In the most common mathematical model for a moving load on acontinuously- supported flexible plate, the plate is assumed thin andelastic. An exception is the inclusion of viscoelasticity in thetheory for the response of a floating ice plate, where the deflexion atthe critical load speed corresponding to the minimum phase speed ofhybrid flexural-gravity waves consequently approaches a steady state.This is in contrast to the elastic theory, where the response ispredicted to grow continuously at this critical load speed. In thetheory for a floating ice plate, the dominant pressure due to theunderlying water is inertial, introduced via a velocity potentialand the Bernoulli equation (assuming non-cavitation at theplate-water interface). On the other hand, the classical Winklerrepresentation used in early railway engineering analysiscorresponds to retaining a term which is generally negligible in theice plate context. Critical load speeds are consequently predictedto be much higher, at wavelengths correspondingly much lower, forcommonly accepted railway engineering parameters. Other models mightbe considered.
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