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Acoustic testing using commercial sound system components is becoming more popular as a cost effective way of generating the required environment both in and out of a reverberant chamber. This paper will present the development of such a sound system that uses a state-of-the-art random vibration controller to perform closed-loop control in the reverberant chamber at Sandia National Laboratories. Test data will be presented that demonstrates narrow-band controlability, performance and some limitations of commercial sound generation equipment in a reverberant chamber.

The dynamic response of critical aerospace components is often strongly dependent upon the dynamic behavior of bolted connections that attach the component to the surrounding structure. These bolted connections often provide the only structural load paths to the component. The bolted joint investigated in this report is an inclined lap-type joint with the interface inclined with respect to the line of action of the force acting on the joint. The accurate analytical modeling of these bolted connections is critical to the prediction of the response of the component to normal and high-level shock environmental loadings. In particular, it is necessary to understand and correctly model the energy dissipation (damping) of the bolted joint that is a nonlinear function of the forces acting on the joint. Experiments were designed and performed to isolate the dynamics of a single bolted connection of the component. Steady state sinusoidal and transient experiments were used to derive energy dissipation curves as a function of input force. Multiple assemblies of the bolted connection were also observed to evaluate the variability of the energy dissipation of the connection. These experiments provide insight into the complex behavior of this bolted joint to assist in the postulation and development of reduced order joint models to capture the important physics of the joint including stiffness and damping. The experiments are described and results presented that provide a basis for candidate joint model calibration and comparison.

The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in weapons systems. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured adequately through direct simulation of the contact mechanics within a structural dynamics analysis. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. This document discusses a road-map for developing such constitutive models.

A family of transients with the property that the initial and final acceleration, velocity, and displacement are all zero is derived. The transients are based on a relatively arbitrary function multiplied by window of the form cosm(x). Several special cases are discussed which result in odd acceleration and displacement functions. This is desirable for shaker reproduction because the required positive and negative peak accelerations and displacements will be balanced. Another special case is discussed which will permit the development of transients with the first five (0-4) temporal moments specified. The transients are defined with three or four parameters that will allow sums of components to be found which will match a variety of shock response spectra.

When embarking on an experimental program for purposes of discovery and understanding, it is only prudent to use appropriate analysis tools to aid in the discovery process. Due to the limited scope of experimental measurement analytical results can significantly complement the data after a reasonable validation process has occurred. In this manner the analytical results can help to explain certain measurements, suggest other measurements to take and point to possible modifications to the experimental apparatus. For these reasons it was decided to create a detailed nonlinear finite element model of the Sandia Microslip Experiment. This experiment was designed to investigate energy dissipation due to microslip in bolted joints and to identify the critical parameters involved. In an attempt to limit the microslip to a single interface a complicated system of rollers and cables was devised to clamp the two slipping members together with a prescribed normal load without using a bolt. An oscillatory tangential load is supplied via a shaker. The finite element model includes the clamping device in addition to the sequence of steps taken in setting up the experiment. The interface is modeled using Coulomb friction requiring a modest validation procedure for estimating the coefficient of friction. Analysis results have indicated misalignment problems in the experimental procedure, identified transducer locations for more accurate measurements, predicted complex interface motions including the potential for galling, identified regions where microslip occurs and during which parts of the loading cycle it occurs, all this in addition to the energy dissipated per cycle. A number of these predictions have been experimentally corroborated in varying degrees and are presented in the paper along with the details of the finite element model.

During the last 20 years there has been a tremendous increase in computational capabilities. It seems to accelerate every year. Models are now constructed with millions of degrees of freedom. Sandia National Laboratories recently computed modes and transient response for a 4,000,000 degree of freedom model. There is also an increase in the cost of testing as the unit price of test items increases and manpower costs escalate. One is reminded of Augustine's Laws, ``Simple systems are not feasible because they require infinite testing.'' Or conversely, extremely complex systems require no testing. In his discussion he uses data from actual systems to show how increasing complexity of systems appears to require less testing. A hundred dollar item required several thousand developments tests, where a ten million dollar item required a few tens of development tests. Of course, this results from the large increase in test costs caused in large part by the large cost of the test hardware that comes with increasing complexity. The complex system (costly) is coupled with the perceived need to reduce nonessential costs. At Sandia National Laboratories they are also faced with the prospect that some of the tests they ran in the past are not even feasible to run today.

It is recognized that some dynamic and noise environments are characterized by time histories which are not Gaussian. An example is high intensity acoustic noise. Another example is some transportation vibration. A better simulation of these environments can be generated if a zero mean non-Gaussian time history can be reproduced with a specified auto (or power) spectral density (ASD or PSD) and a specified probability density function (pdf). After the required time history is synthesized, the waveform can be used for simulation purposes. For example, modem waveform reproduction techniques can be used to reproduce the waveform on electrodynamic or electrohydraulic shakers. Or the waveforms can be used in digital simulations. A method is presented for the generation of realizations of zero mean non-Gaussian random time histories with a specified ASD, and pdf. First a Gaussian time history with the specified auto (or power) spectral density (ASD) is generated. A monotonic nonlinear function relating the Gaussian waveform to the desired realization is then established based on the Cumulative Distribution Function (CDF) of the desired waveform and the known CDF of a Gaussian waveform. The established function is used to transform the Gaussian waveform to a realization of the desired waveform. Since the transformation preserves the zero-crossings and peaks of the original Gaussian waveform, and does not introduce any substantial discontinuities, the ASD is not substantially changed. Several methods are available to generate a realization of a Gaussian distributed waveform with a known ASD. The method of Smallwood and Paez (1993) is an example. However, the generation of random noise with a specified ASD but with a non-Gaussian distribution is less well known.

The role of force measurements in vibration testing is discussed. The rational for a vibration test based on the extremal control of force and acceleration is developed. The differences between force measurements in vibration testing and modal testing is discussed. Several methods for estimating the input force in a vibration test are outlined.

Experimental measurements of force into a ``rigid`` test item representing a typical system level vibration test were conducted to evaluate several methods of force measurements. The methods evaluated included: (1) Direct measurement with force gages between the test item and the fixturing; (2) Measurement of the force at the shaker/fixture interface and correcting the force required to drive the fixturing using two methods, (a) mass subtraction and (b) SWAT (sum of weighted accelerations technique), (3) Force deduced from voltage and current needed to drive the test item. All of the methods worked over a limited frequency range of five to a few hundred Hertz. The widest bandwidth was achieved with force at the shaker/fixture interface with SWAT corrections and from the voltage and current measurements.

A method is described to characterize shocks (transient time histories) in terms of the Fourier energy spectrum and the temporal moments of the shock passed through a contiguous set of bandpass filters. This method is compared for two transient time histories with the more conventional methods of shock response spectra (SRS) and a nonstationary random characteristic.

A method is presented for determining the force spectral density function for a vibration test where a combination of force and acceleration is used for control. First the acceleration spectral density is established based on an envelope of the interface motion between the test item and the mounting structure (the base) in the use (field) environment. The driving point accelerance (acceleration/force) of the test item is measured at the mounting interface. The force required to drive the test item in an acceleration controlled test is then estimated. A force spectral density is then established using the estimated motion controlled force, and a derived force reduction factor. An extremal control vibration test is then performed based on which parameter (input force or input acceleration) reaches based on which parameter (input force or input acceleration) reaches its envelope first. 7 refs., 7 figs., 2 tabs.

A vibration test method has been proposed where control is accomplished using extremal control of the force and acceleration at the input to a test item. This proposal is examined with several examples. The method does limit the acceleration input at frequencies where the test item responses tend to be unrealistically large. However, the method's application is not straightforward and care must be taken in the application of the method. 9 refs., 16 figs.