Advancement in utilization of magnetic resonance imaging and biomarkers in the understanding of schizophrenia

Historically,psychiatric diagnoses have been made based on patient’s reported symptoms applying the criteria from diagnostic and statistical manual of mental disorders.The utilization of neuroimaging or biomarkers to make the diagnosis and manage psychiatric disorders remains a distant goal.There have been several studies that examine brain imaging in psychiatric disorders,but more work is needed to elucidate the complexities of the human brain.In this editorial,we examine two articles by Xu et al and Stoyanov et al,that show developments in the direction of using neuroimaging to examine the brains of people with schizo-phrenia and depression.Xu et al used magnetic resonance imaging to examine the brain structure of patients with schizophrenia,in addition to examining neurotransmitter levels as biomarkers.Stoyanov et al used functional magnetic resonance imaging to look at modulation of different neural circuits by diagnostic-specific scales in patients with schizophrenia and depression.These two studies provide crucial evidence in advancing our understanding of the brain in prevalent psychiatric disorders.

Temporal dynamics of neonatal hypoxic-ischemic encephalopathy injuries on magnetic resonance imaging

Moderate to severe perinatal hypoxic-ischemic encephalopathy occurs in~1 to 3/1000 live births in high-income countries and is associated with a significant risk of death or neurodevelopmental disability.Detailed assessment is important to help identify highrisk infants,to help families,and to support appropriate interventions.A wide range of monitoring tools is available to assess changes over time,including urine and blood biomarkers,neurological examination,and electroencephalography.At present,magnetic resonance imaging is unique as although it is expensive and not suited to monitoring the early evolution of hypoxic-ischemic encephalopathy by a week of life it can provide direct insight into the anatomical changes in the brain after hypoxic-ischemic encephalopathy and so offers strong prognostic information on the long-term outcome after hypoxic-ischemic encephalopathy.This review investigated the temporal dynamics of neonatal hypoxic-ischemic encephalopathy injuries,with a particular emphasis on exploring the correlation between the prognostic implications of magnetic resonance imaging scans in the first week of life and their relationship to long-term outcome prediction,particularly for infants treated with therapeutic hypothermia.A comprehensive literature search,from 2016 to 2024,identified 20 pertinent articles.This review highlights that while the optimal timing of magnetic resonance imaging scans is not clear,overall,it suggests that magnetic resonance imaging within the first week of life provides strong prognostic accuracy.Many challenges limit the timing consistency,particularly the need for intensive care and clinical monitoring.Conversely,although most reports examined the prognostic value of scans taken between 4 and 10 days after birth,there is evidence from small numbers of cases that,at times,brain injury may continue to evolve for weeks after birth.This suggests that in the future it will be important to explore a wider range of times after hypoxic-ischemic encephalopathy to fully understand the optimal timing for predicting long-term outcomes.

Magnetic resonance imaging evaluation and nuclear receptor binding SET domain protein 1 mutation in the Sotos syndrome with attention-deficit/hyperactivity disorder

Sotos syndrome is characterized by overgrowth features and is caused by alterations in the nuclear receptor binding SET domain protein 1 gene.Attentiondeficit/hyperactivity disorder(ADHD)is considered a neurodevelopment and psychiatric disorder in childhood.Genetic characteristics and clinical presentation could play an important role in the diagnosis of Sotos syndrome and ADHD.Magnetic resonance imaging(MRI)has been used to assess medical images in Sotos syndrome and ADHD.The images process is considered to display in MRI while wavelet fusion has been used to integrate distinct images for achieving more complete information in single image in this editorial.In the future,genetic mechanisms and artificial intelligence related to medical images could be used in the clinical diagnosis of Sotos syndrome and ADHD.

High-order plasmon resonances in an Ag/Al_2O_3 core/shell nanorice

Using numerical simulation, we investigate the high-order plasmon resonances in individual nanostructures of an Ag nanorice core surrounded by an Al2O3 shell. The peak positions of localized surface plasmon resonances （LSPRs） are red-shifted exponentially with the increase of the dielectric shell thickness. This is due to the exponential decay of electromagnetic field intensity in the direction perpendicular to the interface. This exponential red-shift depends on the wavelength of the resonance peak instead of the resonance order. In addition, we find that the LSPRs in an Ag nanorice of 60-nm width can be perfectly described by a single linear function. These features make nanorice an ideal platform for sensing applications.

Performance analysis of surface plasmon resonance sensor with high-order absentee layer

A surface plasmon resonance （SPR） sensor with a high-order absentee layer on the top of metallic film is proposed. The performance of the SPR sensor with NaCl, MgO, TiO2 or AlAs high-order absentee layer is analyzed theoretically. The results indicate that the sensitivity and the full width at half maximum of those SPR sensors decrease with the increasing of the order of absentee layer, but the variation of the figure of merit （FOM） depends on the refractive index of absentee layer. By improving the order of absentee layer with high-refractive-index, the FOM of the SPR sensor can be enhanced. The maximum value of FOM for the SPR sensor with high-order TiO2 （or AlAs） absentee layer is 1.059% （or 2.587%） higher than the one with one-order absentee layer. It is believed the proposed SPR sensor with high-order absentee layer will be helpful for developing the high-performance SPR sensors.

Refractive index sensor based on high-order surface plasmon resonance in gold nanofilm coated photonic crystal fiber

We propose a novel kind of wide-range refractive index optical sensor based on photonic crystal fiber(PCF) covered with nano-ring gold film.The refractive index sensing performance of the PCF sensor is analyzed and simulated by the finite element method(FEM).The refractive index liquid is infiltrated into the cladding air hole of the PCF.By comparing the sensing performance of two kinds of photonic crystal fiber structures, a wide range and high sensitivity structure is optimized.The surface plasmon resonance(SPR) excitation material is chose as gold, and large gold nanorings are embedded around the first cladding air hole of the PCF.The higher order surface plasmon modes are generated in this designed optical fiber structure.The resonance coupling between the fundamental mode and the 5 th order surface plasmon polariton(SPP)modes is excited when the phase matching condition is matched.Therefore, the 3 rd loss peaks appear obvious red-shift with the increase of the analyte refractive index, which shows a remarkable polynomial fitting law.The fitnesses of two structures are 0.99 and 0.98, respectively.When the range of refractive indices is from 1.40 to 1.43, the two kinds of sensors have high linear sensitivities of 1604 nm/RIU and 3978 nm/RIU, respectively.

Multi-photon resonance enhanced super high-order harmonic generation

This paper proposes highly charged ions pumped by intense laser to produce very high order harmonics. Numerical simulations and full quantum theory of Ne^9＋ ions driven by laser pulses at 1064 nm in the power range of 109 W/cm^2 1015 W/cm^2 show that the emission spectrum corresponds to the electronic transitions from the excited states to the ground state, which is very different from the spectrum of general high-order harmonic generation. In such situation, harmonic order as high as 1000 can be obtained without producing lower order harmonics and the energy conversion efficiency is close to general high order harmonic generation of hydrogen atom in the same laser field.

High-order rational solutions and resonance solutions for a (3+1)-dimensional Kudryashov–Sinelshchikov equation

We mainly investigate the rational solutions and N-wave resonance solutions for the(3+1)-dimensional Kudryashov–Sinelshchikov equation, which could be used to describe the liquid containing gas bubbles. With appropriate transformations, two kinds of bilinear forms are derived. Employing the two bilinear equations, dynamical behaviors of nine district solutions for this equation are discussed in detail, including bright rogue wave-type solution, dark rogue wave-type solution, bright W-shaped solution, dark W-shaped rational solution, generalized rational solution and bright-fusion, darkfusion, bright-fission, and dark-fission resonance solutions. In addition, the generalized rational solutions, which depending on two arbitrary parameters, have an interesting structure: splitting from two peaks into three peaks.

HIGH-ORDER RUNGE-KUTTA DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR 2-D RESONATOR PROBLEM

The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.

Staging liver fibrosis with various diffusion-weighted magnetic resonance imaging models

BACKGROUND Diffusion-weighted imaging(DWI)has been developed to stage liver fibrosis.However,its diagnostic performance is inconsistent among studies.Therefore,it is worth studying the diagnostic value of various diffusion models for liver fibrosis in one cohort.AIM To evaluate the clinical potential of six diffusion-weighted models in liver fibrosis staging and compare their diagnostic performances.METHODS This prospective study enrolled 59 patients suspected of liver disease and scheduled for liver biopsy and 17 healthy participants.All participants underwent multi-b value DWI.The main DWI-derived parameters included Mono-apparent diffusion coefficient(ADC)from mono-exponential DWI,intravoxel incoherent motion model-derived true diffusion coefficient(IVIM-D),diffusion kurtosis imaging-derived apparent diffusivity(DKI-MD),stretched exponential model-derived distributed diffusion coefficient(SEM-DDC),fractional order calculus(FROC)model-derived diffusion coefficient(FROC-D)and FROC model-derived microstructural quantity(FROC-μ),and continuous-time random-walk(CTRW)model-derived anomalous diffusion coefficient(CTRW-D)and CTRW model-derived temporal diffusion heterogeneity index(CTRW-α).The correlations between DWI-derived parameters and fibrosis stages and the parameters’diagnostic efficacy in detecting significant fibrosis(SF)were assessed and compared.RESULTS CTRW-D(r=-0.356),CTRW-α(r=-0.297),DKI-MD(r=-0.297),FROC-D(r=-0.350),FROC-μ(r=-0.321),IVIM-D(r=-0.251),Mono-ADC(r=-0.362),and SEM-DDC(r=-0.263)were significantly correlated with fibrosis stages.The areas under the ROC curves(AUCs)of the combined index of the six models for distinguishing SF(0.697-0.747)were higher than each of the parameters alone(0.524-0.719).The DWI models’ability to detect SF was similar.The combined index of CTRW model parameters had the highest AUC(0.747).CONCLUSION The DWI models were similarly valuable in distinguishing SF in patients with liver disease.The combined index of CTRW parameters had the highest AUC.

Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

Preoperative prediction of perineural invasion of rectal cancer based on a magnetic resonance imaging radiomics model:A dual-center study

BACKGROUND Perineural invasion(PNI)has been used as an important pathological indicator and independent prognostic factor for patients with rectal cancer(RC).Preoperative prediction of PNI status is helpful for individualized treatment of RC.Recently,several radiomics studies have been used to predict the PNI status in RC,demonstrating a good predictive effect,but the results lacked generalizability.The preoperative prediction of PNI status is still challenging and needs further study.AIM To establish and validate an optimal radiomics model for predicting PNI status preoperatively in RC patients.METHODS This retrospective study enrolled 244 postoperative patients with pathologically confirmed RC from two independent centers.The patients underwent preoperative high-resolution magnetic resonance imaging(MRI)between May 2019 and August 2022.Quantitative radiomics features were extracted and selected from oblique axial T2-weighted imaging(T2WI)and contrast-enhanced T1WI(T1CE)sequences.The radiomics signatures were constructed using logistic regression analysis and the predictive potential of various sequences was compared(T2WI,T1CE and T2WI+T1CE fusion sequences).A clinical-radiomics(CR)model was established by combining the radiomics features and clinical risk factors.The internal and external validation groups were used to validate the proposed models.The area under the receiver operating characteristic curve(AUC),DeLong test,net reclassification improvement(NRI),integrated discrimination improvement(IDI),calibration curve,and decision curve analysis(DCA)were used to evaluate the model performance.RESULTS Among the radiomics models,the T2WI+T1CE fusion sequences model showed the best predictive performance,in the training and internal validation groups,the AUCs of the fusion sequence model were 0.839[95%confidence interval(CI):0.757-0.921]and 0.787(95%CI:0.650-0.923),which were higher than those of the T2WI and T1CE sequence models.The CR model constructed by combining clinical risk factors had the best predictive performance.In the training and internal and external validation groups,the AUCs of the CR model were 0.889(95%CI:0.824-0.954),0.889(95%CI:0.803-0.976)and 0.894(95%CI:0.814-0.974).Delong test,NRI,and IDI showed that the CR model had significant differences from other models(P<0.05).Calibration curves demonstrated good agreement,and DCA revealed significant benefits of the CR model.CONCLUSION The CR model based on preoperative MRI radiomics features and clinical risk factors can preoperatively predict the PNI status of RC noninvasively,which facilitates individualized treatment of RC patients.

Achieving Ultra-Broad Microwave Absorption Bandwidth Around Millimeter-Wave Atmospheric Window Through an Intentional Manipulation on Multi-Magnetic Resonance Behavior

The utilization of electromagnetic waves is rapidly advancing into the millimeter-wave frequency range,posing increasingly severe challenges in terms of electromagnetic pollution prevention and radar stealth.However,existing millimeter-wave absorbers are still inadequate in addressing these issues due to their monotonous magnetic resonance pattern.In this work,rare-earth La^(3+)and non-magnetic Zr^(4+)ions are simultaneously incorporated into M-type barium ferrite(BaM)to intentionally manipulate the multi-magnetic resonance behavior.By leveraging the contrary impact of La^(3+)and Zr^(4+)ions on magnetocrystalline anisotropy field,the restrictive relationship between intensity and frequency of the multi-magnetic resonance is successfully eliminated.The magnetic resonance peak-differentiating and imitating results confirm that significant multi-magnetic resonance phenomenon emerges around 35 GHz due to the reinforced exchange coupling effect between Fe^(3+)and Fe^(2+)ions.Additionally,Mosbauer spectra analysis,first-principle calculations,and least square fitting collectively identify that additional La^(3+)doping leads to a profound rearrangement of Zr^(4+)occupation and thus makes the portion of polarization/conduction loss increase gradually.As a consequence,the La^(3+)-Zr^(4+)co-doped BaM achieves an ultra-broad bandwidth of 12.5+GHz covering from 27.5 to 40+GHz,which holds remarkable potential for millimeter-wave absorbers around the atmospheric window of 35 GHz.

Current status of magnetic resonance imaging radiomics in hepatocellular carcinoma:A quantitative review with Radiomics Quality Score

BACKGROUND Radiomics is a promising tool that may increase the value of magnetic resonance imaging(MRI)for different tasks related to the management of patients with hepatocellular carcinoma(HCC).However,its implementation in clinical practice is still far,with many issues related to the methodological quality of radiomic studies.AIM To systematically review the current status of MRI radiomic studies concerning HCC using the Radiomics Quality Score(RQS).METHODS A systematic literature search of PubMed,Google Scholar,and Web of Science databases was performed to identify original articles focusing on the use of MRI radiomics for HCC management published between 2017 and 2023.The methodological quality of radiomic studies was assessed using the RQS tool.Spearman’s correlation(ρ)analysis was performed to explore if RQS was correlated with journal metrics and characteristics of the studies.The level of statistical significance was set at P<0.05.RESULTS One hundred and twenty-seven articles were included,of which 43 focused on HCC prognosis,39 on prediction of pathological findings,16 on prediction of the expression of molecular markers outcomes,18 had a diagnostic purpose,and 11 had multiple purposes.The mean RQS was 8±6.22,and the corresponding percentage was 24.15%±15.25%(ranging from 0.0% to 58.33%).RQS was positively correlated with journal impact factor(IF;ρ=0.36,P=2.98×10^(-5)),5-years IF(ρ=0.33,P=1.56×10^(-4)),number of patients included in the study(ρ=0.51,P<9.37×10^(-10))and number of radiomics features extracted in the study(ρ=0.59,P<4.59×10^(-13)),and time of publication(ρ=-0.23,P<0.0072).CONCLUSION Although MRI radiomics in HCC represents a promising tool to develop adequate personalized treatment as a noninvasive approach in HCC patients,our study revealed that studies in this field still lack the quality required to allow its introduction into clinical practice.

Magnetic resonance imaging of extraocular rectus muscles abnormalities in acute acquired concomitant esotropia

AIM:To investigate the difference of medial rectus(MR)and lateral rectus(LR)between acute acquired concomitant esotropia(AACE)and the healthy controls(HCs)detected by magnetic resonance imaging(MRI).METHODS:A case-control study.Eighteen subjects with AACE and eighteen HCs were enrolled.MRI scanning data were conducted in target-controlled central gaze with a 3-Tesla magnetic resonance scanner.Extraocular muscles(EOMs)were scanned in contiguous image planes 2-mm thick spanning the EOM origins to the globe equator.To form posterior partial volumes(PPVs),the LR and MR cross-sections in the image planes 8,10,12,and 14 mm posterior to the globe were summed and multiplied by the 2-mm slice thickness.The data were classified according to the right eye,left eye,dominant eye,and non-dominant eye,and the differences in mean cross-sectional area,maximum cross-sectional area,and PPVs of the MR and LR muscle in the AACE group and HCs group were compared under the above classifications respectively.RESULTS:There were no significant differences between the two groups of demographic characteristics.The mean cross-sectional area of the LR muscle was significantly greater in the AACE group than that in the HCs group in the non-dominant eyes(P=0.028).The maximum cross-sectional area of the LR muscle both in the dominant and non-dominant eye of the AACE group was significantly greater than the HCs group(P=0.009,P=0.016).For the dominant eye,the PPVs of the LR muscle were significantly greater in the AACE than that in the HCs group(P=0.013),but not in the MR muscle(P=0.698).CONCLUSION:The size and volume of muscles dominant eyes of AACE subjects change significantly to overcome binocular diplopia.The LR muscle become larger to compensate for the enhanced convergence in the AACE.

High-grade pancreatic intraepithelial neoplasia diagnosed based on changes in magnetic resonance cholangiopancreatography findings:A case report

BACKGROUND High-grade pancreatic intraepithelial neoplasia(PanIN)exhibits no mass and is not detected by any examination modalities.However,it can be diagnosed by pancreatic juice cytology from indirect findings.Most previous cases were diagnosed based on findings of a focal stricture of the main pancreatic duct(MPD)and caudal MPD dilatation and subsequent pancreatic juice cytology using endoscopic retrograde cholangiopancreatography(ERCP).We experienced a case of high-grade PanIN with an unclear MPD over a 20-mm range,but without caudal MPD dilatation on magnetic resonance cholangiopancreatography(MRCP).CASE SUMMARY A 60-year-old female patient underwent computed tomography for a follow-up of uterine cancer post-excision,which revealed pancreatic cysts.MRCP revealed an unclear MPD of the pancreatic body at a 20-mm length without caudal MPD dilatation.Thus,course observation was performed.After 24 mo,MRCP revealed an increased caudal MPD caliber and a larger pancreatic cyst.We performed ERCP and detected atypical cells suspected of adenocarcinoma by serial pancreatic juice aspiration cytology examination.We performed a distal pancreatectomy and obtained a histopathological diagnosis of high-grade PanIN.Pancreatic parenchyma invasion was not observed,and curative resection was achieved.CONCLUSION High-grade Pan-IN may cause MPD narrowing in a long range without caudal MPD dilatation.

Outcomes and efficacy of magnetic resonance imaging-compatible sacral nerve stimulator for management of fecal incontinence: A multi-institutional study

BACKGROUND Fecal incontinence(FI)is an involuntary passage of fecal matter which can have a significant impact on a patient’s quality of life.Many modalities of treatment exist for FI.Sacral nerve stimulation is a well-established treatment for FI.Given the increased need of magnetic resonance imaging(MRI)for diagnostics,the In-terStim which was previously used in sacral nerve stimulation was limited by MRI incompatibility.Medtronic MRI-compatible InterStim was approved by the United States Food and Drug Administration in August 2020 and has been widely used.AIM To evaluate the efficacy,outcomes and complications of the MRI-compatible InterStim.METHODS Data of patients who underwent MRI-compatible Medtronic InterStim placement at UPMC Williamsport,University of Minnesota,Advocate Lutheran General Hospital,and University of Wisconsin-Madison was pooled and analyzed.Patient demographics,clinical features,surgical techniques,complications,and outcomes were analyzed.Strengthening the Reporting of Observational studies in Epidemiology(STROBE)cross-sectional reporting guidelines were used.RESULTS Seventy-three patients had the InterStim implanted.The mean age was 63.29±12.2 years.Fifty-seven(78.1%)patients were females and forty-two(57.5%)patients had diabetes.In addition to incontinence,overlapping symptoms included diarrhea(23.3%),fecal urgency(58.9%),and urinary incontinence(28.8%).Fifteen(20.5%)patients underwent Peripheral Nerve Evaluation before proceeding to definite implant placement.Thirty-two(43.8%)patients underwent rechargeable InterStim placement.Three(4.1%)patients needed removal of the implant.Migration of the external lead connection was observed in 7(9.6%)patients after the stage I procedure.The explanation for one patient was due to infection.Seven(9.6%)patients had other complications like nerve pain,hematoma,infection,lead fracture,and bleeding.The mean follow-up was 6.62±3.5 mo.Sixty-eight(93.2%)patients reported significant improvement of symptoms on follow-up evaluation.CONCLUSION This study shows promising results with significant symptom improvement,good efficacy and good patient outcomes with low complication rates while using MRI compatible InterStim for FI.Further long-term follow-up and future studies with a larger patient population is recommended.

Potential applications of 7 Tesla magnetic resonance imaging in paediatric neuroimaging:Feasibility and challenges

The integration of 7 Tesla magnetic resonance imaging(7 T MRI)in adult patients has marked a revolutionary stride in radiology.In this article we explore the feasibility of 7 T MRI in paediatric practice,emphasizing its feasibility,applications,challenges,and safety considerations.The heightened resolution and tissue contrast of 7 T MRI offer unprecedented diagnostic accuracy,particularly in neuroimaging.Applications range from neuro-oncology to neonatal brain imaging,showcasing its efficacy in detecting subtle structural abnormalities and providing enhanced insights into neurological conditions.Despite the promise,challenges such as high cost,discomfort,and safety concerns necessitate careful consideration.Research suggests that,with precautions,7 T MRI is feasible in paediatrics,yet ongoing studies and safety assessments are imperative.

Tunable spectral continuous shift of high-order harmonic generation in atoms by a plasmon-assisted shaping pulse

We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse.This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics.Notably,we observe a modulated shift in the created harmonic photon energy,spanning an impressive range of 1.2 eV.This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse,directly influencing the position of the peak frequency emission.Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse,offering valuable insights into the underlying mechanisms driving this phenomenon.Furthermore,our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered.We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores.This observation introduces an innovative approach for generating semi-integer order harmonics,thus expanding our understanding of high-order harmonic generation.Ultimately,our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications,particularly those involving precise spectral control and the generation of unique harmonic patterns.

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is established.The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam.Via the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions.In general,the pipe in the supercritical region is more sensitive to the pulsating excitation.The nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the vibration.Besides,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the system.In addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response asymmetry.This work further complements the theoretical analysis of pipes conveying pulsating fluid.