On the use of three-dimensional h- and p-version finite elements in solving vibration response problems

The superior efficiency of p-enrichments compared to h-refinements for resolving regular elastostatic solutions is observed in elasto/viscoelasto-dynamics as well. Requirements on p-enrichments to avoid shear- and volumetric locking are given. The frequently used polynomial interpolation functions employed are shown to produce a mass contribution to the dynamic stiffness, whose condition number deteriorates with increasing polynomial order. The practical implications and limitations of this observation are outlined. The recommended approach is corroborated using the measured frequency response on a laminate consisting of two aluminium plates and a constrained viscoelastic polymer damping treatment.