Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

A hardening load transfer function for rock bolts and its calibration using distributed fiber optic sensing

Confinement of rock bolts by the surrounding rock formation has long been recognized as a positive contributor to the pull-out behavior,yet only a few experimental works and analytical models have been reported,most of which are based on the global rock bolt response evaluated in pull-out tests.This paper presents a laboratory experimental setup aiming to capture the rock formation effect,while using distributed fiber optic sensing to quantify the effect of the confinement and the reinforcement pull-out behavior on a more local level.It is shown that the behavior along the sample itself varies,with certain points exhibiting stress drops with crack formation.Some edge effects related to the kinematic freedom of the grout to dilate are also observed.Regardless,it was found that the mid-level response is quite similar to the average response along the sample.The ability to characterize the variation of the response along the sample is one of the many advantages high-resolution fiber optic sensing allows in such investigations.The paper also offers a plasticity-based hardening load transfer function,representing a"slice"of the anchor.The paper describes in detail the development of the model and the calibration/determination of its parameters.The suggested model captures well the coupled behavior in which the pull-out process leads to an increase in the confining stress due to dilative behavior.

Numerical modelling of resonance mechanisms in jointed rocks using transfer functions

Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions,derived from signals generated through numerical modelling.Resonance is important for a range of engineering situations as it identifies the frequency of waves which will be favourably transmitted.Two different numerical methods are used for this study,adopting the finite difference method and the combined discrete element-finite difference method.The numerical models are validated by replicating results from previous studies.The two methods are found to behave similarly and show the same resonance effects;one operating at low frequency and the other operating at relatively high frequency.These resonance effects are interpreted in terms of simple physical systems and analytical equations are derived to predict the resonant frequencies of complex rock masses.Low frequency resonance is shown to be generated by a system synonymous with masses between springs,described as spring resonance,with an equal number of resonant frequencies as the number of blocks.High frequency resonance is generated through superposition of multiple reflected waves developing standing waves within intact blocks,described as superposition resonance.While resonance through superposition has previously been identified,resonance based on masses between springs has not been previously identified in jointed rocks.The findings of this study have implications for future analysis of multiple jointed rock masses,showing that a wave travelling through such materials can induce other modes of propagation of waves,i.e.spring resonance.

Resting-state brain network remodeling after different nerve reconstruction surgeries:a functional magnetic resonance imaging study in brachial plexus injury rats

Distinct brain remodeling has been found after different nerve reconstruction strategies,including motor representation of the affected limb.However,differences among reconstruction strategies at the brain network level have not been elucidated.This study aimed to explore intranetwork changes related to altered peripheral neural pathways after different nerve reconstruction surgeries,including nerve repair,endto-end nerve transfer,and end-to-side nerve transfer.Sprague–Dawley rats underwent complete left brachial plexus transection and were divided into four equal groups of eight:no nerve repair,grafted nerve repair,phrenic nerve end-to-end transfer,and end-to-side transfer with a graft sutured to the anterior upper trunk.Resting-state brain functional magnetic resonance imaging was obtained 7 months after surgery.The independent component analysis algorithm was utilized to identify group-level network components of interest and extract resting-state functional connectivity values of each voxel within the component.Alterations in intra-network resting-state functional connectivity were compared among the groups.Target muscle reinnervation was assessed by behavioral observation(elbow flexion)and electromyography.The results showed that alterations in the sensorimotor and interoception networks were mostly related to changes in the peripheral neural pathway.Nerve repair was related to enhanced connectivity within the sensorimotor network,while end-to-side nerve transfer might be more beneficial for restoring control over the affected limb by the original motor representation.The thalamic-cortical pathway was enhanced within the interoception network after nerve repair and end-to-end nerve transfer.Brain areas related to cognition and emotion were enhanced after end-to-side nerve transfer.Our study revealed important brain networks related to different nerve reconstructions.These networks may be potential targets for enhancing motor recovery.

Heat and Mass Transfer on Non-Newtonian Peristaltic Flow in a Channel in Presence of Magnetic Field: Analytical and Numerical Analysis

A study has been arranged to investigate the flow of non-Newtonian fluid in a vertical asymmetrical channel using peristalsis. The porous medium allows the electrically conductive fluid to flow in the channel, while a uniform magnetic field is applied perpendicular to the flow direction. The analysis takes into account the combined influence of heat and mass transfer, including the effects of Soret and Dufour. The flow’s non-Newtonian behavior is characterized using a Casson rheological model. The fluid flow equations are examined within a wave frame of reference that has a wave velocity. The analytic solution is examined using long wavelengths and a small Reynolds number assumption. The stream function, temperature, concentration and heat transfer coefficient expressions are derived. The bvp4c function from MATLAB has been used to numerically solve the transformed equations. The flow characteristics have been analyzed using graphs to demonstrate the impacts of different parameters.

Two-Stream Approximation to the Radiative Transfer Equation:A New Improvement and Comparative Accuracy with Existing Methods

Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.

Effect of Mitochondrial Function of Ovarian Granulosa Cells on In Vitro Fertilization and Embryo Transfer Outcomes in Obese Polycystic Ovary Syndrome Patients

Objective:To investigate the effect of abnormal ovarian granulosa cell metabolism on in vitro fertilization and embryo transfer(IVF-ET)outcomes in obese polycystic ovary syndrome(PCOS)patients.Methods:Patients with PCOS who met the study criteria were screened according to the inclusion criteria.A total of 32 patients with obese PCOS were recruited into the study group,and 39 patients with non-obese PCOS were recruited into the control group.The general data(age,body mass index,and years of infertility),insulin resistance index(HOMA-IR),follicle-stimulating hormone(FSH),luteinizing hormone(LH),granulosa cell mitochondrial function,and IVF-ET outcome of patients in the study group and control group were retrospectively analyzed.Results:The differences in age and years of infertility between the study group and the control group were insignificant(P>0.05),and the body mass index(BMI)of the study group and control group was 30.5±1.24 kg/m2 and 22.3±1.12 kg/m2,respectively,in which the difference was statistically significant(P<0.05);the HOMA-IR of the study group was significantly higher than that of the control group(P<0.05);the reactive oxygen species(ROS)in the study group was significantly higher than that in the control group(P<0.05),and the ATP content in the study group was significantly lower than that in the control group(P<0.05);comparing the FSH and LH levels between the two groups,the difference was not statistically significant(P>0.05);the rate of IVF-ET failure was significantly higher in the study group than in the control group.Conclusion:PCOS is a complex endocrine disorder,and obesity is one of the independent risk factors for the development of PCOS.

Analysis of the optical quality by determining the modulation transfer function for anterior corneal surface in myopes

AIM: To describe the characteristics of modulation transfer function (MTF) of anterior corneal surface, and obtain the the normal reference range of MTF at different spatial frequencies and optical zones of the anterior corneal surface in myopes. METHODS: Four hundred eyes from 200 patients were examined under SIRIUS corneal topography system. Phoenis analysis software was applied to simulate the MTF curves of anterior corneal surface at vertical and horizontal meridians at the 3, 4, 5, 6, 7mm optical zones of cornea. The MTF values at spatial frequencies of 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60 cycles/degree (c/d) were selected. RESULTS: The MTF curve of anterior corneal surface decreased rapidly from low to intermediate frequency (0-15cpd) at various optical zones of cornea, the value decreased to 0 slowly at higher frequency (>15cpd). With the increase of the optical zones of cornea, MTF curve decreased gradually. 3) In the range of 3 mm- 6 mm optical zones of the cornea, the MTF values measured at horizontal meridian were greater than the corresponding values at horizontal meridian of each spatial frequency, the difference was statistically significant (P<0.05). At 7 mm optical zones of cornea, the MTF values measured at horizontal meridian were less than the corresponding values at vertical meridian at 10-60 spatial frequencies (cpd), and the difference was statistically significant in 25, 30, 35, 40, 45, 50 cpd(P<0.05). CONCLUSION: MTF can be used to describe the imaging quality of optical systems at anterior corneal surface objectively in detail.

Temperature and Water Vapor Weighting Functions from Radiative Transfer Equation with Surface Emissivity and Solar Reflectivity

Linearization of Radiative Transfer Equation (RTE) is the key step in physical retrieval of atmospheric temperature and moisture profiles from InfRared (IR) sounder observations. In this paper, the successive forms of temperature and water vapor mixing ratio component weighting functions are derived by applying one term variation method to RTE with surface emissivity and solar reflectivity contained. Retrivals of temperature and water vapor mixing ratio profiles from simulated Atmospheric Infrared Sounder (AIRS) observations with surface emissivity and solar reflectivity are presented.

Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus

Based on the fact that the real inductor and the real capacitor are fractional order in nature and the fractional calculus,the transfer function modeling and analysis of the open-loop Buck converter in a continuous conduction mode（CCM） operation are carried out in this paper.The fractional order small signal model and the corresponding equivalent circuit of the open-loop Buck converter in a CCM operation are presented.The transfer functions from the input voltage to the output voltage,from the input voltage to the inductor current,from the duty cycle to the output voltage,from the duty cycle to the inductor current,and the output impedance of the open-loop Buck converter in CCM operation are derived,and their bode diagrams and step responses are calculated,respectively.It is found that all the derived fractional order transfer functions of the system are influenced by the fractional orders of the inductor and the capacitor.Finally,the realization of the fractional order inductor and the fractional order capacitor is designed,and the corresponding PSIM circuit simulation results of the open-loop Buck converter in CCM operation are given to confirm the correctness of the derivations and the theoretical analysis.

Transfer function measurement for the SSRF SRF system

A digital transfer function measurement system has been embedded in the low-level radio frequency (LLRF) system of the storage ring of the Shanghai Synchrotron Radiation Facility. The measurement results indicate that the decreased control accuracy at high current is primarily owing to ripples from the high-voltage power supply, the transient beam loading effect, and the digital aliasing effect. The current LLRF algorithm is not able to suppress these disturbances.

Repetitive PD control strategy with inverse transfer function compensation for CVCF inverter

A novel repetitive control strategy for the output waveform of single-phase CVCF inverters is presented. In this scheme, the inverse transfer function of inverter is used as a compensator to obtain stable and satisfy harmonic rejection. Besides, PD controller is adopted to improve transient performance. Simulation and experimental results, which are gotten from a DSP-based 400Hz, 5.5KW inverter, indicate that the proposed control scheme can achieve not only low THD during steady-state operation but also fast transient response during load step change.

Modulation transfer function characteristic of uniform-doping transmission-mode GaAs/GaAlAs photocathode

The resolution characteristic can be obtained by the modulation transfer function （MTF） of a GaAs/GaA1As photocathode. After establishing the theoretical model of GaAs（100）-oriented atomic configuration and the formula for the ionized impurity scattering of the non-equilibrium carriers, this paper calculates the trajectories of photoelectrons in a photocathode. Thus the distribution of photoelectron spots on the emit-face is obtained, which is namely the point spread function. The MTF is obtained by Fourier transfer of the line spread function obtained from the point spread function. The MTF obtained from these calculations is shown to depend heavily on the electron diffusion length, and enhanced considerably by decreasing the electron diffusion length and increasing the doping concentration. Furthermore, the resolution is enhanced considerably by increasing the active-layer thickness, especially at high spatial frequencies. The best spatial resolution is 860 lp/mm, for the GaAs photocathode of doping concentration 1 ×10^19 cm 3 electron diffusion length 3.6 μm and the active-layer thickness 2 μm, under the 633-nm light irradiated. This research will contribute to the future improvement of the cathode＇s resolution for preparing a high performance GaAs photocathode, and improve the resolution of a low light level image intensifier.

Influence of heme oxygenase-1 gene transfer on the viability and function of rat islets in in vitro culture

AIM. To investigate the influence of heme oxygenase-1 （HO-1） gene transfer on the viability and function of cultured rat islets in vitro. METHODS： Islets were isolated from the pancreata of Sprague-Dawley rats by intraductal collagenase digestion, and purified by discontinuous Ficoll density gradient centrifugation. Purified rat islets were transfected with adenoviral vectors containing human HO-1 gene （Ad- HO-1） or enhanced green fluorescent protein gene （Ad- EGFP）, and then cultured for seven days. Transfection was confirmed by fluorescence microscopy and Western blot. Islet viability was evaluated by acridine orange/ propidium iodide fluorescent staining. Glucose-stimulated insulin release was detected using insulin radioimmunoassay kits and was used to assess the function of islets. Stimulation index （SI） was calculated by dividing the insulin release upon high glucose stimulation by the insulin release upon low glucose stimulation. RESULTS： After seven days culture, the viability of cultured rat islets decreased significantly （92% ± 6% vs 52% ± 13%, P 〈 0.05）, and glucose-stimulated insulin release also decreased significantly （6.47 ± 0.55 mIU/ L/30IEO vs 4.57 ± 0.40 mIU/L/3OIEO., 14.93 ± 1.17 mIU/L/30IEQ vs 9.63 ± 0.71 mIU/L/30IEQ, P 〈 0.05）. Transfection of rat islets with adenoviral vectors at an 1±10 of 20 was efficient, and did not impair islet function. At 7 d post-transfection, the viability of Ad-HO-1 transfected islets was higher than that of control islets（71% ± 15% vs 52% ± 13%, P 〈 0.05）. There was no significant difference in insulin release upon low glucose stimulation （2.8 mmol/L） among Ad-HO-1 transfected group, Ad-EGFP transfected group, and control group （P 〉 0.05）, while when stimulated by high glucose （16.7 mmol/L） solution, insulin release in Ad-HO-1 transfected group was significantly higher than that in Ad-EGFP transfected group and control group, respectively （12.50 ±2.17 mIU/L/30IEQ vs 8.87 ± 0.65 mIU/L/30IEQ, 12.50 ± 2.17 mIU/L/30IEQ vs 9.63 ± 0.71 mIU/L/30IEQ, P 〈 0.05）. The SI of Ad-HO-1 transfected group was also significantly higher than that of Ad-EGFP transfected group and control group, respectively （2.21 ± 0.02 vs 2.08 ± 0.05; 2.21 ± 0.02 vs 2.11 ± 0.03, P 〈 0.05）. CONCLUSION： The viability and function of rat islets decrease over time in in vitro culture, and heine oxygenase-1 gene transfer could improve the viability and function of cultured rat islets.

Spectrum Characteristics and Transfer Function of the Hydrograph of the Deep Aqueous System

The fluctuation of most of the hydrograph in the deep aqueous system records the fluid pulsation in lithosphere and variation of the earth's crust. Many observations have verified that groundwater is an ideal information carrier of the crust. In this paper, the series of input (precipitation, air pressure, Earth tide etc.) and output (water level, artesian flow) of the deep aqueous system are studied by using the spectrum analysis and system theory. The application concepts of transfer function and the spectral structure of the hydrograph enrich the knowledge of the deep aqueous system. Two typical spectral structures of the hydrograph of the deep aqueous system are obtained by comparing with many water-bearing systems of the Jizhong depression. One is from well Ma-17 and the other is from the well Xinze-5. Finally, the physical models of forming the spectrum of the hydrograph are constructed on the basis of the spectrum research on the deep aqueous system.

Establishment of a diatom-total phosphorus transfer function for lakes on the Songnen Plain in northeast China

To understand the relationship between planktonic diatoms and environmental variables in the lakes on the Songnen Plain,northeast(NE)China,we investigated water quality and planktonic diatoms from 71 sampling points in 27 lakes,based on which Canonical Correspondence Analysis(CCA)was conducted.The result show that planktonic diatoms displayed certain responses to environment gradients,and the total phosphorus(TP)explained the maximum variation of planktonic diatom species among the 15 environmental variables,suggesting that TP was the most important and significant environmental parameter affecting the distribution of diatom species.In addition,we established a diatom-total phosphorus transfer(DTPT)function,of which component 5 of the weighted averaging partial least squares regression(WAPLS)was chosen to and compared with a series of weighted average regression(WA)models and WA-PLS models.According to the jackknifing statistical test,the component 5 of WA-PLS models provided a lower root-mean-square error prediction(RMSEP=0.202)and a higher correlation coefficient between observation and prediction(R^2_Jack=0.759).After deletion of three outliers,the root-mean-square error prediction of the DTPT function was reduced(RMSEP=0.169)while the correlation coefficient between observation and prediction was increased(R^2_Jack=0.823).Therefore,this DTPT function performed better than other regional TP models in the world.However,it remains demanding for expanding the background dataset to improve the prediction ability of the model.

Mathematical simulations of the galvanic coupling intra-body communication by using the transfer function method

The galvanic coupling intra-body communication （IBC） was mathematically simulated based on the proposed transfer function. Firstly, a galvanic coupling IBC circuit model was developed and the corresponding parameters were discussed. Secondly, the transfer function of the galvanic coupling IBC was derived and proposed. Finally, the signal attenuation characteristics of the galvanic coupling IBC were measured along different signal transmission paths of actual human bodies, while the corresponding mathematical simulations based on the proposed transfer function were carried out. Our investigation showed that the mathematical simulation results coincided with the measured results over the frequency range of 100kHz to 5MHz, which indicated that the proposed transfer function could be useful for theoretical analysis and application of the galvanic coupling IBC.

Oxygen Atom Transfer Reaction of Manganese-oxo Corrole toward Dimethyl Sulfide: a Density Functional Study

The effects of axial ligand on the oxygen atom transfer(OAT)reaction from 5,10,15-tris(pentafluorophenyl)corrole((tpfc)MnVO)to dimethyl sulfide(DMS)have been investigated by density functional theory(DFT)calculations.Imidazole(Im),4-methylimidazole(4-MI)and pyridine(Py)were selected as the axial ligands.The results revealed that the axial ligand can form coordinate bond with(tpfc)MnVO in the transition state(TS)of the OAT reaction.The axial coordination favored charge transferring from(tpfc)MnVO to DMS,and weakened the Mn≡O bond in both singlet and triplet states.Furthermore,axial coordination can reduce the energy barrier of neutral(tpfc)MnVO from 23.62 kJ·mol^-1 to less than 3 kJ·mol^-1 in the triplet state,which is significantly lower than in the singlet state.This makes(tpfc)MnVO tend to direct the OAT reaction via triplet state pathway.On the other hand,the energy barriers of[(tpfc)MnVIO]+species from disproportionation pathway increased from 1.26 to 33.95 kJ·mol^-1 in a doublet state.This suggests axial ligands were conducive for direct(tpfc)MnVO OAT reaction pathway.

Optical Transfer Function Reconstruction in Incoherent Fourier Ptychography

An optical transfer function （OTF） reconstruction model is first embedded into incoherent Fourier ptychography （IFP）. The leading result is a proposed algorithm that can recover both the super-resolution image and the OTF of an imaging system with unknown aberrations simultaneously. This model overcomes the difficult problem of OTF estimation that the previous IFP faces. The effectiveness of this algorithm is demonstrated by numerical simulations, and the superior reconstruction is presented. We believe that the reported algorithm can extend the original IFP for more complex conditions and may provide a solution by using structured light for characterization of optical systems＇ aberrations.

Grey GM(1,1) Model with Function-Transfer Method for Wear Trend Prediction and its Application

Trend forecasting is an important aspect in fault diagnosis and work state supervision. The principle, where Grey theory is applied in fault forecasting, is that the forecast system is considered as a Grey system; the existing known information is used to infer the unknown information's character, state and development trend in a fault pattern, and to make possible forecasting and decisions for future development. It involves the whitenization of a Grey process. But the traditional equal time interval Grey GM (1,1) model requires equal interval data and needs to bring about accumulating addition generation and reversion calculations. Its calculation is very complex. However, the non equal interval Grey GM (1,1) model decreases the condition of the primitive data when establishing a model, but its requirement is still higher and the data were pre processed. The abrasion primitive data of plant could not always satisfy these modeling requirements. Therefore, it establishes a division method suited for general data modeling and estimating parameters of GM (1,1), the standard error coefficient that was applied to judge accuracy height of the model was put forward; further, the function transform to forecast plant abrasion trend and assess GM (1,1) parameter was established. These two models need not pre process the primitive data. It is not only suited for equal interval data modeling, but also for non equal interval data modeling. Its calculation is simple and convenient to use. The oil spectrum analysis acted as an example. The two GM (1,1) models put forward in this paper and the new information model and its comprehensive usage were investigated. The example shows that the two models are simple and practical, and worth expanding and applying in plant fault diagnosis.