Abstract
A method for describing the behaviour of a class of linear, modally dense systems is given. The class of systems is such that each member of it responds to a particular input in a slightly different way. This means that while the gross features of the response may change little from member to member, the detailed response may be different. The class of systems is characterized in terms of the average bandlimited impulse response envelope. This is achieved by considering the natural frequencies, the amplitudes and relative phases of the modes in a particular frequency band to be random variables with known probability density functions. The statistics of the bandlimited impulse response envelope are discussed and an upper limit, in addition to the expression for the average bandlimited impulse response envelope, is derived. By generalizing this to different input signals an upper bound for the response of a system in a frequency band is generated from the input and impulse response envelopes in that band. Using this and the statistical description of the bandlimited impulse response envelope yields an upper bound for the response of a class of systems. The relationship between these envelope techniques and shock spectra is discussed and an alternative procedure for shock spectra generation is described that takes into account the characteristics of the system under test.
Published Version
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