Engineering topics
Publications and source records attributed to Hart, G. C..
Program revises initial or prior estimate of stiffness and mass parameters to parameters yielding frequency and mode characteristics in agreement with test data. Variances are also calculated and consequently define uncertainties of final estimates.
A method is presented for calculating the statistics of the natural frequencies and mode shapes of vibration for a structure acted upon by an external static loading which results in the structure being stressed for eigenvalue analysis. The analytical tools presented apply to the probabilistic eigenvalue problem, and it is apparent that structural parameter uncertainty will significantly influence all aspects of the structure's response. The treatment of a sample problem serves the purpose of furthering understanding for the importance of considering structural parameters as random variables.
A method is formulated for systematically using experimental measurements of the natural frequencies and mode shapes of a structure to modify stiffness and mass characteristics of a finite element model. Throughout the modification process, which does not require complete data, the finite element model remains consistent. An additional feature is that the engineer's confidence in the modeling of the various finite elements is quantified and incorporated into the revision procedure. Examples demonstrate the convergence and versatility of the method.
Several methods are presented for developing proportional substructure damping matrices from modal test data. Examples demonstrate the significance of the nonuniqueness of the resulting proportional damping matrices. Several alternate modal synthesis procedures are presented for the systematic calculation of system modal damping from substructure damping information. The relative merits of these procedures are discussed, and one procedure is recommended.
The results of research in applying statistical methods to the problem of structural dynamic system identification are presented. The study is in three parts: a review of previous approaches by other researchers, a development of various linear estimators which might find application, and the design and development of a computer program which uses a Bayesian estimator. The method is tried on two models and is successful where the predicted stiffness matrix is a proper model, e.g., a bending beam is represented by a bending model. Difficulties are encountered when the model concept varies. There is also evidence that nonlinearity must be handled properly to speed the convergence.
Several criteria that may be used to evaluate the merits of some of the existing techniques for the dynamic analysis of large structures which involve division into substructures or components are examined. These techniques make use of component displacement modes to synthetize global systems of generalized coordinates and, for that reason, they have come to be known as modal synthesis or component mode methods. Two techniques have been found to be particularly useful - i.e., the modal synthesis method with fixed attachment modes, and the modal synthesis method with free attachment modes. These two methods are treated in detail, and general flow charts are presented for guidance in computer programming.
Several modal synthesis procedures for the dynamic analysis of largy composite structural systems are surveyed. The matrix formulation of the free-free modal synthesis procedures is presented. Also given are schematic flow charts of the analysis procedure used in three prominent methods. The advantages and disadvantages of several modal synthesis methods for different classes of structural problems are presented in order to enable the engineer to select the best procedure for his particular type of problem.
A theory is developed to predict eigenvalue and eigenvector uncertainty in large dynamic models. The uncertainty is based on physical property uncertainty and should not be confused with numerical roundoff, although the method can be extended to include the latter. The theory, when implemented on a computer, is used to analyze the uncertainties in frequencies and mode shapes based on uncertainties in mass, stiffness, modulus of elasticity, etc. The method incorporates a linear statistical model which is quite adequate for handling property uncertainties of 10% or more. The model is not limited to small systems but uses certain statistical assumptions as well as selective matrix manipulations to keep the size of all matrix operations to within the number of degrees of freedom of the system. Examples are given for two longitudinal vibration problems, and the results are supported by a Monte Carlo analysis.
Computer program for predicting structural bending vibrational data