Abstract: The effect of prescribed delamination on natural frequencies of laminated composite beam specimens is examined both experimentally and theoretically. Delamination is of particular interest because it can cause catastrophic failure of the composite structure. One consequence of delamination in a composite structure is a change in its stiffness. This change in stiffness will degrade the modal frequencies of the composite structure. Modal testing of a perfect beam and beams with different delamination size is conducted using polyvinylidene fluoride film (PVDF) sensors and piezoceramic (PZT) patch with sine sweep actuation. Modal testing of beams is also conducted using PVDF sensors and instrumented hammer excitation. The results of piezoceramic patch excitation and instrumented hammer excitation are discussed. The experimental modal frequencies are compared with the results obtained using a simplified beam theory. Also, backpropagation neural network models are developed using the results from the beam theory and used to predict delamination size. The effect of learning rate and momentum rate on neural network performance are discussed. Modal frequencies can be easily and accurately obtained with PZT patch excitation and PVDF sensing. There is good agreement between modal frequencies from modal testing and those from the simplified beam theory. The neural network models developed successfully predict delamination size.

Abstract: For low‐frequency applications, a modal approach can be useful to describe vibro‐acoustical coupling. Based on combined vibrational/acoustical frequency response function measurements, either with respect to acoustical or structural excitation, modal vibro‐acoustical analysis can be carried out. This paper presents a consolidation of the theory behind the vibro‐acoustical modal model. The model formulation is shown to be a nonsymmetrical formulation. It is shown that this is not contradictory to the well‐known vibro‐acoustical reciprocity principle. The implications of the nonsymmetry for the modal model are discussed. It is pointed out which variables must be measured and what kind of scaling must be used in order to end up with a consistent modal formulation. The theory is illustrated and verified by measurements on an experimental vibro‐acoustical system, consisting of a rigid cavity with one flexible wall.

Abstract: This paper introduces an automated approach to pick-up and exciter placement for modal testing purposes and its application to a car body component. It is a two step procedure which in the first step localizes a subset of structural degrees of freedom of an analytical model as measurement points such that the linear independence of the mode shapes to be measured is maximized. In the second step a given number of exciter locations are chosen among the selected measurement points which allow an excitation of the mode shapes. The approach is based on the QR-decomposition of the modal matrix and the QR- decomposition of the product of the mass matrix with the modal matrix.

Abstract: A dynamic modal testing technique has been developed to noninvasively assess the interface surrounding an endosseous dental implant with a lateral tap from an impedance head hammer. The technique assesses the rotational stiffness of the interface based on the shape of the power spectrum of the force-time curve produced on impact. In vitro experiments were performed to determine the sensitivity of the technique for detecting clinically relevant structural differences between interfaces. The modal test data were able to distinguish interfaces based on the type of bone at the interface and the degree of fixation between the implant and the interface.

Abstract: Modal interaction refers to the way that the modes of a structure interact when its geometry and material properties are perturbed. The amount of interaction between the neighboring modes depends on the closeness of the natural frequencies, the mode shapes, and the magnitude and distribution of the perturbation. By formulating the structural eigenvalue problem as a normalized modal eigenvalue problem, it is shown that the amount of interaction in two modes can be simply characterized by six normalized modal parameters and the difference between the normalized frequencies. In this paper, the statistical behaviors of the normalized frequencies and modes are investigated based on a perturbation analysis. The results are independently verified by Monte Carlo simulations.Copyright © 1996 by ASME

Abstract: Three measures of modal dynamic importance are studied for the purpose of ranking Craig-Bampton substructure fixed interface mode shapes based upon their contribution to forces at the substructure interface, modal velocity, or modal displacement. These measures can be employed to identify mode shapes which are dynamically important and thus should be retained in a reduced analytical representation, or identified during a modal survey of the substructure. The first method considered, Effective Interface Mass, has been studied previously. However, new results are presented showing the relation between Effective Interface Mass and a commonly used control dynamics measure of modal importance called approximate balanced singular values. In contrast to the general case of approximate balanced singular values, Effective Interface Mass always gives an absolute measure of the dynamic importance of mode shapes. The EIM method is extended to consider modal velocity and modal displacement outputs. All three measures are applied to a simple substructure called the General Purpose Spacecraft. It is shown that each of these measures provides an efficient method for ranking the dynamic importance of Craig-Bampton fixed interface modes such that a reduced representation will accurately reproduce the substructure's response in the frequency range of interest.

Abstract: General means for evaluating the vibration behaviour of turbogenerator installations where the foundation has natural frequencies in the operating range have not been satisfactorily developed because one does not normally have access to an accurate foundation model and modal testing of the foundation is suspect owing to the already installed rotor. Hence, various techniques have been proposed to devise equivalent foundations which produce the same system dynamic response over the speed range of interest. The approach in this paper is to represent foundations in terms of their modal parameters. The unbalance responses are evaluated at selected speeds. By minimising an objective function derived from these responses, the foundation is approximated via modal parameters to give a so-called equivalent foundation, the adequacy of which is tested by comparing the vibration behaviour of the actual system with that using the simplified foundation. Provided measurement accuracy to three significant digits can be achieved, natural frequency and unbalance response comparisons showed good agreement.

Abstract: Modal parameter identification from ambient responses due to a general unknown random inputs is investigated. Existing identification techniques which are based on the assumptions of white noise and or stationary random inputs are utilized even though the inputs conditions are not satisfied. This is accomplished via adding. in cascade. a force conversion system to the structure’s system under consideration. The input to the force conversion system is white noise and the output of which is the actual force(s) applied to the structure. The white noise input(s) and the structure’s responses are then used to identify the combined system. Identification results are then sorted as either structural parameters or input force(s) characteristics.

Abstract: The authors have measured modal damping using strain-gauge data from an operating wind turbine. This new technique for measuring modal damping is easier and less expensive than previously used methods. Auto-correlation and cross-correlation functions of the strain-gauge data have been shown to consist of decaying sinusoids which correspond to the modal frequencies and damping ratios of the wind turbine. The authors have verified the method by extracting damping values from an analytically generated data set. Actual operating response data from the DOE/Sandia 34-m Test Bed has been used to calculate modal damping ratios as a function of rotor rotation rate. This capability will allow more accurate fatigue life prediction and control.

Abstract: In this paper, the modal properties of the Alamosa Canyon Bridge obtained using ambient data are compared to those obtained from impact hammer vibration tests. Using ambient sources of excitation to determine the modal characteristics of large civil engineering structures is desirable for several reasons. The forced vibration testing of such structures generally requires a large amount of specialized equipment and trained personnel making the tests quite expensive. Also, an automated health monitoring system for a large civil structure will most likely use ambient excitation. A modal identification procedure based on a statistical Monte Carlo analysis using the Eigensystem Realization Algorithm is used to compute the modal parameters and their statistics. The results show that for most of the measured modes, the differences between the modal frequencies of the ambient and hammer data sets are statistically significant. However, the differences between the corresponding damping ratio results are not statistically significant. Also, one of the modes identified from the hammer test data was not identifiable from the ambient data set.

Abstract: Recent advances in design and manufacturing of aerospace systems have significantly enhanced the application of fiber-reinforced composite materials. In addition to their high stiffness-to-weight and strength-to-weight ratios, this paper demonstrates experimentally that, without sacrificing these structural advantages, the piezoelectric element embedded in composite laminated structures can be applied both as the in situ vibration sensor and as the vibration suppression actuator. The modal parameters of two composite laminated plates, and , are predicted by a finite element model and they are validated by experimental modal testing. Experiments show that both the bending and torsional vibration can be effectively reduced by the velocity feedback from embedded piezoelectric sensor(s) and actuator(s).

Abstract: Selective modal transducers are developed for piezolaminated anisotropic plate systems that are capable of sensing and exciting any specified set of vibrational modes according to a specified set of modal participation factors. Transduction of selected modes is accomplished through combining the effect of three piezolaminate pairs whose piezoelectric fields are varied spatially. Each coupled pair contains a single layer located anywhere strictly above the reference plane, which is complemented by a second layer colocated below the reference plane. Piezoelectric constitutive properties associated with each layer in a given couple must be identical, whereas the constitutive properties of all three couples must be uniquely different. If all selective modal transducer layers are formed from the same stock material, the stock material must be piezoelectrically biaxial and the skew angles of all couples must be unique. Individual actuator inputs must be proportional to a common control function or, conversely, the sensed output must be a weighted sum of the measurements acquired by individual layers. An algorithm is presented that dictates how the piezoelectric field strength of each selective modal transducer layer must be varied spatially and is an explicit function of piezoelectric constants, mode shapes, and designer-chosen modal participation factors. Selective modal transducers for orthotropic systems are shown to require three piezolaminate layers rather than three coupled pairs.

Abstract: This paper deals with the identification of effective masses and modal masses from base-driven tests. When preforming a base-driven test with an elastomechanical structure, the structural responses can be related to the base accelerations and a modal identification of the structure can be accomplished. If, in addition, the base forces are measured, it is possible to determine the effective and modal masses of the structure. Here, the required equations describ- ing the dynamic behaviour are first developed and discussed.An analytical vibration system with simulated measurement errors is usedfor demonstrating the identification. In addition, a method to improve the accuracy of the identified parameters is shown.Based on the encouraging results, the application to real test data is en- visaged for further investigations.

Abstract: This paper describes an experimental modal analysis system which can effectively be used to obtain the modal parameters of small structures. The system uses an electromagnetic exciter to produce the excitation force, a piezoelectric transducer to measure this force, and a Laser Doppler Vibrometer to measure the response. Several designs of the magnetic actuator are discussed and evaluated. The system is verified by obtaining the modal parameters ofa miniature cantilever plate, using two preferred exciter designs, and comparing the measured parameters with those acquired from a finite element model. Favorable agreement is obtained between the experimental and computational results. Finally, the two preferred exciters are compared and an optimal configuration is discussed.

Abstract: A method for performing ground modal vibration tests of structural components, such that the resulting natural frequencies and vibration modes can be combined with those of neighboring components, is presented. The cost and technical difficulties associated with testing large and multiple-configuration structures can be greatly reduced with this approach. The method is based on testing the components with the interface coordinates loaded with rigid, heavy dummy masses supported by soft springs. With these boundary masses, the low-frequency modes contain local deformations near the interface and thus can be used to obtain accurate dynamic properties of the assembled structure. The method is demonstrated with measured natural frequencies and modes of a 19-m spacetype truss, loaded at one end with a dummy mass. The measured data are used to predict the frequencies and modes of the original truss with free and damped boundary conditions, and those of the double-length truss. The good agreement of the predicted results with test results on the unloaded structure and with analytical results on a tuned finite element model indicates that low-cost applications of the method to more complex structures are feasible.

Abstract: This paper presents the analysis of modal parameters (natural frequencies, damping and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joints with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

Abstract: Damping factor and modal damping of carbon/epoxy laminated composite beams with the piezoceramic sensor and actuator are predicted theoretically and measured experimentally. Finite element method is used for the analysis of dynamic characteristics of the laminated composite beams with and without the piezoceramics. The impulse technique is applied to measure the fundamental frequency, the damping ratio and the modal damping for the first bending mode of the beams. When a pair of piezoceramics is attached to the clamping side of the beam as a sensor and an actuator, the damping and the stiffness of the beam are changed. Taking into account the damping and the stiffness of the adhesive layer and the piezoceramics in the finite element modeling, damping ratio, fundamental frequency and modal damping are in good agreement with those of the measured values. To investigate the effects of sensor/actuator dynamics, vibration analysis of the beam without piezoceramics is also carried out. Damping ratio, fundamental frequency and modal damping of the beams without piezoceramics agree very well with those of measured values, as for the beams with piezoceramics. It is suggested that the modal damping (2ζω) is a more appropriate performance index rather than the damping ratio (ζ) for the vibration suppression in the structure, since one of the goals of structural vibration control is to suppress vibrational amplitude as fast as possible and the modal damping is directly related to the settling time of the vibration.

Abstract: The state-of-the-art of experimental structural dynamic's investigations and of Finite Element model updating based on such experimental results as well as the purpose of such investigations are discussed and illustrated. The methods presented are Forced Vibration Testing and Ambient Vibration Testing. It is the goal of both methods to evaluate the structure's modal parameters which reflect the structure's actual static and dynamic boundary conditions and its stiffness and mass properties.

Abstract: A general selective modal control design methodology is presented for piezolaminated anisotropic plate systems that utilizes selective modal transducers to realize any number of possible modal control strategies. A selective modal control design procedure is specified that defines a step-by-step framework through which the structural and control subdesign processes are effectively integrated. Several conditions that sufficiently ensure asymptotic stability are derived and then discussed in the context of deriving selective modal control methods that are stability robust to modeling and implementation errors Several selective modal control examples are then given in which selective modal transducers are designed and control laws chosen so as to allow for 1) the contributions of any given mode to the active energy extraction rate to be directly specified and 2) pole locations to be selectively and dynamically varied or 3) both pole locations and selective modal transducer design constants to be optimally determined. A numerical example is presented in which a stability-robust optimal selective modal control method is developed for a cantilevered anisotropic plate. Maintaining a linear feedback law, a single self-sensing selective modal transducer is employed whose design parameters were chosen to optimize the system response to a given initial excitation. Frequency and transient response analyses show a dramatic enhancement in system performance and accurately concur with theoretical predictions. The example serves both to illustrate the design process and to independently validate selective modal transducer and selective modal control theoretical results.

Abstract: The automotive industry has particular interest in obtaining modal models of panel-like structures in the higher frequency range where the accuracy of FE-models normally is not longer sufficient to predict the dynamic response of a car body structure to a given operational excitation. Experimental modal analysis can fill this gap. However, the sensors which are currently used for the acquisition of vibrational data (accelerometers, laser vibrometer) are limited in spatial resolution and therefore higher-order panel modes are hard to be investigated. Holographic interferometry is widely used for qualitative and quantitative measurements of the mode shapes of dynamic systems, where its high spatial resolution outperforms any other kind of vibrational dynamic sensor. The limitations of holography with respect to the sampling rate can be overcome in the context of modal analysis by using stepped sine testing. A large number of holograms is then automatically recorded and evaluated. First results on a test structure which exhibits narrow-spaced eigenmodes are shown using this kind of measurement setup with a high frequency resolution. The dense vibration data enables the modal analysis software to separate the eigenmodes.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Abstract: The integrity of structures may be determined by either one of two methods. In a first method, an impulse of energy is introduced into the structure (20), such as by striking the structure (20), and the induced vibration is measured and the modal damping factor is calculated, the modal damping factor being directly related to the integrity of the structure (20). In a second method, a continous energy input is provided to the structure (20) for inducing a continous vibration in the structure (20). This continous vibration is measured with a transducer (28) and a modal damping factor is calculated with a computer (32). The computer uses an algorithm to estimate the modal damping factor of the structure by calculating a theoretical response of an idealized system from several assumed parameters and varying those parameters.

Abstract: The mode shapes, frequencies, and modal mass and stiffness coefficients of multibody systems such as tracked vehicles can be determined using experimental identification techniques. In multibody simulations, however, knowledge of the modal parameters of the individual components is required, and consequently, a procedure for extracting the component modes from the mode shapes of the assembled system must be used if experimental modal analysis techniques are to be used with general purpose multibody computer codes. In this investigation, modal parameters (modal mass, modal stiffness, modal damping, and mode shapes), which are determined experimentally, are employed to simulate the nonlinear dynamic behavior ofa multibody tracked vehicle which consists of interconnected rigid and flexible components. The equations of motion of the vehicle are formulated in terms of a set of modal and reference generalized coordinates, and the theoretical basis for extracting the component modal parameters of the chassis from the modal parameters of the assembled vehicle is described. In this investigation, the track of the vehicle is modeled as a closed kinematic chain that consists of rigid links connected by revolute joints, and the effect of the chassis flexibility on the motion singularities of the track is examined numerically. These singularities which are encountered as the result of the change in the track configuration are avoided by using a deformable secondary joint instead of using the loop-closure equations.

Abstract: Complex modal testing is employed to obtain the directional frequency responses of a four-axis active magnetic bearing system. In the test, magnetic bearings are used as exciters while the system is in operation. The directional frequency response estimates are then used to effectively identify the parameters of the active magnetic bearing system. Experimental results show that the directional frequency response function, which is properly defined in the complex domain, is a powerful tool for identification of bearing as well as modal parameters of the system.

Abstract: Tracking the aeroelastic modes of an aircraft through changing flight conditions is an essential element of flight flutter testing, which is made difficult by corrupted data and high modal density. The modal assurance criterion (MAC), a method of evaluating the consistency of two modal vectors, is shown to simplify the mode tracking procedure by putting a numerical value on the correlation between pairs of modes identified at consecutive flight conditions. Representation of the resulting MAC values as a colour map gives a clear visual indication of modal consistency. An automated approach to mode tracking is introduced and shown to work on aircraft-type systems, over significant changes in flight condition up to and beyond the flutter speed. Some potential problems of a practical implementation are discussed.

Abstract: This paper proposes a method whereby a set of computed mode shapes for a structure and set of measured mode shapes may be compared through the mass matrix. The errors between the two are found to fall into three categories: (a) mutual orthogonality of the measured modes is not satisfied, (b) the sets of modal vectors do not span the same subspaces, and (c) the modes are not perfectly aligned with the common subspace. In all three cases, the errors emerge as a set of angles, and the number of angles associated with each class of error is the same as the number of modes in the sets being compared. The sets of angles can each be combined into a single error angle for each class and ultimately a single angle, which reflects the degree of agreement between the measured and computed mode shapes.