The response of beams resting on viscoelastically damped foundation under moving SDoF oscillators is scrutinized through a novel state-space formulation, in which a number of internal variables is introduced with the aim of representing the frequency-dependent behaviour of the viscoelastic foundation. A suitable single-step scheme is provided for the numerical integration of the equations of motion, and the Dimensional Analysis is applied in order to define the dimensionless combinations of the design parameters that rule the responses of beam and moving oscillator. The effects of boundary conditions, span length and number of modes of the beam, along with those of the mechanical properties of oscillator and foundation, are investigated in a new dimensionless form, and some interesting trends are highlighted. The inaccuracy associated with the use of effective values of stiffness and damping for the viscoelastic foundation, as usual in the present state-of-practice, is also quantified.

The effects of a composite overwrapped gun barrel with viscoelastic damping layers are investigated. Interlaminar stresses and constrained layer damping effects are described. The Modal Strain Energy method is developed for measuring the extent to which the barrel is damped. The equations of motion used in the finite element analysis are derived. The transient solution process is outlined. Decisions for selected parameters are discussed. The results of the finite element analyses are presented using the program written in FORTRAN. The static solution is solved with a constant internal pressure resulting in a calculated loss factor from the Modal Strain Energy Method. The transient solution is solved using the Newmark-Beta method and a variable internal pressure. The analyses conclude that strategically placed viscoelastic layers dissipate strain energy more effectively than a thick single viscoelastic layer. The optimal angle for maximizing the coefficient of mutual influence in a composite cylinder is not necessarily the optimal angle when viscoelastic layers are introduced between layers.