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The paper investigates the hypothetical assumption of neglecting transverse normal stress in vibration analysis for cantilevered thick plates and rectangular parallelepiped. The analysis solves the three-dimensional elasticity energy functional including, as well as excluding, transverse normal stress 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 practically unknown. The inconsistency of assuming constant transverse normal displacement through thickness for thick-plate models is also addressed. The paper concludes that for a rectangular parallelepiped with thickness exceeding a certain limit, there is considerable discrepancy if transverse normal stress is neglected. ; published_or_final_version
The paper investigates the hypothetical assumption of neglecting transverse normal stress in vibration analysis for cantilevered thick plates and rectangular parallelepiped. The analysis solves the three-dimensional elasticity energy functional including, as well as excluding, transverse normal stress 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 practically unknown. The inconsistency of assuming constant transverse normal displacement through thickness for thick-plate models is also addressed. The paper concludes that for a rectangular parallelepiped with thickness exceeding a certain limit, there is considerable discrepancy if transverse normal stress is neglected. ; published_or_final_version
Three-dimensional vibration analysis of a cantilevered parallelepiped: Exact and approximate solutions
Lim, CW (author)
1999-01-01
Article (Journal)
Electronic Resource
English
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