a routine ACS and CNM analysis of the vibrational spectra of complex and large systems with hundreds of atoms, providing new access to important encoded electronic structure information.

Effect of heat source on kinetic energy transfer in compressible homogeneous shear turbulence

The effects of heat sources on kinetic energy transfer in compressible homogeneous shear turbulence are studied using numerical simulations at turbulent Mach numbers 0.1 and 0.4 for two levels of heat source. It is found that the strong heat source can significantly enhance both positive and negative components of subgrid-scale (SGS) kinetic energy flux and pressure–dilatation. After adding a strong heat source, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux at a low turbulent Mach number. According to the Helmholtz decomposition, we found that the solenoidal and dilatational components of pressure–dilatation and SGS kinetic energy flux are increased greatly by a strong heat source at a low turbulent Mach number. The solenoidal mode plays a dominant role in the kinetic energy transfer process, but the contribution of the dilatational mode is not negligible. The dilatational component of the production term is increased by a strong heat source at a low turbulent Mach number, providing the main source of kinetic energy to the dilatational mode. The strong heat source also enhances the kinetic energy exchange between solenoidal mode and dilatational mode through nonlinear advection at a low turbulent Mach number. Moreover, the strong heat source enhances pressure anisotropy, redistribution of the kinetic energy of two transverse components, and energy transfer from internal energy to the kinetic energy through pressure–dilatation term. At a high turbulent Mach number, the strong heat source has little impact on the solenoidal and dilatational components of kinetic energy transfer terms.

How incoming turbulence affects wake recovery of an NREL-5MW wind turbine

The present work aims at investigating the effect of inflow turbulence on the wake recovery of the NREL-5MW reference wind turbine. The wake produced by a utility-scale wind turbine invested by both a laminar uniform inflow and a turbulent flow, is analyzed by means of proper-orthogonal decomposition (POD). The considered turbine is the NREL-5MW at tip-speed ratio λ = 7 and a diameter-based Reynolds number of the order 108. The flow is simulated through Large Eddy Simulation, where the forces exerted by the blades are modeled using the Actuator Line Method, whereas tower and nacelle are modeled employing the immersed boundary method. The main flow structures identified by modal decomposition in both of the considered cases are compared, and some differences emerge, which can be of great importance for the formulation of a reduced-order model. Among the most energetic modes, a high-frequency mode directly related to the tip vortices is found only in the flow case with laminar inflow. In the presence of inflow turbulence, the most energetic modes are all composed by large-scale low-frequency structures filling the whole domain. We evaluate the contribution of each POD mode to wake recovery reconstructing the total flux of mean kinetic energy due to turbulent fluctuations on a closed surface enclosing the wake of the wind turbine. In the laminar-inflow case, we have found that the POD modes related to the tip and root vortices do not contribute positively to the wake recovery, but they rather sustains the velocity gradient, as already established by Lignarolo et al. (2015) for a wind-turbine model. Whereas, in the turbulent-inflow case, all the most energetic modes contribute positively to wake recovery. These results clearly indicate that inflow turbulence should be taken into account for accurately estimate the entrainment process in the wake of wind turbines.NREL 5MW wind turbine, POD, laminar or turbulent inflow, wake recovery, turbulent kinetic energy entrainment.

Identification of temperature-dependent elastic and damping parameters of carbon–epoxy composite plates based on experimental modal data

High-strength composite materials are receiving increased attention within the aerospace and transportation industries. These materials, although light in weight, still impart high stiffness when compared to conventional structural materials, e.g., aluminum and steel. Fibers and matrix are the basic constituents of composite materials. During high-speed maneuvering of aircraft and high-speed trains, the composite materials are subjected to dynamic loads in changing temperatures. The dynamic behavior of composites strongly depends on the ambient thermal environment. Furthermore, during the in-situ operation, the quantification of real-time dynamic loads is a challenging task. Therefore, the experimental investigation of the dynamic behavior of several carbon-fiber epoxy laminated composite plates at different temperatures, namely 0°C, 25°C, 50°C, 75°C, 100°C, and 125°C, is carried out using operational modal analysis, to identify the modal characteristics of the structure, and the temperature-dependent modal data of the tested composite plates is given in the supplementary data. The temperature-dependent elastic and damping parameters of the carbon–epoxy laminate are estimated using a genetic algorithm-based parameter identification scheme for different sets of modal contribution. A combined experimental and numerical simulation procedure is implemented to estimate deterministic material parameters at different temperatures. To obtain the in-situ material parameters for a given operating frequency range, the modal contribution is selected such that the operating frequency of interest lies within the considered resonance modes. As an example of matrix-dominated elastic parameter, the shear modulus, has been found to degrade significantly with increasing temperature, and shown a strong correlation with temperature.

Estimating Average Velocities of Particle Arrival Using the Time Duration of the Current Signal in Stochastic Blocking Electrochemistry.

In stochastic blocking electrochemistry, microparticles generate individual current steps when they adsorb on a microelectrode and decrease the current and flux of a redox mediator reacting at the surface. The amplitude of the current step informs on particle size and landing locus, while step frequency correlates with particle transport. Here, we report a new method to estimate the average arrival velocities of single rod-shaped bacteria (bacilli). The method relies on simulating the nearby threshold distance from the surface where the bacillus no longer perturbs mediator flux and the current step approaches zero. We estimated the average velocities of bacillus arrival by dividing the threshold distance over the current step duration, a parameter that here we detect for the first time and increases with bacillus length. By comparing diffusional fluctuations to bacillus average velocity, we estimated diffusion and migration contributions as a function of bacterium size. Average arrival velocities increase with bacillus length at the same time as migration intensifies and diffusion weakens. Our analysis is universal and more effective in determining transport mode contributions than the present approach of comparing theoretical and experimental step frequencies. Uncertainty in landing locus is inconsequential because the step duration used to calculate the average arrival speed already contains such information and knowing bacillus electrophoretic mobility or ζ-potential is not needed. Additionally, by simulating and assigning edge landings to the most repeated values of current steps in a recording, we obtain bacilli lengths and widths similar to scanning electron microscopy, from which we infer landing orientation.

Investigations into mode characteristics of wind fields off the Guangdong coast using Empirical Orthogonal Function

As one of the clean and renewable energy sources, wind energy has received increasing attentions from the public in recent years. Large-scale investigations into wind speeds and directions can provide guidance and reference for regional wind energy assessment. In this paper, ECMWF-ERA5 wind field data were used to explore wind field characteristics off the Guangdong coast, where Empirical Orthogonal Function (EOF) analysis was employed to characterize the spatial and temporal patterns of wind fields over a long period. The results show that: (1) According to the characteristics of wind speeds, the research domain can be divided into three major sub-domains, including the landward sub-domain where the wind speed is lower and the wind direction are highly variable, the transitional sub-domain where the wind field has a gradual trend and the wind direction are the most dispersed, and the seaward sub-domain where the wind speed is higher and the wind direction are more concentrated; (2) Variance contributions of the first EOF mode for east–west and north–south components of wind speed vectors are 99.3% and 99.5%, respectively. This indicates that the seasonal oscillation of winter–summer has a one-year cycle. Additionally, variance contributions of the second EOF mode are only 1.4% and 1.5%, respectively, showing a spring–autumn monsoonal oscillation with a six-month to one-year cycle. Variance contributions of the third EOF mode for east–west and north–south components are only 0.5% and 0.7%, respectively. This indicates that a one-year to two-year cycle of oscillations exists, which may be related to the Tropospheric Biennial Oscillation (TBO) of the inter-annual variability of the East Asian summer wind.

Transport characteristics and lattice dynamics with phonon topology accentuation in layered CuTlX (X: S, Se)

In recent years, numerous Cu-based compounds have attracted a great deal of interest for enhanced thermoelectric energy conversion. Here, we demonstrate that CuTlX (X: S, Se), a layered semiconductor, exhibits low lattice thermal conductivity (κ l ) and a high thermoelectric figure of merit (ZT), using density functional theory calculations and Boltzmann transport theory beyond relaxation time approximation. To evaluate the absolute values of thermoelectric coefficients, different scattering mechanisms such as acoustic deformation potential scattering, impurity phonon scattering, and polar optical phonon scattering are analysed. This low lattice thermal conductivity, which is complemented by a low group velocity and a low phonon lifetime, accounts for the remarkable thermoelectric efficiency in these compounds. In CuTlS, the contribution of the in-plane optical phonon mode to κ l results in a decrease in its value, which might be attributed to the occurrence of Dirac-like crossings with non-trivial topological characteristics, as corroborated by the non-zero Berry curvature value. Overall, the thermoelectric behavior of both compounds is favorable at ambient temperature. Specifically, the out-of-plane direction in CuTlSe presents elevated thermoelectric performance with a high value for the thermoelectric figure of merit, with 1.08 and 1.16 for holes and electrons, respectively, at 300 K at the optimal carrier density of 1019 cm−3 , which well aids in both the electron and phonon transport. We also undertook monolayer examinations of these compounds due to the existence of van der Waals interactions, which predicted strong thermoelectric performance for both carrier concentrations at 300 K. As a result, our study presents a theoretical prediction on transport phenomena that requires experimental verification and should motivate additional research into prospective thermoelectric materials in the same crystal family for device applications.

Recursive one-way Navier-Stokes equations with PSE-like cost

Spatial marching methods, in which the flow state is spatially evolved in the downstream direction, can be used to produce low-cost models of flows containing a slowly varying direction, such as mixing layers, jets, and boundary layers. The parabolized stability equations (PSE) are popular due to their extremely low cost but can only capture a single instability mode; all other modes are damped or distorted by regularization methods required to stabilize the spatial march, precluding PSE from properly capturing non-modal behavior, acoustics, and interactions between multiple instability mechanisms. The one-way Navier-Stokes (OWNS) equations properly retain all downstream-traveling modes at a cost that is a fraction of that of global methods but still one to two orders of magnitude higher than PSE. In this paper, we introduce a new variant of OWNS whose cost, both in terms of CPU time and memory requirements, approaches that of PSE while still properly capturing the contributions of all downstream-traveling modes. The method is formulated in terms of a projection operator that eliminates upstream-traveling modes. Unlike previous OWNS variants, the action of this operator on a vector can be efficiently approximated using a series of equations that can be solved recursively, i.e., successively one after the next, rather than as a coupled set. In addition to highlighting the improved cost scaling of our method, we derive explicit error expressions and elucidate the relationship with previous OWNS variants. The properties, efficiency, and accuracy of our method are demonstrated for both free-shear and wall-bounded flows.

High-Mobility Naphthalene Diimide Derivatives Revealed by Raman-Based In Silico Screening.

Charge transport in crystalline organic semiconductors (OSCs) is considerably hindered by low-frequency vibrations introducing dynamic disorder in the charge transfer integrals. Recently, we have shown that the contributions of various vibrational modes to the dynamic disorder correlate with their Raman intensities and suggested a Raman-based approach for estimation of the dynamic disorder and search for potentially high-mobility OSCs. In the present paper, we showcase this approach by revealing the highest-mobility OSC(s) in two series of crystalline naphthalene diimide derivatives bearing alkyl or cycloalkyl substituents. In contrast to our previous studies, Raman spectra are not measured, but are instead calculated using periodic DFT. As a result, an OSC with a potentially high charge mobility is revealed in each of the two series, and further mobility calculations corroborate this choice. Namely, for the naphthalene diimide derivatives with butyl and cyclopentyl substituents, the estimated room-temperature isotropic electron mobilities are as high as 6 and 15 cm2 V-1 s-1, respectively, in the latter case even exceeding 20 cm2 V-1 s-1 in a two-dimensional plane. Thus, our results highlight the potential of using the calculated Raman spectra to search for high-mobility crystalline OSCs and reveal two promising OSCs, which were previously overlooked.

Spurious Modes in Model Order Reduction in Variational Problems in Electromagnetics

In this work, we address an everlasting issue in model order reduction (MOR) in electromagnetics that has remained unnoticed until now. Contrary to what has been previously done, we identify for the very first time spurious modes in MOR for time-harmonic Maxwell’s equations and propose a methodology to remove their negative influence on the reduced order model (ROM) response. These spurious modes have nonzero resonance frequency and may have shown up in the past giving rise to spikes in the frequency response, in effect, deteriorating the accuracy and efficiency of the MOR process. However, they were never characterized as spurious mode contributions, rather they were most likely considered as poor localized approximation issues in the MOR process. When we try to get further physical insights from the ROM, rather than simple frequency domain data, we cannot afford any poorly localized approximation issue, that is, any spurious mode in the band of analysis. Otherwise, these mathematical, but nonphysical, modes will mislead the physical behavior of the device under analysis. A computationally inexpensive variational divergence condition is established to identify spurious modes in the band of analysis, since any physical in-band mode must be divergence-free. In addition, once a spurious mode is identified in the band of analysis, its influence is removed from the ROM by a physics-based coupling strategy. As a result, a robust spurious mode contribution-free MOR in electromagnetics is proposed. Finally, several actual microwave circuits, such as a quad-mode filter and a triple-mode triple-band filter, will illustrate the capabilities and efficiency of the proposed approach.

Feasibility of a nonlinear spectral approach for peak floor acceleration of multi-story bilinear hysteretic buildings

To protect the acceleration-sensitive non-structural components in a multi-story building, a proper seismic design of them against the peak floor acceleration (PFA) is needed. The PFA, therefore, should be estimated in advance. To efficiently estimate the PFA of multi-story buildings at the inelastic stage, a nonlinear modal combination approach is provided in this study. First, for the single-story building (single-degree-of-freedom system), a PFA spectral ratio δ, defined as the ratio between the inelastic PFA and the elastic spectral amplitude, is proposed to measure the nonlinear reductions in PFA. A series of time history analysis (THA) revealed that there is a dependable relationship between the PFA spectral ratio δ, the strength reduction factor R, the post-yield stiffness ratio α, and the period T of the structure. The scatter of δ is notably smaller than the ductility demand, showing the good feasibility of a δ-R-T-α relationship for predicting δ. Second, for the multi-story building (multi-degree-of-freedom system), the floor acceleration is decoupled in the modal space, the contribution of each mode to the elastic PFA is multiplied by δ to account for the nonlinear reduction in PFA at the inelastic stage. Here δ can be determined by an appropriate δ-R-T-α relationship, while R and α are determined via a modal pushover analysis. The modified modal contributions are combined via the complete-quadratic combination (CQC) rule, forming the inelastic CQC approach. The PFAs of some 2-, 5-, and 8-story building structures with different degrees of nonlinearity are computed via the THA and the inelastic CQC approach. Results demonstrate the satisfactory accuracy of the latter. Notably, the effects of nonlinearities associated with the higher-order modes on the nonlinear PFA are well considered in the inelastic CQC, thus the un-acceptable over-estimations of the inelastic PFA, which occurs in conventional methods, are avoided.

Optimal Design and Experimental Verification of Low Radiation Noise of Gearbox

Reducing the radiated noise of a gearbox is a difficult problem in aviation, navigation, machinery, and other fields. Structural improvement is the main means of noise reduction for a gearbox, and it is realized primarily through contribution analysis and structure optimization. However, these approaches have certain limitations. In this study, a low-noise design method for a gearbox that combines the two approaches is proposed, and experimental verification is performed. First, a finite element/boundary element model is established using a single-stage herringbone gearbox. Considering the vibration excitation of the gear system, the radiation noise of a single-stage gearbox is predicted based on the modal acoustic transfer vector (MATV) method. Subsequently, the maximum field point of the radiated noise is determined, and the acoustic transfer vector (ATV) analysis and modal acoustic contribution (MAC) analysis are conducted to determine the region that contributes significantly to the radiated noise of the field point. The optimization region is selected through the panel acoustic contribution (PAC) analysis. Next, to reduce the normal speed in the optimization region, topology optimization is performed. According to the topology optimization results, four different noise reduction structures are added to the gearbox, and the low-noise optimization models are established respectively. Finally, by measuring the radiated noise of the gearbox before and after optimization under a given working condition, the validity of the radiated noise prediction method and the low-noise optimization design method are verified by comparing the simulation and experimental data. A comparison of the four optimization models proves that the noise reduction effect can be achieved only by adding a noise reduction structure to the center of the density nephogram.