Resonant-Frequency-Distribution of Internal Mass Inferred From Mechanical Impedance Matrices, With Application to Fuzzy Structure Theory

The partitioning of internal mass among bands of resonant frequencies is addressed for a prototype internal vibrating structure with small damping, attached via an arbitrary number NA of attachment points to an external structure. Insofar as the dynamics of the latter are concerned, the internal structure is adequately described by a frequency-dependent impedance matrix, any given column of which lists the ratios of the 3NA force components induced by one of the attachment points’ velocity components when all of the other velocity components are held to zero. The properties of matrix elements and their frequency dependence are discussed in relation to principles of mechanics, especially the requirements of translational and rotational invariance of the potential energy functions. Among the deductions are that modal masses can be defined with values calculable solely from the impedance matrix measurements, and that the modal masses sum to the total mass of the internal vibrating system.

Relation of the Sound Insulating and Reflecting Properties With Noise Dampening Effect of the Construction With Coatings

Calculated evaluation of the relation of the sound insulating and reflecting properties taking into account noise damping effect of an external coating put on construction elements in water is presented by the example of a measurement made using “Underwater Measuring Tubes” installation. The expressions permitting to determine first frequency range and the frequency of largest negative effect in dependence on the parameters of a construction and coating and their materials are obtained.

A New Methodology for the Accurate and Consistent Identification of Modal Parameters Using Multi-FRF Analysis

A new method for the estimation of modal parameters is presented in this paper. Unlike the majority of the existing methods which involve complicated curve fitting and interpolative procedures, the proposed method calculates the modal parameters by solving eigenvalue problem of an equivalent eigensystem derived from measured frequency response function (FRF) data. It is developed based on the practical assumption that only one incomplete column of the FRF matrix of the test structure has been measured in a frequency range of interest. All the measured FRFs are used simultaneously to construct the equivalent eigensystem matrices from which natural frequencies, damping loss factor and modeshape vectors of interest can be directly solved. Since the identification problem is reduced to an eigenvalue problem of an equivalent system, natural frequencies and damping loss factors identified are consistent. Further procedures for normalizing the identified eigenvectors so that they become mass-normalized are developed. Numerical case examples are given to demonstrate the practicality of the proposed method and results obtained are indeed very promising. It is believed that with the availability of such identification method, modal analysts’ dream of intelligent and full automatic modal analysis will become a reality.

Modal Balancing of Quasi-Rigid Jet Engine Rotors With Exchangeable Rotor Modules

Flexible rotor assemblies often consist of two or more rotor modules which are index-balanced against each other with the purpose of eliminating the need for re-balancing if a module should have to be exchanged. However, the index procedure may cause vibration problems because it ignores certain flexible rotor balancing requirements. This paper describes a modal balancing approach based on jet engine rotors which are typically balanced as ISO Class 2 (quasi-rigid) rotors. Appreciation is expressed to Prof. R. Gasch of TU Berlin for his valuable suggestions.

Cracked Shaft Detection Using the Unbalance Excitation Technique

The ever-growing interest of the modern rotordynamicist in the early detection of rotor cracks in turbomachinery has been the direct result of multiple catastrophic experiences that industry has faced in recent times due to cracked rotors. The complete failure of the rotor due to crack propagation is easily recognized as one of the most serious modes of plant failure. Even though the past decade has witnessed some laudable attempts that have been moderately successful in detecting cracked rotors, this aspect has not received the attention it warrants. A complete test rig has been designed and constructed for experimental research on the response characteristics of cracked rotors, the results of which will permit increased confidence in detecting the presence of rotor cracks in turbomachinery. The rig is capable of testing cracked shafts under the effect of lateral and coupled lateral/torsional vibrations. Conventional vibration signature analysis has been employed for the purpose of crack detection. This paper presents the details of the rig capabilities and results from the unbalance excitation technique applied for crack detection. The response of a cracked shaft differs markedly from that of an uncracked shaft when subjected to a known unbalance. This paper shows that unbalance excitation is a promising tool for cracked shaft detection.

Analytical, Numerical and Experimental Study of the Vibro-Acoustic Behaviour of a Stiffened Shell Structure

The main objectives of this study are a better understanding of the vibro-acoustic behaviour of an airplane fuselage type structure including stiffeners and a better comprehension of the measuring techniques and the modelization approaches for this type of problem. In order to meet the above objectives, three different models were developed. The first one is an experimental model where the measured accelerations and acoustic pressures are used as a reference for the validation of predicted results. The second model is based on a semi-analytical approach. This model is derived from variational and integral approaches and solved, approximately using a Rayleigh-Ritz method. Finally, the last model is based on the finite element method. Several iterations have been necessary before reaching an excellent agreement between all three approaches, especially regarding acoustic responses. From the initial correlation between the measured and predicted results, two major problems were identified. The first one is related to convergence problem associated with the semi-analytical model when stiffeners are incorporated in the model. The second problem is associated with the proper definition of the fluid-structure intermodal coupling in the numerical and analytical approaches. This paper will present the various approaches and models. Furthermore, the investigation on the previous problems will be discussed in detail. In conclusion, new modelization limitations were identified and new modelization criteria for the intermodal coupling were developed from the present study. These results will be used for an in-depth study on the vibro-acoustic behaviour of 1/3 scale model of airplane fuselage.

Acoustic Design of a Local Scatterer in a Phase-Space

A spatially local region of mechanical property heterogeneity is a source of scattering, by which a structure-borne mechanical wavefield is released as sound, to a surrounding fluid. We consider the case of a scatterer which is of the order of the size of the wavelength of a plate-wave field for a frequency which is below coincidence. A design strategy for reducing the strength of the scattered sound field in the fluid, at far-field distances from the scatterer, by adding a small-scale structure to the heterogenity, is presented. The design is accomplished in a wavelet-based phase-space. Emphasized is a significant distinction required of the added structure, depending on the heterogeneity applying to a measure of the local mass density or the local bending stiffness.

Development of an Engine System Model for Predicting Structural Vibration

A finite-element based engine system model is developed for predicting the structural vibration of the engine. The engine system model combines modal models of the major bolted-together sub-structures of the engine, with non-structural mass models of the remaining engine components added to bring the inertial properties to those of the running engine. The model is developed and experimentally evaluated with impact and shaker excitation tests. Comparisons are made of the predicted and measured vibration response for various partially assembled engine configurations, as well as for the fully assembled engine. The comparisons illustrate the accuracy of the model in predicting the narrow-band and one-third octave-band vibration response for excitation frequencies up to 2 kHz.

Nonlinear Transient Response and its Sensitivity Using Finite Elements in Time

The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the sensitivity of the transient response with respect to various design parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and its sensitivity to system parameters. Mostly, the results were obtained using the Legendre polynomials as basis functions, though, in some cases other orthogonal polynomials namely, the Hermite, the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease in which the sensitivity of the transient response with respect to various system parameters can be obtained.

Analysis of Pulsations and Vibrations in Fluid-Filled Pipe Systems

Pressure pulsations and mechanical vibrations in pipe systems may cause excessive noise and may even lead to damage of piping or machinery. In fluid-filled pipe systems pulsations and vibrations will be strongly coupled. A calculation method has been developed for the simulation of coupled pulsations and vibrations in pipe systems. The analytical method is based upon the transfer matrix method. It describes plane pressure waves in the fluid and extensional, bending and torsional waves in the pipe wall. Fluid pulsations and pipe wall vibrations are coupled at discontinuities (e.g. elbows and T-junctions) and via Poisson contraction of the pipe wall. For a given source description, the model calculates levels of vibration, mode shapes, vibro-acoustic energy flow, etc. The method has been validated experimentally on a test rig consisting of two straight pipes and an elbow. The predicted pulsation and vibration levels agree reasonably well with the measurements.