Three-dimensional vibration analysis of a cantilevered parallelepiped: Exact and approximate solutions

The paper investigates the hypothetical assumption of neglecting transverse normal stress in vibration analysis for cantilevered thick plates and rect angular parallelepiped. The analysis solves the three-dimensional elasticit y energy functional including, as-well as excluding, transverse normal stre ss and obtains free vibration solutions for a cantilevered parallelepiped, Although it is widely accepted, the omission of transverse normal stress is well justified in Kirchhoff-Love thin-plate theory and higher-order thick- plate models; the transverse normal stress effects and thickness extent to which the thick-plate models apply as the thickness increases are practical ly unknown. The inconsistency of assuming constant transverse normal displa cement through thickness for thick-plate models is also addressed. The pape r concludes that for a rectangular parallelepiped with thickness exceeding a certain limit, there is considerable discrepancy if transverse normal str ess is neglected. (C) 1999 Acoustical Society of America. [S0001-4966(99)02 312-7].