Modal Analysis Approach Research Articles

A frequency domain blind identification method for operational modal analysis using a limited number of sensors

Operational modal analysis is an experimental modal analysis approach, which uses vibration data collected when the structure is under operating conditions. Amongst the methods for operational modal analysis, blind source separation–based methods have been shown to be efficient and powerful. The existing blind source separation modal identification methods, however, require the number of sensors to be at least equal to the number of modes in the frequency range of interest to avoid spatial aliasing. In this article, a frequency domain algorithm that overcomes this problem is proposed, which is based on the joint diagonalization of a set of weighted covariance matrices. In the proposed approach, the frequency range of interest is partitioned into several frequency ranges in which the number of active modes in each band is less than the number of sensors. Numerical simulations and an experimental example demonstrate the efficacy of the method.

Modal analysis and modelling approach for piezoelectric transducers based energy harvesting applications

Modal analysis and modelling approach for piezoelectric transducers based energy harvesting applications

Modal analysis and modelling approach for piezoelectric transducers based energy harvesting applications

The use of piezoelectric elements to recover energy from machine vibrations, motor vehicle interactions with roads and human motion has been an area of serious research in academia and industry for...

Study of interactions between close HVDC links inserted in an AC grid: A mixed nonlinear and modal analysis approach

This paper focuses on interaction between two closed-connected high-voltage DC (HVDC) lines. This interaction is studied by employing high-fidelity nonlinear modeling in MATLAB R /Simulink R software environment. In order to describe the mechanism behind the HVDCs interaction, both nonlinear time-domain simulations and modal analysis of the coupled HVDC links, have been performed. System small-signal stability has been assessed and the path of interactions has been identified by computing the participations of various states in the oscillatory modes; this sets the preliminaries for a global, grid-oriented HVDCs control design approach. After the detailed analysis of newly-identified coupling oscillations , the minimal modeling requirements to put them into evidence have also been studied; this significantly facilitates the analysis in a realistic large-scale grid context.

Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

The dynamics of flexible multibody systems (FMBSs) is governed by ordinary differential equations or differential-algebraic equations, depending on the modeling approach chosen. In both the cases, the resulting models are highly nonlinear. Thus, they are not directly suitable for the application of the modal analysis and the development of modal models, which are very useful for several advanced engineering techniques (e.g., motion planning, control, and stability analysis of flexible multibody systems). To define and solve an eigenvalue problem for FMBSs, the system dynamics has to be linearized about a selected configuration. However, as modal parameters vary nonlinearly with the system configuration, they should be recomputed for each change of the operating point. This procedure is computationally demanding. Additionally, it does not provide any numerical or analytical correlation between the eigenpairs computed in the different operating points. This paper discusses a parametric modal analysis approach for FMBSs, which allows to derive an analytical polynomial expression for the eigenpairs as function of the system configuration, by solving a single eigenvalue problem and using only matrix operations. The availability of a similar modal model, which explicitly depends on the system configuration, can be very helpful for, e.g., model-based motion planning and control strategies towards to zero residual vibration employing the system modal characteristics. Moreover, it allows for an easy sensitivity analysis of modal characteristics to parameter uncertainties. After the theoretical development, the method is applied and validated on a flexible multibody system, specifically using the Equivalent Rigid Link System dynamic formulation. Finally, numerical results are presented and discussed.

An alternative approach for modal analysis of stiffened thin-walled structures with advanced plate elements

Nowadays, many vehicles and buildings are built using the structural concept of stiffened structure, in order to achieve greater strength with relatively less material. In the present work, a plate finite element with advanced higher-order kinematic field is proposed for the free-vibration analysis of stiffened thin-walled plate structures. A novel approach is introduced to simplify the modelization and assembling phase for the analysis of stiffened structures. The mechanical continuity between skin and stiffener deformed geometry is automatically verified with the present approach. On the basis of the Principle of Virtual Displacements, Equivalent-Single-Layer and Layer-Wise models related to linear up to fourth order variations of the unknown variables in the thickness direction are treated. The Mixed Interpolated Tensorial Components (MITC) method, in conjunction with the Finite Element Method (FEM), is employed to contrast the shear locking effect. Various stiffener shapes are considered for the assessment of the approach: T shape, double-T shape and Z shape. Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the present plate finite element for the modal analysis of stiffened structures, comparing the present results with those from classical finite element formulations based on solid elements available in commerical software.

The surrogate system hypothesis for joint mechanics

Abstract The main challenges in the design and analysis of jointed structures deal with the prediction of dissipation across bolted interfaces. Since friction is thought to be one of the main mechanisms for this, the current study investigates the utility of frictional parameter identification applied across different structures. Based on recent discoveries, a Surrogate System Hypothesis has been formulated to systematize this: the hypothesis states in brief, that the physical properties of a joint are independent of its structural context. The current work seeks to obtain a better understanding of the underlying systems by evaluating a confidence metric for the hypothesis for a relatively simple set of systems—physically perturbed configurations of the Brake-Reus Beam. Interfacial friction is modeled using whole jointed patches with distributed hysteretic (Iwan) elements and simulations are conducted using the Quasi-Static Modal Analysis (QSMA) approach to estimate the modal characteristics of the system response (amplitude dependence of natural frequency and dissipation). Posing the estimation as a Multi-Objective Optimization Problem (MOOP) is shown to reveal important features of both the employed constitutive model as well as the structure that is modeled. Consequently, the approach is used to evaluate the epistemic uncertainty inherent in three different friction models. The studies reveal that a confidence metric for the hypothesis can be formulated in such a way that it is nearly independent of the friction constitutive model that is employed.

An exact modal analysis approach to vibration analysis of structures with mass-spring subsystems and rotational joints

A novel exact modal analysis approach is presented for vibration analysis of plane continuous structures, which are coupled with discrete mass-spring subsystems and include elastic rotational joints modelling local flexibility. Using the theory of generalised functions to handle the discontinuities of the response variables, every continuous member with any number of mass-spring subsystems and joints is treated as a two-node element, for which a 6 × 6 exact dynamic stiffness matrix is obtained in closed form. As a result, the global dynamic stiffness matrix is built by a standard finite-element assembling procedure, with size depending only on the number of nonzero nodal degrees of freedom of member-to-member nodes. Upon deriving pertinent orthogonality conditions for the modes, the system response under arbitrary loads is obtained by modal impulse and modal frequency response functions, under the assumption of proportional damping. The solutions are exact and can be used as benchmark for classical finite-element solutions. The approach is formulated for various mass-spring subsystems, acting in transverse and axial directions relative to every member.

An analytical investigation into the propagation properties of uncertainty in a two-stage fast Bayesian spectral density approach for ambient modal analysis

Abstract This paper investigates the uncertainty propagation properties of a two-stage fast Bayesian spectral density approach (two-stage fast BSDA) with separated modes proposed previously by the authors Yan and Katafygiotis (2015a,b) [1,2], deriving explicit formulas for the dependence of the posterior coefficients of variation (c.o.v.) of the identified modal parameters in terms of different parameters influencing the identification. For this, an approximation analysis strategy proposed in Au (2014a,b) [3,4] is adopted. Although the explicit closed-form approximation expressions are relatively complex, the expressions for the approximate dependence of uncertainty are simple and informative. The analysis reveals a strong correlation among the prediction error, the damping ratio and the power spectral density (PSD) of the modal excitation. While similar correlation trends have been observed in the posterior uncertainty analysis of the fast Bayesian FFT (fast BFFT) approach Au (2014a) [3], the present method shows that the identification results are more sensitive to modeling error. Note that this is not a contradicting result, as the uncertainty propagation properties of different methods may generally differ. Note that fast BFFT is a more fundamental method, in the sense that it processes FFT data directly, while the two-stage fast BSDA uses spectral density data in a manner that allows for decoupling of the mode shape data. Validation studies using synthetic data and field data measured from a laboratory model provide a practical verification of the rationality and accuracy of the theoretical findings.

A new simplified approach for assessing nonlinear seismic response of plan-asymmetric structures considering soil-structure interaction

An innovative approximate method is presented to consider the plan asymmetry, nonlinear structural behaviour and soil-structure interaction (SSI) effects simultaneously. The proposed method so-called Flexible base 2DMPA (F2MPA) is an extension of 2 degrees of freedom modal pushover analysis (2DMPA) approach to consider foundation flexibility in seismic response analysis of plan asymmetric structures which itself were developed based on Uncoupled Modal Response History Analysis method for inelastic fixed-base asymmetric structures. In F2MPA for each mode shape using 2DMPA procedure, the elastic and inelastic properties of 2DOF modal systems corresponding to the fixed-base structure are initially derived. Then in each time step, displacements and inelastic restoring forces of the superstructure are computed from modal equations of the flexibly-supported structure. In each time step, the nonlinear secant stiffness matrix corresponding to the n-th MDOF modal equations of soil-structure system is updated using the corresponding modal 2DOF system of fixed-base structure. To update the transformed modal stiffness matrix of the SSI system, this matrix is partitioned and it is assumed that the non-linear variation of the superstructure can be estimated from the variation of modal stiffness matrix of the fixed-base structure. Accuracy of the proposed method was verified on an 8-story asymmetric-plan building under different seismic excitations. The results obtained from F2MPA method were compared with those obtained by nonlinear response history analysis of the asymmetric soil-structure system as a reference response. It was shown that the proposed approach could predict the results of the nonlinear time history analysis with a good accuracy. The main advantage of F2MPA is that this method is much less time-consuming and useful for the practical aims such as massive analysis of a nonlinear structure under different records with multiple intensity levels.

Exact frequency response of two-node coupled bending-torsional beam element with attachments

• Coupled bending-torsional dynamics of beams with dampers/masses is addressed. • Exact analytical frequency response is built for any harmonic point/polynomial loads. • Exact two-node 6 × 6 dynamic stiffness matrix and 6 × 1 load vector are built in closed form. • Dynamic stiffness matrix and load vector hold same size for any number of dampers/masses and loads. • Modal frequency responses and modal impulse responses are derived by complex modal analysis. This paper addresses the frequency response of coupled bending-torsional beams carrying an arbitrary number of in-span viscoelastic dampers and attached masses. Using the elementary coupled bending-torsion theory, along with appropriate generalized functions to treat the discontinuities of the response variables at the application points of dampers/masses, exact analytical expressions are derived for the frequency response of the beam under harmonically-varying, arbitrarily-placed point/polynomial loads. On this basis, the exact 6 × 6 dynamic stiffness matrix and 6 × 1 load vector of a two-node coupled bending-torsional beam finite element, with any number of in-span dampers/masses and harmonic loads, are obtained in a closed analytical form. Finally, the modal frequency response functions of the beam are built by a complex modal analysis approach, upon deriving pertinent orthogonality conditions for the modes. In this context, the modal impulse response functions are also obtained for time-domain analysis under arbitrary loads.

OMA analysis of a launcher under operational conditions with time-varying properties

The objective of this paper is the investigation of the capability of operational modal analysis approaches to deal with time-varying system in the low-frequency domain. Specifically, the problem of the identification of the dynamic properties of a launch vehicle, working under actual operative conditions, is studied. Two OMA methods are considered: the frequency-domain decomposition and the Hilbert transform method. It is demonstrated that both OMA approaches allow the time-tracking of modal parameters, namely, natural frequencies, damping ratios, and mode shapes, from the response accelerations only recorded during actual flight tests of a launcher characterized by a large mass variation due to fuel burning typical of the first phase of the flight.

A practical scheme of vibration monitoring and modal analysis for caisson breakwater

In this study, a practical vibration analysis approach to obtain the dynamic characteristics of an in-situ caisson breakwater under the ambient wave load is presented. Firstly, a scheme of vibration monitoring and modal analysis is designed for the caisson breakwater. The limits of vibration monitoring on the caisson system is examined based on sensor placement and excitation source. An output-only modal analysis approach which combines the time-domain stochastic subspace identification method and the frequency domain decomposition method is designed to estimate modal parameters from wave-induced ambient vibration signals. Secondly, in-situ tests on a real caisson breakwater are described. Acceleration signals recorded under ambient wave-induced excitation are experimentally analyzed for a few caisson units under sea-level variation. Finally, experimental modal analyses are performed on the measured acceleration signals to evaluate the practicality of the proposed scheme. The numerical modal analysis of the caisson-foundation system was also conducted to support the experimental mode identification result. Relative modal responses of three adjacent caisson units are analyzed to estimate relative differences in dynamic characteristics due to their structural conditions. Also, the effect of water-level variation on modal parameters such as natural frequencies, modal damping and mode shapes is analyzed from the in-situ vibration records of a single caisson unit.

Operational modal identification in the presence of harmonic excitation

The dynamic behavior of structures can be studied by the identification of their modal parameters. Classical modal analysis methods are based on the relation between the forces applied to structures (inputs) and their vibration responses (outputs). In real operational conditions it is difficult, or even impossible, to measure the excitation. For this reason, operational modal analysis approaches which consider only output data are proposed. However, most of these output-only techniques are proposed under the assumption of white noise excitation. If additional components, like harmonics for instance, are present in the exciting force, they will not be separated from the natural frequencies. Consequently, this assumption is no longer valid. In this context, an operational modal identification technique is proposed in order to only identify real poles and eliminate spurious ones. It is a method based on transmissibility functions.The objective of the proposed paper is to identify modal parameters in operational conditions in the presence of harmonic excitations. Identification is performed using a method based on transmissibility measurements and then with the classical stochastic subspace identification method, which is based on white noise excitation. These two methods are first applied to numerical examples and then to a laboratory test. Results validate the novel ability of the method based on transmissibility measurements to eliminate harmonics, contrary to the stochastic subspace identification approach.

Modeling of second-harmonic generation of circumferential guided wave propagation in a composite circular tube

This paper investigated modeling of second-harmonic generation (SHG) of circumferential guided wave (CGW) propagation in a composite circular tube, and then analyzed the influences of interfacial properties on the SHG effect of primary CGW. Here the effect of SHG of primary CGW propagation is treated as a second-order perturbation to its linear wave response. Due to the convective nonlinearity and the inherent elastic nonlinearity of material, there are second-order bulk driving forces and surface/interface driving stresses in the interior and at the surface/interface of a composite circular tube, when a primary CGW mode propagates along its circumference. Based on the approach of modal expansion analysis for waveguide excitation, the said second-order driving forces/stresses are regarded as the excitation sources to generate a series of double-frequency CGW modes that constitute the second-harmonic field of the primary CGW propagation. It is found that the modal expansion coefficient of each double-frequency CGW mode is closely related to the interfacial stiffness constants that are used to describe the interfacial properties between the inner and outer circular parts of the composite tube. Furthermore, changes in the interfacial stiffness constants essentially influence the dispersion relation of CGW propagation. This will remarkably affect the efficiency of cumulative SHG of primary CGW propagation. Some finite element simulations have been implemented of response characteristics of cumulative SHG to the interfacial properties. Both the theoretical analyses and numerical simulations indicate that the effect of cumulative SHG is found to be much more sensitive to changes in the interfacial properties than primary CGW propagation. The potential of using the effect of cumulative SHG by primary CGW propagation to characterize a minor change in the interfacial properties is considered.

Modal pushover analysis of self-centering concentrically braced frames

Self-centering concentrically braced frames (SCCBFs) are emerging as high performance seismically resistant braced framing system, due to the capacity of withstanding strong earthquake attacks and promptly recovering after events. To get a further insight into the seismic performance of SCCBFs, systematical evaluations are currently conducted from the perspective of modal contributions. In this paper, the modal pushover analysis (MPA) approach is utilized to obtain the realistic seismic demands by summarizing the contribution of each single vibration mode. The MPA-based results are compared with the exact results from nonlinear response history analysis. The adopted SCCBFs originate from existing buckling-restrained braced frames (BRBF), which are also analyzed for purpose of comparison. In the analysis of these comparable framing systems, interested performance indices that closely relate to the structural damage degree include the interstory drift ratio, floor acceleration, and absorbed hysteretic energy. The study shows that the MPA approach produces acceptable predictions in comparison to the exact results for SCCBFs. In addition, the high-modes effect on the seismic behavior increases with the building height, and is more evident in the SCCBFs than the BRBFs.

Design, Analysis, Fabrication and Testing of a Formula Car Chassis

Formula car racing is always a rich sport and millions of research is been done on the development of highly optimised cars. The work shown in this paper consists of the design and fabrication of formula car chassis and testing of its weak points and expected life. CAD software is adopted to chassis design and further finite element analysis like static analysis, modal analysis, transient analysis and fatigue analysis were performed in ANSYS software before fabrication. Vibration transfer path analysis demonstrates the resulting performance of chassis as an alternative to the modal analysis approach for solving noise and vibration problems.

Output-Only Modal Analysis of Micromilling Systems

An output-only modal analysis (OMA) approach is presented to obtain the direct frequency response function (FRF) at the tip of the tool in micromilling setups. White noise input is provided using acoustic excitation and the resulting vibrations are measured using a laser Doppler vibrometer (LDV). Autoregressive (AR) identification is used to extract the natural frequencies and damping ratios of the structural modes of the milling setup, and mass-sensitivity analysis is used to obtain modal stiffness values. The accuracy of the tool tip FRFs that are constructed using OMA is verified by comparing them against the FRFs that are measured using impulse hammer tests. The direct FRF at the tool tip is an essential component in predicting and avoiding excessive and unstable vibrations in milling operations, and the presented approach provides a practical method for the direct measurement of the tool tip FRF in micromilling where the application of traditional hammer tests is not possible.

Experimental investigation on multi-mode flow-induced vibrations of two long flexible cylinders in a tandem arrangement

Laboratory tests of flow-induced vibrations (FIV) of two tandem long flexible cylinders were conducted in a towing tank. The two identical cylinder models with an aspect ratio of 350 and a mass ratio of 1.90 were towed along the tank by a carriage to generate a uniform flow. The towing velocity was in the range of 0.05–1.0 m/s, and the corresponding Reynolds number approximately ranged from 800 to 16,000. Strain gauges were used to measure the time-varying strains in both cross-flow (CF) and in-line (IL) directions. A modal analysis approach was adopted to reconstruct the displacement response based on the strain signals in measurement positions. Five center-to-center separation distances (T/D = 4.0, 6.0, 8.0, 10.0 and 16.0) were tested in the experiments. The influence of separation distance on the multi-mode FIV behaviors of two tandem flexible cylinders was investigated from various aspects, e.g. strain and displacement responses, dominant frequencies and modes, mean drag force coefficients. Experimental results show that the multi-mode FIV behaviors of the upstream cylinder are similar to an isolated single cylinder within the separation distance range tested. The response of the downstream cylinder obviously differs from the upstream one due to the wake shielding effects generated by the upstream cylinder. In addition, there are no clear trends associated with the separation distance regarding the response amplitude of the downstream cylinder.

Experimental application of OMA solutions on the model of industrial structure

It is very important and sometimes even vital to maintain reliability of industrial structures. High quality control during production and structural health monitoring (SHM) in exploitation provides reliable functioning of large, massive and remote structures, like wind generators, pipelines, power line posts, etc. This paper introduces a complex of technological and methodical solutions for SHM and diagnostics of industrial structures, including those that are actuated by periodic forces. Solutions were verified on a wind generator scaled model with integrated system of piezo-film deformation sensors. Simultaneous and multi-patch Operational Modal Analysis (OMA) approaches were implemented as methodical means for structural diagnostics and monitoring. Specially designed data processing algorithms provide objective evaluation of structural state modification.