Natural frequencies of composite plates with tailored thermal residual-stresses

Thermal residual!stresses introduced during manufacture and their e}ect on the natural frequencies and vibration modes of stringer sti}ened composite plates is investigated[ The principal idea in the work is to include sti}eners on the perimeter of a composite plate in which the laminate design of the sti}eners and plate are di}erent[ Such an arrangement yields manufacturing induced thermal residual!stresses^ these stresses result from the di}erence in manufacturing and operating temperatures as well as the di}erence in thermal expansion coe.cients and elastic properties of the plate and the sti}eners[ The analysis is based on an enhanced Reissner Mindlin plate theory and involves two separate calculations[ In the _rst\ the thermal residual!stress state is determined for an unconstrained plate[ In the second\ the free vibration problem is solved^ thermal e}ects from the _rst calculation are included by way of nonlinear membrane!bending coupling which in turn de_nes the free vibration reference state[ The problem is solved using a 05!node bi! cubic Lagrange element in a _nite element formulation[ Three di}erent plate!sti}ener geometries are used to illustrate the e}ects of stringer size\ stringer placement and temperature di}erence[ Two principal results are obtained] _rst\ it is shown that thermal residual!stresses can have a signi_cant e}ect on the natural frequencies^ secondly\ thermal residual!stresses can be tailored to increase natural frequencies[ Therefore it is concluded that an evaluation of these stresses and a judicious analysis of their e}ects must be included in the design of this class of composite structures