五层房屋缩尺模型实验模态分析

Performing forced vibration tests on full-scale structures is the most reliable way of determining the relevant modal parameters in structural dynamics, such as modal frequencies, mode shapes, modal damping, and modal masses. This study describes the modal identification of a double-level curved cable-stayed bridge with separate deck systems for pedestrians and vehicles via forced vibration tests. The steady-state structural responses to sinusoidal excitations produced by an electrodynamic shaker are recorded under varying excitation frequencies, and the frequency response functions are established. The measured frequency response functions are curve fitted to estimate the modal parameters. The numerical simulation of frequency response function–based modal parameter identification of an elastically multi-supported continuous beam structure is carried out, and the emphasis has been placed on the evaluation of the effect of an additional shaker mass, excitation frequency step and range, multi-mode vibration, and noise on identification results. Finally, the modal parameters for the first lateral mode of a double-level curved cable-stayed bridge are identified by forced vibration experiments, and the results are compared with those from ambient vibration tests and free vibration tests. The effect of the unmeasured wind excitation on identification is discussed. It is shown that the effect of ambient vibration is minor for wind velocity of 3–5 m/s. The damping ratios identified by forced and free vibration tests are comparable, while those from ambient vibration are subject to large variations. The modal mass obtained from forced vibration tests is in good agreement with finite element prediction, which provides design basis for mass-type dampers.

Modal parameters, i.e., modal frequencies, damping ratios, and mode shapes of a two disk-shaft system are estimated in Multiple Input/Multiple Output (MIMO) scheme. The response at the output degrees of freedom (dof) of the considered structure due to the excitation at the input dofs is estimated from theoretical analysis. The generated theoretical data is used to estimate the Frequency Response Function (FRF) matrix, which relates the output (vibration) at response points with the input at the excitation points in the frequency domain. The corresponding Impulse Response Function (IRF) matrix, which relates response and excitation in the time domain, is obtained by Inverse Fast Fourier Transform (IFFT) of the FRF matrix. The unified Matrix Polynomial Approach (UMPA) is employed in the frequency and time domains with the estimated FRF and IRF matrices, respectively, to estimate the desired modal parameters. The obtained results are compared with results from Theoretical Modal Analysis (TMA).

This paper presents the system identification technique by applying PZT actuators and PVDF sensors. An array of finite-length PVDF films is equally spaced and distributed over a cantilever beans acting as sensors. Two finite-length PZT patches are bonded symmetrically and excited 180°out-of-phase for pure bending excitation. The theoretical base of modal analysis for system identification of piezoceramic beams is presented to derive the frequency response functions (FRFs) in conventional modal format. The physical interpretation of P11 and PVDF mode shape functions are characterized respectively. The FRFs between the PZT actuators and PVDF sensors are experimentally measured. By the operation of a series of FRFs and the application of modal parameter extraction method, the modal parameters. including system natural frequencies, mode shapes and modal damping ratios, can be obtained. Both theoretical and experimental approaches agree very well. The system information can be used for control applications and also be applicable to structural failure diagnosis.

This paper presents the use of piezoceramic transducers, Lead Zirconia Titanate (PZT) actuators and Polyvinylidene Fluoride (PVDF) sensors, for experimental modal testing of a simply supported plate. A series of rectangular-shaped PVDF films are evenly distributed over the plate and act as the sensing devices instead of traditional acceleration sensors. Pairs of rectangular PZT patches are bounded to opposite sides of the plate to form actuators and when they are excited by 180° out-of-phase stimulation, they will cause pure bending. The theoretical formulation of frequency response functions (FRFs) of the piezoceramic transducers is developed. The mode shape functions of the PZT actuator and the PVDF sensor are identified, respectively. Experiments are performed to obtain a column of FRF matrix. The structural modal parameters, including natural frequencies, modal damping ratios and mode shapes, can then be extracted by a modal parameter extraction method. Results show the modal parameters can be properly obtained and physically interpreted. This paper presents the concepts of smart structural testing (SST) with the use of piezoceramic transducers and leads to the applications of smart structures to health monitoring of structural systems.

As all experimental procedures, Experimental Modal Analysis (EMA) is subject to a wide range of potential testing and processing errors. The modal identification methods are sensitive to these errors, yielding modal results which are uncertain up to certain error bounds. The question hence is what these error bounds on test data and modal parameters are. In this paper, the studied source of uncertainty is related to the variance (noise) on the Frequency Response Function (FRF) measurements. Under the H1 assumptions and in single-input cases, the FRF variances can be computed from the coherences and the FRFs. In multiple-input cases, some more measurement functions are required. Advanced system identification methods like the Maximum Likelihood Estimator (MLE) and PolyMAX Plus have the possibility to take the uncertainty on the measurement data into account and to propagate the data uncertainty to (modal) parameter uncertainty. This paper will review FRF variance estimation techniques, including some pragmatic approaches. The basic concepts of Maximum Likelihood Estimation and the calculation of confidence bounds will be discussed. Some typical structural testing and modal analysis cases will be used as illustration of the discussed concepts.

Vehicle–road coupled system is inherently time–varying, and its responses are traditionally calculated using time–domain methods which involves significant computational effort. Aiming to improve the efficiency of response calculation for the coupled system, this paper proposes a fast calculation method in frequency domain, based on the newly developed moving frequency response function (FRF). Firstly, considering the vibration characteristics of an infinitely long road, the road response is straightforwardly expressed using the road impulse response function (IRF). Subsequently, the concept of the road moving IRF is proposed and derived with respect to the moving observation points. The moving FRF is then obtained by applying Fourier transform, which allows the responses of the road moving observation points to be established in frequency domain for fast calculation under moving loads. Furthermore, by analyzing the vehicle–road coupled vibrations, based on the vehicle FRF and road moving FRF, a formula for the vehicle–road coupling force is derived in frequency domain, along with an expression for the responses at the vehicle–road contact points. Finally, the approach is illustrated in numerical simulations of vehicle–road coupled systems, and its computational efficiency and accuracy are verified through comparison with currently popular methods.

Accurate and timely identification of modal parameters of long-span bridges is important for bridge health monitoring and wind tunnel tests. Wavelet analysis is one of the most advantageous methods for identification because of its good localization characteristics in both time and frequency domain. In recent years, the wavelet method has been applied more frequently in parameter identification of linear and nonlinear systems. In this article, based on wavelet ridges and wavelet skeleton, the improved modal parameter identification method was studied. To find the appropriate time-frequency resolution, an optimal wavelet basis design principle based on minimum Shannon entropy was proposed. Aiming at endpoint effect in wavelet transform, a prediction continuation method based on support vector machine (SVM) was proposed, which can effectively suppress the endpoint effect of the extended samples. In view of the fact that the ridges of metric matrices obtained by the traditional crazy climber algorithm cannot fully reflect the distribution of ridges of modulus value matrices of wavelet coefficients, an improved high-precision crazy climber algorithm was put forward to accurately identify the position of the ridge of wavelet coefficients. Finally, taking a long-span cable-stayed bridge and a long-span suspension bridge as the engineering background, improved continuous wavelet transform (CWT) was applied to modal parameter identification of bridge under ambient excitation. The modal parameters such as modal frequency, damping ratio, and mode shape were obtained. Compared with the calculation value of the numerical simulation of long-span cable-stayed bridge and wind tunnel test of long-span suspension bridge, the reliability of CWT for modal parameter identification of long-span bridges under ambient excitation was verified.

In this paper, the dynamic behavior of a cantilever beam without and with crack is observed. An elastic Aluminum cantilever beams having surface crack at various crack positions are considered to analyze dynamically. Crack depth, crack length and crack location are the foremost parameters for describing the health condition of beam in terms of modal parameters such as natural frequency, mode shape and damping ratio. It is crucial to study the influence of crack depth and crack location on modal parameters of the beam for the decent performance and its safety. Crack or damage of structure causes a reduction in stiffness, an intrinsic reduction in resonant frequencies, variation of damping ratios and mode shapes. The broad examination of cantilever beam without crack and with crack has been done using Numerical analysis (Ansys18.0) and experimental modal analysis. To observe the exact higher modes of beam, discretize the beam into small elements. An experimental set up was established for cantilever beam having crack and it was excited by an impact hammer and finally the response was obtained using PCB accelerometer with the help sound and vibration toolkit of NI Lab-view. After obtaining the Frequency response functions (FRFs), the natural frequencies of beam are estimated using peak search method. The effectiveness of experimental modal analysis in terms of natural frequency is validated with numerical analysis results. This paper contains the study of free vibration analysis under the influence of crack at different points along the length of the beam.

Auxiliary harmonic excitation generalized method for random vibration analysis of linear structures under non-stationary Gaussian excitation

Viscoelastic materials are used in vibration damping applications as they have the ability to dissipate energy, they are used in machine basis, bridges and many other applications. In this paper four plates with the same thickness but different material lamination are investigated for their modal properties. Namely,natural frequencies, mode shapes and damping loss factors. Experimental modal analysis is carried out using impact hammer for excitation and accelerometer for measurement. Data is processed using computer package to obtain frequency response function (FRF) for each plate and modal parameters are extracted from the plot. Results are compared to finite element model that was created using ANSYS package. It showed very well agreement between experimental and finite element. Damping effect on the shift in natural frequencies was obvious due to the viscoelastic material thickness in the laminated plates. It is concluded that the finite element analysis using ANSYS software is a powerful tool in predicting natural frequencies and mode shapes even in laminated plates with viscoelastic core, it is also confirmed the effect of damping increase due to the use of viscelastic cores on the plate natural modes and vibration behaviour.

High-speed digital image correlation is a camera-based displacement measurement technique that has experienced increasing popularity for modal analysis. It is due to a high spatial density of measurement that provides an outstanding interpretation of mode shapes or operational deflection shapes. However, its sensitivity is typically lower than other techniques and transducers such as accelerometers or laser vibrometry. With these measurements, the estimation of any transfer function in the frequency domain is noisier in valley regions of the response, including anti-resonances. Therefore, an accurate analytical model of the response should be used for modal identification. Modal analysis algorithms perform an identification of the modal parameters and a reconstruction of the response based on the transfer function between force excitation and displacement response. This is called the frequency response function. However, force measurements are not available in many experiments, where the motion excitation is recorded instead. This is the case when the vibration is applied to the specimen through a motion in its base. This transfer function, also known as the transmissibility function, relates the motion of excitation and response, whose shape differs from the frequency response function. This difference in the response function is relevant in a relatively noisy measurement like using digital image correlation. Hence, in this work, a transformation of the transmissibility function into equivalent frequency response function, based on theoretical models, is performed prior to modal identification in base motion tests. More suitable experimental response functions are obtained, increasing the accurateness of the modal parameter estimation.KeywordsModal analysisTransmissibility functionsFull-field measurement

Experimental modal analysis (EMA) with oblique excitation (i.e. oblique impact testing) is useful in improving the long test time problem of conventional EMA with normal excitation (i.e. triaxial normal impact testing), in order to extract all the important dynamic characteristics of a 3D complex structure. In this study, a new methodology involving a vector projection method is introduced to find the driving point frequency response function (FRF) in the oblique direction, without the need for a special fixture with an obliquely oriented impedance head. Hence, this presents a low cost and practical solution for scaling the mode shape, as compared to the traditional approach. Moreover, the concurrent forces characteristic of oblique excitation are used in the development of the theoretical relationship between FRFs with oblique excitation and those with normal excitation. This is important for the validation of the oblique impact testing result, such as the FRF and modal parameter estimations. The experimental results show that oblique impact testing has reliable and effective results, as compared with the triaxial normal impact testing, in terms of the FRF correlation, natural frequency discrepancy, modal damping ratio error and modal assurance criterion of the unit modal mass mode shape.

Measurement of Frequency Response Functions (FRFs) on the Millennium Bridge in London was a key part in the validation of the retrofit solution for excessive sway vibration caused by walking pedestrians during the bridge opening in June 2000. The measured FRFs were employed to verify the analytical response analysis and to estimate and confirm analytical predictions of natural frequencies, modal damping ratios, mode shapes and modal masses corresponding to various configurations of prototype viscous and tuned mass dampers. These results were used to experimentally assess the effectiveness of the proposed retrofit solution. Although FRF measurement technology is fairly standard in many engineering disciplines, its application on the Millennium Bridge was quite problematic and required some unique solutions which are described in this paper. Modal testing of the Millennium Bridge clearly demonstrated that it was possible to measure good quality FRFs around a frequency as low as 0·5 Hz, which was the natural frequency of the first lateral mode of vibration. This was achieved by designing, constructing and installing a bespoke hydraulic shaker featuring a translatory moving mass of 1000 kg. As the shaker was not able to produce perfectly sinusoidal excitation for stepped-sine testing, FRFs were successfully estimated using the so-called Resolver method in conjunction with an Hc estimator. The standard H1 FRF estimator, which is used in the vast majority of modern digital spectrum analysers nowadays, was demonstrably unable to produce meaningful FRF estimates when using the Resolver approach. The FRF estimation and curve-fitting performed in situ proved to be crucial for the success of the modal testing of the Millennium Bridge. By evaluating the estimates of the experimental FRFs and the corresponding modal properties during the testing programme on site, a number of test errors were spotted. This, in turn, enabled immediate repetition of measurements and/or evaluation of the structural behaviour which would have been impossible if the FRF data analysis had been performed after the testing had been completed.

Identification of modal parameters of unmeasured modes using multiple FRF modal analysis method

Cyclostationarity and the cepstrum for operational modal analysis of MIMO systems—Part II: Obtaining scaled mode shapes through finite element model updating