Modal Force Research Articles

Dynamic Analysis of Cylindrical Shells with Flexoelectric Actuation

The converse flexoelectric effect can be utilized to actuate and control flexible structures. Assessing the precision flexoelectric actuation and control effectiveness of cylindrical shells is the main objective of this study. The application of voltage to the line electrode on the external surface of a flexoelectric patch, coupled with the bottom surface electrode layer, causes an inhomogeneous electric field to be generated, which consequently induces internal actuation stresses. The stress-induced membrane control force and bending control moment generate modal control effects, which regulate the cylindrical shell vibration. For an elastic cylindrical shell with flexoelectric actuation, the modal forces and microscopic behaviors are studied to evaluate the flexoelectric actuation effects. For the transverse direction, the electric field gradient drops sharply with increasing distance from the line electrode; thus, the induced internal actuation stresses concentrate on the upper surface. Due to the inhomogeneous electric field gradient distributions, the membrane control force and bending control moment concentrate like spikes. To evaluate the actuation effects, modal force distributions of the elastic cylindrical shell with flexoelectric actuation are analyzed with respect to design parameters, such as the flexoelectric patch thickness, line-electrode radius, cylindrical shell thickness, and shell radius.

Equivalent static wind loads on canopies of regular railway stations

Wind-induced response, spectrums of the modal generalized force, and equivalent static wind loads (ESWLs) of railway station canopies with single-span and three-span frame are investigated. The results show that the first mode dominates horizontal displacements and frame column stresses, and the second mode dominates vertical displacements and frame beam stresses of the canopy frames. The unfavorable wind directions are determined for the center, near-center and end frames. Based on wind tunnel test results, parameters of simplified mean wind dynamic pressure coefficients and the generalized modal force spectrum formula for the first and second modes are proposed for different canopy span, opening widths and building height ratios of the station building to the canopy. Combining above-mentioned wind-induced response characteristics with the analysis method of universal ESWLs, the ESWLs are derived as the superposition of the peak inertia forces of the two dominating modes, and all nodal displacements and all member stresses under this unique ESWLs are equivalent to the actual dynamic peak responses. The numerical example verifies that all nodal displacements and member stresses calculated by the proposed semi-analytical formula simultaneously agree well with the actual dynamic peak response.

Effects of Mass Attachments on Flutter Characteristics of Thin-Walled Panels

Mass attachments may exist in the design and use of an aircraft panel, such as sensor layout, internal wiring, surface icing, etc. These mass attachments can change the flutter characteristics of the panel in supersonic flight and have important impacts on structural safety. In order to investigate the flutter characteristics of the panel with mass attachments, an assumed mode method is proposed to deal with the changes in the modal properties of the panel structure. Combined with the first order piston theory and p-k method, the flutter velocities and flutter frequencies of the panel under different cases can be obtained in the frequency domain. Firstly, based on the large displacement with a small strain assumption proposed by von Kármán and the proposed assumed mode method, the structural dynamic model of a simply supported panel with mass attachments and artificial dampers is constructed. Then, modal aerodynamic forces of the simply supported panel can be obtained based on first-order piston theory. Finally, flutter equations are transformed into the frequency domain and solved by the p-k method. The results showed that the existence of mass attachments can significantly change the flutter velocities and flutter frequencies of the panel. However, the flutter characteristics of the panel can be enhanced or recovered through some appropriate damper configuration schemes. Calculating the flutter characteristics of thin-walled panels with mass attachments can more accurately simulate real situations during flight, and one can obtain a safer design scheme of thin-walled panels.

Reconstruction of dynamic wind forces on a transmission steel lattice tower using aeroelastic wind tunnel test data

This article reports a methodology for estimating dynamic wind forces on a steel lattice tower by using limited structural displacements. The methodology involves combining the modal state-space system model and a Kalman filter-based algorithm. For convenient application, the equivalent concentrated forces are taken as the inversing objects, representing the distributed wind forces on a lattice tower. The corresponding equivalent cantilever model of the lattice tower is utilized, in which the stiffness matrix is estimated by a modified flexibility approach. Based on the modal superposition principle, the dynamic wind forces in physical space are reconstructed using the identified input modal wind forces. The scheme of the dynamic wind force reconstruction is designed in detail. A typical transmission steel lattice tower is considered, and the aeroelastic wind tunnel experiments are performed. The performance and effectiveness of the proposed scheme are investigated based on numerical simulations and wind tunnel tests. It is indicated that the reconstructed dynamic wind forces can produce equivalent dynamic responses to the actual. Besides, it performs robustly on the effect of measurement noise. Although the modal force identification is sensitive to the modeling error of structural natural frequency, the effect can be judged according to the change in the power spectra of the identified modal force. The proposed inversing approach can serve as a useful tool to evaluate dynamic wind forces on steel lattice towers with limited response measurements.

Forced Response Induced by Low Engine Order Under Circumferential Inlet Distortions With Different Extents

Abstract Boundary-layer ingestion systems have the potential to improve propulsion efficiency using fluid with lower momentum near the airframe. However, they also bring variations in the velocity and total pressure, leading to a complex distortion of the flow at the inlet stage in the form of a circumferential step variation with significant strength. Previous simulation of NASA Rotor 67 under a 120-deg sector distortion revealed the occurrence of first-order bending mode excited by the second engine order (2EO) under circumferentially distorted inflow. To explore if the variation of distortion extent could affect the excited mode, five cases are simulated for different sector angles of distortion extent: 60, 90, 120, 150, and 180 deg. The result of modal-force analysis demonstrates that the modal force increases from the 60-deg case to the 90-deg case and then decreases from the 90-deg case to the 180-deg case, and the lowest value is reached in the 180-deg case. To further investigate the excitation sources leading to such variations of modal force, the harmonic force caused by periodic flow is analyzed based on the Fourier decomposition. The results indicate two main sources for the excitation of 2EO: (1) the harmonic force induced by the distorted inflow, and (2) the dynamic response of the fan blade caused by a sudden drop of inlet total pressure and controlled by the time constant.

Effects of Asymmetric Vane Pitch on Reducing Low-Engine-Order Forced Response of a Turbine Stage

Asymmetric vane pitch is a key technique to suppress the forced response of downstream rotor blades. To address the problem of low-engine-order (LEO) excitation with high amplitude under an asymmetric configuration (half-and-half layout) widely recognized in the previous literature, we first apply the in-house computational fluid dynamics code Hybrid Grid Aeroelasticity Environment to perform full-annulus unsteady aeroelasticity simulations of the turbine stage, comparing the resonance response of rotor blades on different asymmetric configurations and analyzing the flow field at the vane exit, as well as the excitation force, modal force, and maximum vibrational amplitude on the rotor blades. Second, we reveal that the potential field of the vane row is the main source of the LEO excitation caused by asymmetric configuration on rotor blades, the vane wake and potential field jointly determine the LEO excitation strength of rotor blades, and the vane pitch difference ΔS can be used to regulate the strength of the LEO excitation. Finally, based on an in-depth understanding of flow physics under an asymmetric configuration, a more preferable and effective asymmetric configuration (non-half two-segment layout) is proposed. Our findings demonstrate that, with the proposed asymmetric configuration, the amplitude of the vane passing frequency was reduced by 48.32% compared to the uniform configuration; furthermore, the maximum vibrational amplitude of the three-nodal-diameter response of the rotor blade at the three-engine-order crossing decreased by 45.49% compared to the half-and-half layout. The non-half two-segment layout also significantly improves upon the half-and-half layout in terms of aerodynamic performance. The results presented in this paper provide a good theoretical basis for reducing blade vibration by applying asymmetric vane pitch in engineering practice.

Accelerating convergence in Bayesian operational modal analysis with Fisher information matrix

Bayesian operational modal analysis (BAYOMA) has been increasingly applied to ambient vibration tests, providing a fundamental means for estimating modal properties as well as quantifying their identification uncertainty consistent with probability rules and modelling assumptions. Computing the most probable value of modal parameters in BAYOMA involves a high-dimensional numerical optimisation of the negative log-likelihood function (NLLF). Brute-force optimisation using generic algorithms treating the NLLF as a black box is computationally prohibitive and often non-converging. Efficient iterative algorithms have been developed over the past decade, but challenges still exist, e.g., for very close modes that may require significantly more iterations or (in some cases) may not be converging. Leveraging on recent advance in the mathematics and understanding of the Fisher Information Matrix (FIM) of modal parameters, an efficient method based on Newton-type iterations is proposed in this work to improve computational efficiency and convergence robustness. The MPV estimate in each iteration is updated based on two characteristic types of principal directions of the FIM. Move of the first type involves mode shapes only and is orthogonal to the subspace spanned by the current mode shape estimates. The second type involves updates of all modal parameters, where the mode shapes move within the subspace. Compact analytical expressions are derived for the gradient of NLLF to ensure accurate and efficient use in determining each iteration move. The performance of the proposed method is investigated with a comprehensive study based on synthetic, laboratory and field data. Results reveal that the proposed algorithm generally outperforms existing ones in terms of computational time by an order of magnitude, and it has better convergence robustness especially for challenging cases with very close modes and high modal force coherence.

Quantification, localization, and reconstruction of impact force on interval composite structures

Impact force identification has been intensively studied owing to its profound effects on health monitoring and safety assessment. This study investigates a novel uncertainty-oriented impact force identification framework for composite structures considering signal noises, material dispersion, and fabrication errors. The quantification of multi-point impact forces is achieved by the principal component analysis of the modal forces, which are deduced by the Newmark difference scheme using acceleration measurements. The localization and reconstruction of impact forces are obtained by a series of interactive iterations containing time-domain inversion of impact forces and correlation assessment of simulated/measured responses. Particularly, the partition optimization and polynomial fitting strategies are presented to alleviate the computation burden of impact localization and an optimum sensor allocation method based on two derived condition numbers and an original convergence criterion is developed to improve the identification precision of force reconstruction. Moreover, interval modeling and the first-order Talor series expansion are introduced for uncertainty quantification and propagation. Eventually, two numerical examples are discussed to demonstrate the validity and feasibility of the developed approach. The results suggest its promising applications in complicated engineering structures and various loading conditions.

Initial studies into camera-based modal force reconstruction

Much work has been done toward the reconstruction of an unknown force using measured response. Modal Force Reconstruction (MFR) attempts a solution by using measured modes and vibrations at some number of degrees of freedom. While developed by way of traditional sensors (e.g., accelerometers), the full-field nature of cameras may be exploited for such tasks. In particular, the spatial density of an image can re-establish the traditionally underdetermined problem into one that is overdetermined. Not only does this make the reconstruction well-posed, but the modal matrix being that which needs inversion establishes a niche solution in certain force reconstruction scenarios. This talk will explore the proposed theory behind camera-based MFR and present proofs of concept using analytical models. Limitations and points of error will also be discussed, helping to further establish credibility and understanding. Initial results suggest camera-based MFR to be a viable reconstruction technique with high spatial and temporal accuracy.

Effects of Elastically Supported Boundaries on Flutter Characteristics of Thin-Walled Panels

In order to investigate flutter characteristics of thin-walled panels with elastically supported boundaries, a method for dealing with the stiffness matrix constraint relationship is developed based on penalty functions. Combined with the first-order piston theory, flutter velocities and frequencies of thin-walled panels with the different cases of elastically supported boundaries are calculated. Firstly, a thin-walled panel is discretized by the finite element method, and springs with real stiffness coefficients are introduced to simulate elastically supported boundaries. Then, the pressure difference between the outer and inner surfaces of the panel and modal aerodynamic expressions are obtained by introducing the first-order piston theory. Finally, flutter equations are obtained in the time domain by combining the structural dynamic equations with the modal aerodynamic forces. Subsequently, they are transformed to the frequency domain at the flutter state. Then, flutter characteristics of the panel are obtained using the U−g method. The results show that the existence of elastically supported boundaries may reduce the flutter velocity and flutter frequency of the panel but can be enhanced and recovered through some appropriate damping configuration schemes. Calculating the flutter characteristics of thin-walled panels under elastically supported boundaries can more accurately simulate real supported situations and result in a safer design scheme for thin-walled panel structures.

The incoherence challenge for subject combination: an analytic assessment

ABSTRACT Panpsychism is now a bona fide potential solution to the metaphysical quandary of consciousness. Much of the debate concerning the viability of panpsychism is centered on the combination problem (CP). Intriguingly, the literature analyzing this problem displays two competing interpretations which differ in their modal force. According to the first, which we call the ‘no-necessitation view', CP consists in the absence of a priori necessitation of macro-level phenomenal facts from micro-level phenomenal facts. In contrast, the second interpretation, which we label the ‘incoherence charge’ (IC), goes further by insisting that it can be positively demonstrated that micro-experiences cannot combine to yield integral macro-experiences. While conceivability arguments are vulnerable to debates over conflicting intuitions, as well as to the claim that a more complete picture will grant the desired necessitation, IC has the advantage that, if true, it removes these concerns and approaches a more final verdict. Nevertheless, while conceivability arguments are widely discussed IC has not been equally well understood or recognized. In this paper we conduct a systematic investigation and reevaluation of IC, as it applies to constitutive micropsychism (or, micro-reductive panpsychism). We argue that the problem is real and therefore that constitutive micropsychism is a blind alley.

Grounding: De Re and De Dicto

Abstract Is the macro grounded in the micro? That is, is every truth about a macroscopic object fully grounded in a truth wholly about its microscopic parts? In a recent interesting paper, Martin Glazier argued for a negative answer. Following him, call the position that the macro is grounded in the micro ‘priority micro pluralism’ (‘pluralism’ for short). In this discussion note, I propose a way out for the pluralist. In brief, it consists in the recognition that some metaphysical positions, including pluralism, are best expressed by fundamentally de dicto grounding claims. In that these claims have a distinctive modal force, this recognition has far-reaching consequences that go beyond a defence of pluralism.

Zhi-{yao, you} ‘only-{need, have}’: on two conditional connectives in Mandarin

This paper offers a compositional take on two internally complex conditional connectives in Mandarin, zhi-yao ‘only-need’ and zhi-you ‘only-have’. While the former conveys the antecedent proposition’s minimal sufficiency, the latter conveys its necessity for the consequent proposition to come true. Both connectives will be treated as pairing an exclusive particle, zhi, with a modal, an assumption that is less controversial for the necessity modal yao than for you, which will be treated as a possibility modal. Accepting this treatment, however, we have two connectives that openly differ in modal force. While the surface order will be preserved for zhi-you, an inversion will be shown to lead to better results for zhi-yao. In both cases, a possible extension to monoclausal uses is considered.

Eigenfrequencies of rotating discs in dense fluid: imposed modal motion approach

The mode split on disc like structures rotating in a dense fluid leads to a deviation of eigenfrequencies at high rotational speeds compared to their values in still water. Predicting eigenfrequencies correctly is essential to avoid fatigue cracks on prototype turbine runners. Analytical models for simple geometric configurations and complex numerical models using fully coupled fluid structure interaction to predict the mode split on arbitrary geometries exist. We are presenting a complementary approach of intermediate complexity applicable to arbitrary geometries. Mode shapes and modal parameters are computed by finite element analysis in still water. These mode shapes are imposed with a harmonic variation in time during an unsteady computational fluid dynamics computation. From the interaction between the flow and the modal motion, the modal force and the modal work can be computed. These can be converted into added modal mass and hydrodynamic damping and further into the shift of the eigenfrequency under rotation due to the fluid for a given mode. The tendencies of the frequencies with rotation compare reasonably well with experimental data. The numerical method can be applied to disc rotation speeds far beyond the range of experimental data revealing interesting tendencies and a phenomenological interpretation of the cause of the mode split.

Modal analysis-based initial axial force recognition method for jacket platform

Jacket platform is the marine structure that anchor piles to the sea floor, among which the leg is one of the most important components of fixed marine structure. Most of the existing stress and strain monitoring methods for offshore platform ignore the existing forces in the structures caused by deck load and installation errors before the monitoring, which cannot be ignored in the subsequent monitoring and evaluation. Based on this, a method for axial force identification of marine structures is proposed in this paper. The partial differential equation of free vibration of Timoshenko beams with axial force under the influence of damping is derived. This method can accurately identify the axial force of beams without knowing the boundary conditions. The simulation results of the single beam show that this method can be used to identify the axial forces of beams with various cross sections and sizes. Then, the method is applied to the axial force identification of the legs of a four-legged jacket platform. The results show that the method can be applied to the axial force identification of the legs with the relative error (RE) of the identification results is less than 6.5%.

Gaussian Stochastic Process Modeling of Blend Repaired Airfoil Modal Response Using Reduced Basis Mode Shape Approach

Abstract A machine learning (ML) approach is developed to predict the effect of blend repairs on airfoil frequency, modal assurance criterion (MAC), and modal displacement vectors. The method is demonstrated on a transonic research rig compressor rotor airfoil. A parametric definition of blend geometry is developed and shown to be capable of encompassing a large range of blend geometry. This blend repair geometry is used to modify the airfoil surface definition and a mesh morphing process transforms the nominal finite element model (FEM) to the repaired configuration. A multilevel full factorial sampling of the blend repair design space provides training data to a Gaussian stochastic process (GSP) regressor. The frequency and MAC results create a vector of training data for GSP calibration, but the airfoil mode shapes require further mathematical manipulation to avoid creating GSP models for each nodal displacement. This paper develops a method to significantly reduce blended airfoil mode shape emulation cost by transforming the mode shape training data into a reduced basis space using principal component analysis (PCA). The coefficients of this reduced basis are used to train a GSP that can then predict the values for new blended airfoils. The emulated coefficients are used with the reduced basis vectors in a reconstruction of blended airfoil mode shape. Validation data is computed at a full-factorial design that maximizes the distance from training points. It is found that large variations in modal properties from large blend repairs can be accurately emulated with a reasonable number of training points. The reduced basis approach of mode shape variation is shown to more accurately predict MAC variation when compared to direct MAC emulation. The added benefit of having the full modal displacement field also allows determination of other influences such as tip-timing limits and modal force values.

Integrated Power, Attitude, and Vibration Control of Gyroelastic Body

Gyroelastic body refers to a flexible structure with distributed angular momentum exchange devices, such as variable speeds control moment gyros (VSCMGs). A VSCMG contains a rotor with high rotating speeds. The direction and the magnitude of the rotor’s angular momentum can be simultaneously tuned.When distributing a set of VSCMGs on a flexible structure, they could simultaneously produce control torques for attitude control and modal forces for vibration suppression. Meanwhile, the high spinning rotor in the VSCMGs can be used for energy storage. Thus, an integrated power, attitude, and vibration control system (IPAVCS) for a free flexible structure can be obtained. In this work, the control scheme for the IPAVCS is developed. A nonlinear controller is first designed to calculate the desired attitude control torques and vibration suppression modal forces for attitude stabilization and vibration suppression. Then, a robust pseudoinverse gimbal steering law and a pseudoinverse rotor acceleration law are developed to generate the desired control input and meet the power requirement, respectively. Numerical examples are conducted to verify the effectiveness of the proposed control scheme.

Modal state vectors of a free-hanging drilling riser during deployment and retrieval

To prevent marine risers' resonance and eliminate potential threats, sufficient inherent dynamic characteristics such as natural frequency, modal displacement, slope, bending moment, and shear are necessary to be calculated and analyzed. However, most studies calculate the natural frequencies and modal displacements directly rather than the modal slopes and forces. The additional calculations of modal slopes and forces likely result in issue complications, time-consuming, or even errors especially when the boundaries at both ends are solved by a finite difference method. To solve the above problems, a state-vector approach is developed herein based on the precise integration method. Two traditional methods, i.e., differential transformation method and finite element method, are utilized to verify the validation of the approach. The modal state vectors of a marine drilling riser, i.e., not only modal displacements but also modal slopes, bending moments, and shears, are studied in detail under four classic cases according to the hard and soft hang-off modes and the deployment and retrieval processes. Besides, the natural frequencies versus the riser suspension lengths are investigated during the deployment and retrieval. The critical resonance suspension lengths of the riser are discussed via a double-peaked sea irregular wave spectrum. Based on the analyses presented in this study and their generic findings, powerful tools can be designed to prevent riser resonance and associated threats in operation.

Wind-Induced Response and Equivalent Static Wind Loads on Waiting Hall Building of Regular Railway Stations

This paper investigates the influence of the canopy span, canopy opening width and waiting hall building height on the loads and equivalent static wind loads (ESWL) of the waiting hall building. The results show both the mean and standard deviation wind pressure coefficients at the roof of waiting hall buildings are affected by the interference effects caused by the upstream canopies. The wind-induced response of the waiting hall building roof is usually dominated by the first vibration mode, 0∘, 90∘ and 180∘ are the three adverse wind directions. Based on the wind tunnel tests, parameters of the fitted spectrum of the first modal generalized wind pressure for waiting hall buildings are obtained at the adverse wind directions. The semi-analytical expressions of equivalent static wind loads (ESWL) on waiting hall building roofs are derived using the first modal inertial force as a function of the structural reduced frequency. The good accuracy of the proposed ESWL is verified by comparing the nodal displacements and member stresses calculated by the proposed method to the actual dynamic peak results.

Vehicle weight identification based on equivalent loads reconstructed from responses of beam-like bridge

Moving force identification (MFI) is an effective way for closely monitoring vehicle weight in a dynamic state. Time-varying position of vehicle is usually needed. This applying condition may limit the applicability because the measurement of time-varying position has certain difficulty. To tackle this problem, this study proposes an equivalent load-based method for identifying the gross weight of a vehicle moving on a beam-like bridge. The proposed method is developed based on an innovative concept of equivalent load and the application of force reconstruction. Herein, the equivalent loads are expressed as some concentrated loads whose acting positions are time invariant. Modal forces induced by the equivalent loads are equal to the ones caused by the vehicle-induced moving forces. Under the crucial assumption of equivalent loads, the first key step is to reconstruct the equivalent loads by using a force identification method that is implemented via matrix regularization. Since the equivalent loads have been estimated, the second step aims to introduce a practical strategy for identifying the vehicle weight from the sum of the identified equivalent loads rather than the sum of moving forces. Because of this, a highlight is that time-varying position of vehicle is not needed. To verify the effectiveness and feasibility of the proposed method, beam structures with single span are carried out for numerical simulations and experimental validations. Illustrated results show that the proposed method can be applied for identifying the gross weight of a vehicle moving on a beam-like bridge with high accuracy and strong robustness. Some related issues are discussed as well.