Modal Functions Research Articles

Accurate detection method of traveling wave shape based on EEMD and L1 norm regularization

Aiming at the problem of waveform distortion of the secondary traveling wave obtained from the primary traveling wave signal transmitted by the voltage traveling wave sensor, an accurate detection method of voltage traveling wave based on ensemble empirical mode decomposition (EEMD) and L1 norm least squares regularization is proposed in this paper. Firstly, the forward transfer function model of the specialized voltage traveling wave sensor is established, and the inversion model is derived to analyze the phase frequency and amplitude frequency characteristics of the secondary traveling wave after transmission. EEMD is used to decompose the secondary traveling wave into the intrinsic modal function (IMF) components of different frequency bands. The L1 norm least square regularization inversion algorithm was used to invert each IMF component. Finally, the IMF' components after inversion are synthesized to obtain the primary traveling wave. Simulation and experimental results demonstrate that the proposed method is not affected by noise, mode aliasing effect and regularization parameter accuracy, and the obtained waveform has high similarity to the simulated waveform, which enables precise identification of fault traveling wave.

Model refinements with experimental validation in piezoelectric plate actuators

The axisymmetric vibration analysis of circular plates with piezoelectric layers and step changes in plate thickness is conducted. For the chosen configurations, it is necessary to solve a coupled system of differential equations for extensional and flexural vibration to obtain accurate modal results. The adopted computational approach is based upon the classical transfer matrix method. Instead of employing analytical solutions in the form of e.g. Bessel functions, matrix exponentials of the system matrix are directly computed in the transfer matrices for finding highly accurate solutions. The developed approach has enabled the complete quantitative modal analysis in piezoelectric actuators. The procedure is firstly verified against available analytical results for natural frequencies and modes shapes in circular homogeneous plates, and by using finite element simulations for plates with asymmetric step changes in thickness. Ultimately, the developed approach is validated against experimental results of relevance to applications in piezoelectric synthetic jet actuation. The obtained numerical results for modal parameters and frequency response functions are in excellent agreement with the available analytical results, and with previous and newly presented in the paper experimental data, when considering the inherent uncertainty in parameter values. Based on extensive experimental results, realistic damping is introduced in the model of piezoelectric plate actuators. Importantly, it is shown that solutions of high accuracy can be obtained by a more general coordinate system than that traditionally linked to the plate neutral plane(s).

A hybrid optimization prediction model for PM2.5 based on VMD and deep learning

PM2.5 has caused serious harm to human health and the environment, so it is particularly important to accurately predict PM2.5 concentration. Aiming at the problem that the nonlinear features of PM2.5 data are difficult to be learned accurately, which results in low prediction accuracy, the WOA-VMD-BiLSTM hybrid model is proposed in this paper. This model optimizes the parameters of the variational modal decomposition (VMD) by the Whale Optimization Algorithm (WOA), after which the PM2.5 sequence is broken down into several intrinsic modal function (IMF) using the VMD. Next, the nonlinear and temporal features of each IMF are captured using a bidirectional long short-term memory neural network (BiLSTM). Finally, all features are fused to get the prediction of PM2.5 concentration. According to the experimental findings, in contrast to the most accurate baseline model, the proposed model reduced the values of RMSE by 18.12, 20.17, and 5.36 in 1∼6 h, 7–12 h, and 13–24 h, respectively. In addition, the model can successfully capture the trend of PM2.5 concentration changes in the long-term prediction.

Association of anesthetic modality and other variables on 1-year functional patency of cephalic-based arteriovenous fistulae

ObjectiveSome studies suggest that regional anesthesia provides better patency for arteriovenous fistula (AVF) for hemodialysis access as compared to local and general anesthesia. This study evaluates the impact of anesthetic modality on long term fistula function at 12 months. MethodsA retrospective review of patients undergoing cephalic vein-based hemodialysis access in consecutive cases between 2014 and 2019 was conducted from five safety net hospitals. The primary endpoint was functional patency at 12 months. Subset analysis individually evaluated cephalic-based lower forearm and wrist vs upper arm AVFs. Bivariate and multivariate logistic regression models evaluated the relationship between anesthetic modality and fistula function at 12 months. ResultsThere were 818 cephalic-based fistulas created during the study period. The overall 12-month functional patency rate was 78.7%, including an 81.3% patency for upper arm AVF and 73.3% for wrist AVF (P = .009). There was no statistically significant difference among patients with functional and nonfunctional AVFs at 12 months with respect to anesthetic modality when comparing regional, local, and general anesthesia (P = .343). Multivariate regression analysis identified that history of AVF/arteriovenous graft (odds ratio [OR], 0.24; P = .007), receiving intraoperative systemic anticoagulation (OR, 2.49; P < .001), and vein diameter (OR, 1.85; P = .039) as independently associated with AVF functional patency at 12 months. ConclusionsThere was no association between anesthetic modality and functional patency of cephalic-based AVFs at 12 months. Further studies are needed to better define which patients may benefit from regional anesthesia.

Abstract 4208: In-vitro modeling of Sonic Hedgehog signaling identifies the extracellular matrix as a regulator of tumor invasion outcomes

Abstract Preclinical models of Sonic Hedgehog (SHH)-driven tumors support the therapeutic benefit of pharmacological inhibitors, yet clinical outcomes are conflicted due to biphasic tumor responses that include complete remission or faster disease progression. In such studies, the activity of the SHH pathway in the tumor-adjacent stroma supported or restrained tumor progression. Our prior studies show that altered SHH ligand levels can lead to faster tumor growth during pharmacological inhibition suggesting a role for the SHH pathway strength in the biphasic tumor responses of a triple-negative breast cancer (TNBC) model. In this study, the role of SHH pathway strength altered by tumor-fibroblast proximity was examined on the tumor growth, invasion, and transcriptional activity using in vitro and in vivo models. Tumor spheroid models composed of TNBC cell lines and fibroblasts were used to monitor SHH signal strength as a function of the culture modality and SHH ligand levels. In vitro, SHH signal strength was altered by tumor-fibroblast proximity and ligand concentration. Mixed cultures exhibited significantly higher SHH activity and reduced invasion than adjacent cultures. This effect was reversed by pharmacological inhibition of SMO, confirming the involvement of an SHH-dependent mechanism. In a tumor xenograft model, tumor metastasis outcomes were suppressed by pharmacological inhibition of the SHH pathway, but opposite results were observed in tumor xenografts composed of co-injected with fibroblasts indicating that the biphasic tumor response can be driven by the fibroblasts. Spatial transcriptional analysis identified extracellular matrix (ECM) activities in fibroblasts as the top altered bioprocesses in both in vitro and in vivo. This finding was confirmed in cultures, where fibroblast-derived decellularized matrix stimulated tumor invasion of single TNBC spheroids at levels observed in co-cultures. Further analysis of differentially expressed genes (DEGs) identified a small leucine-rich repeat proteoglycan (SLRP) as the primary ECM target altered by variations in SHH signal strength in fibroblasts. Furthermore, we confirmed the role of SLRP cues in governing tumor invasion potency within spheroid cultures embedded in a collagen hydrogel matrix. While high levels of SLRP in the matrix inhibited spheroid invasion, low SLRP matrix promoted spheroid invasion and increased secondary invasion sites. These findings agreed with the Vimentin expression levels observed in TNBC cells and confirmed the potency of SLRP in regulating tumor invasion outcomes. In summary, our study underscores the significance of ECM remodeling activities in fibroblasts and the role of SLRPs in governing tumor invasion, with implications for understanding the impact of altering SHH signaling activity in TNBC. Citation Format: Emanuel A. Carrasquillo-Dones, Heizel M. Rosado-Galindo, Ana M. Reyes-Ramos, Wandaliz Torres-Garcia, Said Cifuentes, Jan P. Rios-Grant, Gabriela Ortiz-Soto, Natalia A. Ramos-Acevedo, Miosotis Acevedo-Esquilin, Monica Colon-Vargas, Israel Almodovar-Rivera, Camilo Mora, Michelle M. Martinez-Montemayor, Maribella Domenech. In-vitro modeling of Sonic Hedgehog signaling identifies the extracellular matrix as a regulator of tumor invasion outcomes [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 4208.

Nonlinear broadband vibration reduction of nitinol-steel wire rope: Mechanical parameters determination and theoretical-experimental validation

This study validates the nonlinear broadband vibration reduction capability of Nitinol steel wire rope (NiTi-ST). Hysteresis tests on NiTi-ST provide hysteresis force-displacement data, and mechanical parameter calculations are performed by developing a fitting model. A dynamic model of a composite laminated cantilever plate embedded with NiTi-ST is developed. The modal analysis is performed using the Rayleigh-Ritz method, and accurate modal functions are obtained. The dynamical equations are solved using the Galerkin truncation and harmonic balance methods. Experimental results demonstrate NiTi-ST’s global broadband vibration reduction at various temperatures, with a decrease in effectiveness as temperature rises. These experimental results are consistent with the theoretical analysis. This study firstly experimentally validates NiTi-ST’s nonlinear behavior, and provides technical support for NiTi-ST’s use as a nonlinear vibration reduction device.

An analytical method for free vibrations of the fuel rod with non-uniform mass of small modular reactor

The intricate internal structure of fuel rods results in a non-uniform mass distribution, making it imperative to employ analytical methods for accurate assessment. The study utilizes Euler beam theory to derive the transverse vibration equation for beams with varying mass distribution. The approach involves transforming the non-uniform mass beam into a multi-segment beam with concentrated mass points. Modal function relationships between adjacent uniform segments are established based on continuous conditions at connection points. This transformation leads to the conversion of the variable coefficient differential equation into a nonlinear matrix equation. The Newton-Raphson method is then applied to calculate the characteristic equation and mode shapes, essential for determining natural frequencies. To validate precision, the results obtained are compared with those derived from the finite element method. Furthermore, the developed method is employed to assess the impact of gas plenum location and length on the natural frequency of fuel rods. The proposed methodology serves as a rapid design tool, particularly beneficial during the design phase of fuel rods with non-uniform mass distribution, aiding in configuring structural aspects effectively.

An Improved Sparrow Search Algorithm for the Optimization of Variational Modal Decomposition Parameters

Variational modal decomposition (VMD) is frequently employed for both signal decomposition and extracting features; however, the decomposition outcome is influenced by the quantity of intrinsic modal functions (IMFs) and the specific parameter values of penalty factors. To tackle this issue, we propose an algorithm based on the Halton sequence and the Laplace crossover operator for the sparrow search algorithm–VMD (HLSSA-VMD) to fine-tune the parameters of VMD. First, the population initialization by the Halton sequence yields higher-quality initial solutions, which effectively addresses the issue of the algorithm’s sluggish convergence due to overlapping and the lack of diversity of the initial solutions. Second, the introduction of the Laplace crossover operator (LX) to perturb the position of the best individual in each iteration helps to prevent the algorithm from becoming ensnared in a local optimum and improves the convergence speed of the algorithm. Finally, from the simulation of 17 benchmark test functions, we found that the HLSSA exhibited superior convergence accuracy and accelerated convergence pace, as well as better robustness than the particle swarm optimization (PSO) algorithm, the whale optimization algorithm (WOA), the multiverse optimization (MVO) algorithm, and the traditional sparrow search algorithm (SSA). In addition, we verified the effectiveness of the HLSSA-VMD algorithm on two simulated signals and compared it with PSO-VMD, WOA-VMD, MVO-VMD, and SSA-VMD. The experimental findings indicate that the HLSSA-VMD obtains better parameters, confirming the superiority of the algorithm.

Moving harmonic source depth estimation by MDFMD-v in a weakly range-depend waveguide

To estimate the depth of a non-cooperative moving sound source in a range-depend waveguide, a passive depth estimation method combining depth-polarity search for a harmonic moving source is proposed in this paper. Firstly, the method obtains each mode parameters at the source and horizontal linear array (HLA) locations by utilizing the modal depth function constrained modal Doppler velocity estimation (MDFMD-v) and matrix pencil (MP) methods, respectively. Subsequently, mode amplitudes are calculated by compressive sensing. To determine the polarity of each mode amplitude, a depth-polarity search method is given in this paper. Finally, a depth ambiguity function with mode amplitude polarity is used to obtain the depth estimation results. Simulation results verify the effectiveness of the method.

Mode-informed complex-valued neural processes for matched field processing

Matched field processing (MFP) is a key technique for passive underwater source localization, estimating the source position by matching array measurements with acoustic model replicas. Its effectiveness relies on matching environmental parameters with the actual oceanic environment, but performance declines with environmental mismatches and lower signal-to-noise ratios. This paper proposes a novel approach that integrates neural networks (NNs) and complex Gaussian processes with modal depth functions for acoustic field reconstruction that is more accurate and efficient compared to Gaussian process regression. A meta-learning strategy is used to optimize parameters of the NN. The reconstructed data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFP. Replicas are also computed at the virtual receivers. This mode-informed complex-valued neural processes enhance MFP performance, particularly in low SNR and mismatched environments. It captures the propagation properties of underwater acoustic fields more comprehensively, showing superior localization performance in both simulated and real-world data from the SWellEx-96 Event S5 environment.

Eyes of the beholders: Multi-method relationships between internalizing and externalizing symptom dimensions and aggression risk.

Although aggression occurs across a range of disorders, associations between dimensions of psychopathology and self- and other-directed aggression are not well understood. Investigating associations between psychopathology dimensions and aggression helps further understanding about the etiology of aggression, and ultimately, can inform intervention and prevention strategies. This study adopted a multi-method approach to examine associations between internalizing and externalizing dimensions of psychopathology and self- and other-directed aggression as a function of reporter (participant and informant) and modality of aggression measurement (subjective and objective). Participants were an unselected sample of 151 racially diverse adults recruited from the community. Dimensions of psychopathology were assessed using interview and questionnaire reports from participants and collateral informants, and forms of aggression were measured via subjective reports and an objective, laboratory aggression paradigm. Analyses of participant-reported psychological symptom data consistently linked externalizing symptoms to other-directed aggression, and internalizing symptoms to self-directed aggression. Results across informant and participant reporters replicated prior findings showing a significant interaction between internalizing and externalizing dimensions in predicting intimate partner violence. Most other effects in informant models were nonsignificant. The findings uncover consistency in and replicability of relationships between dimensions of psychopathology and certain manifestations of aggression and highlight the importance of examining multiple forms of aggression in etiological research. Examining aggression through a transdiagnostic lens can help us better understand and intervene upon processes implicated in devasting forms of self- and other-directed aggression.

Integration of Deep Learning with Vibration-Based Identification Method

The vibration-based identification method has long been used as an alternative to mechanical tests for material characterization. Its non-destructive nature, high efficiency in parameter identification of anisotropic materials and its ability to achieve structure-level homogenization make it very attractive for both academic community and industry. Due to the absence of explicit mapping from the result of vibration test to elastic constants, conventional vibration-based identification approaches generally rely on the minimization of a cost function built on modal properties or Frequency Response Function (FRF) curve. In this paper, a direct relation from FRFs to mechanical properties is established by deep neural network, which offers a new perspective to solve the inverse identification problem. Specifically, this mapping is approximately built with Multilayer Perceptrons (MLPs) and the network’s weights are learned from massive training data. The training data-i.e., the FRF curves, is generated by a finite element model whose input parameters are selected by Latin Hypercube Sampling (LHS). After training, the obtained model is validated by dataset unseen during training process and will be further used to predict mechanical properties of materials from FRFs obtained by vibration test. The effectiveness and efficiency of the developed method are demonstrated on the case study of an aluminum plate. Both the Young’s modulus and Poisson’s ratio are retrieved with high accuracy.

Theory of nonlocal modal hydrodynamic functions for beam and plate vibrations in viscous fluids

In this paper, we introduce a new nonlocal modal hydrodynamic theory for fluid–structure interactions (FSI) of light, flexible cantilever beams and plates undergoing small amplitude vibrations in Newtonian, incompressible, viscous, heavy fluids otherwise at rest. For low aspect ratio flexible structures and high mode numbers, three dimensional (3D) and nonlocal fluid effects become prominent drivers of the coupled dynamics, to the point that existing local hydrodynamic theories based on two dimensional (2D) fluid approximations become inadequate to predict the system response. On the other hand, our approach is based on a rigorous, yet efficient, 3D treatment of the hydrodynamic loading on cantilevered thin structures. The off-line solution of the FSI problem results in the so-called nonlocal modal hydrodynamic function matrix, that is, the representation of the nonlocal hydrodynamic load operator on a basis formed by the structural modes. Our theory then integrates the nonlocal hydrodynamics within a fully coupled structural modal model in the frequency domain. We compare and discuss our theory predictions in terms of frequency response functions, mode shapes, hydrodynamic loads, quality factors, added mass ratios with the predictions of the classical local approaches, for different actuation scenarios, identifying the limitations of the hypotheses underlying existing treatments. Importantly, we also validate our new model with experiments conducted on flexible square plates. While computationally efficient, our fully coupled theory is exact up to numerical truncation and can bridge knowledge gaps in the design and analysis of FSI systems based on low aspect ratio flexible beams and plates.

The Critical Analysis of the Lesotho Language Planning and Policy and Its Implications on Education

The paper aimed at analysing the Lesotho language policy to unmask how power is assumed to be exercised by the Lesotho policy-makers through linguistic elements and structure .The main analytical tool of this paper was critical sociolinguistics, using IGMs in Systemic Functional Linguistics, rhetorical strategies and the CDA model in which the paper analysed the relationship between discourse and society. The paper unveiled performativity (mode, censorship and interpellation and the grammatical aspects from the point of functions of co-ordination, modality and nominalisation as effective and dominant principles and tropes used by the Lesotho language policy makers to convince the citizens to acknowledge the language policy irrespective of how it overshadows the minority languages in Lesotho.

STODOLA-VIANELLO ITERATION METHOD FOR FREE TORSIONAL VIBRATION ANALYSIS OF MONOSYMMETRIC BOX-BEAM BRIDGES

Box-beam bridges are used in large spans and wider decks due to their high strength and greater torsional and flexural stiffness. They are usually prone to vibration due to moving vehicular traffic. Their eigenfrequency analysis is a crucial aspect of their design in order to ensure that the natural frequency is not close to the excitation frequency to avert resonance failures. The free torsional vibration equation is a fourth order partial differential equation (PDE) with variable parameters. For prismatic cross-sections, homogeneous and isotropic materials the governing PDE have constant parameters. This paper explores the Stodola-Vianello iteration method (SVIM) for solving the PDE for isotropic, homogeneous prismatic box-beams. Harmonic response is assumed, decoupling the PDE to two equations, one in terms of time and the second an ordinary differential equation (ODE) in terms of space coordinates. The Stodola-Vianello method is used by the method of four successive integrations to express the ODE as an algebraic iteration problem with four constants of integration. The four boundary conditions are used to solve for the four constants of integration, thus making the problem determinate. Application of the boundary conditions results in the full determination of the iteration equations. For simply supported boundaries studied in the work, a trigonometric buckling shape function that satisfies all the boundary conditions is employed in the SVIM formula to obtain the next bucking modal shape function. The requirement for convergence is then used to establish the characteristic buckling equation from which the eigenvalues are obtained. The solution to the characteristic buckling equation gave the exact mathematical expression for the natural torsional frequency at the nth vibration mode. The frequencies are determined for the first eight vibration modes and compared with previously obtained values. It was found that the natural frequencies are identical with previously found values of the exact natural frequencies. The natural frequency obtained is exact because it satisfies the PDE and the boundary conditions at all points in the domain.

Simulation and experimental study on transverse nonlinear vibration of axially moving yarn

This article focuses on the nonlinear dynamics of transverse vibration of the axially moving yarn system. In this article, the motion of yarn in actual production is analyzed, and the transverse nonlinear vibration equation of the viscoelastic axially moving yarn system with Kelvin model is established by using Newton’s second law. In the modeling process, the viscoelasticity of yarn material and the periodic fluctuation of tension in the process of movement are considered. The partial differential control equations of the system are transformed into ordinary differential equations by the Galerkin method. In the first three modes, when the speed is low, the related trial functions occupy the main part, and with the increase of speed, the trial functions of other orders occupy more proportion in the modal functions. Through numerical analysis, it is found that when the moving yarn is subjected to external excitation, the lateral vibration displacement has an increasing trend, and it is found that the nonlinear dynamic phenomenon alternates with the change of system parameters, such as single periodic motion, double periodic motion, and multiple periodic motion. Finally, an experimental platform for lateral vibration of yarn transmission was built and its working principle introduced. The lateral vibration of axially moving yarn was studied from the experimental point of view. It was proved that there are abundant phenomena of periodic motion, period doubling motion, and chaotic motion in the axially moving yarn system, which provides an experimental reference for theoretical research of lateral nonlinear vibration of axially moving yarn.

Stability and modal evolution characteristics of pipe-in-pipe system with internal intermediate support

In this paper, the stability of the pipe-in-pipe (PIP) conveying fluid system with intermediate supports are studied. The focus of the study is mainly on the influence of the intermediate supports on the critical velocity boundary. The governing equations of the coupled system are established according to Hamilton’s principle, and the modal functions in analytical solution form and the frequency equation in implicit function form are obtained by using the Laplace transform technique. In the numerical discussion part, the influence of the stiffness and position of the support on frequencies, modal functions, and critical flow velocity of the system is discussed. In the stability region diagrams of the cantilever PIP system, it is found that when the position and stiffness of the support change, the minimum critical flow velocity is frequently converted between different modes, and there are two different types of critical flow velocity conversion phenomena (CFVC). And high-order flutter instability, ‘jump’ phenomenon, S-shaped critical velocity boundary and modal conversion phenomenon are discussed in detail. In addition, the effective and negative regions of the support in the cantilever PIP and simply supported PIP systems are given.

CEEMDAN-LWT De-Noising Method for Pipe-Jacking Inertial Guidance System Based on Fiber Optic Gyroscope.

An inertial guidance system based on a fiber optic gyroscope (FOG) is an effective way to guide long-distance curved pipe jacking. However, environmental disturbances such as vibration, electromagnetism, and temperature will cause the FOG signal to generate significant random noise. The random noise will overwhelm the effective signal. Therefore, it is necessary to eliminate the random noise. This study proposes a hybrid de-noising method, namely complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-lifting wavelet transform (LWT). Firstly, the FOG signal is extracted using a sliding window and decomposed by CEEMDAN to obtain the intrinsic modal function (IMF) with N different scales and one residual. Subsequently, the effective IMF components are selected according to the correlation coefficient between the IMF components and the FOG signal. Due to the low resolution of the CEEMDAN method for high-frequency components, the selected high-frequency IMF components are decomposed with lifting wavelet transform to increase the resolution of the signal. The detailed signals of the LWT decomposition are de-noised using the soft threshold de-noising method, and then the signal is reconstructed. Finally, pipe-jacking dynamic and environmental interference experiments were conducted to verify the effectiveness of the CEEMDAN-LWT de-noising method. The de-noising effect of the proposed method was evaluated by SNR, RMSE, and Deviation and compared with the CEEMDAN and LWT de-noising methods. The results show that the CEEMDAN-LWT de-noising method has the best de-noising effect with good adaptivity and high accuracy. The navigation results of the pipe-jacking attitude before and after de-noising were compared and analyzed in the environmental interference experiment. The results show that the absolute error of the pipe-jacking pitch, roll, and heading angles is reduced by 39.86%, 59.45%, and 14.29% after de-noising. The maximum relative error of the pitch angle is improved from -0.74% to -0.44%, the roll angle is improved from 2.07% to 0.79%, and the heading angle is improved from -0.07% to -0.06%. Therefore, the CEEMDAN-LWT method can effectively suppress the random errors of the FOG signal caused by the environment and improve the measurement accuracy of the pipe-jacking attitude.

한국어 '보다' 구문과 중국어 '看' 구문의 대조 연구 - 양태의 중의성을 중심으로 -

The purpose of this study is to compare the syntactic characteristics and examine the modal meanings of ‘boda' and ‘kan', which denote visual perceptual acts, in Korean and Chinese. The lexical meanings of ‘boda' and ‘kan' acquire their modal meanings through a process of semantic abstraction. Both ‘boda' and ‘kan' can convey the speaker's objective attitude towards a proposition and also express the occurrence of an event, thus exhibiting a dual modality function. They can be interpreted as either epistemic modals or event modals. This duality of modality function in ‘boda' and ‘kan' presents different syntactic characteristics, which are interpreted in terms of the structure of modality realization.

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.