This paper evaluates transverse normal stress XX e!ect on vibration of multilayered structures. To this purpose a mixed plate model initially introduced by Toledano and Murakami has been extended to dynamics analysis of double curved shells. These models allow both continuous interlaminar transverse shear and normal stresses as well as the zigzag form of the displacement distribution in the shell thickness directions to be modelled. Governing equations have been derived by employing a Reissner's mixed theorem. Classical models on the basis of standard displacement formulations have been considered for comparison purposes. The evaluations of transverse stress e!ects have been conducted by comparing constant, linear and higher order distributions of transverse displacement components in the plate thickness directions. Free vibrational response of layered, simply supported plates, cylindrical and spherical shells made of isotropic as well as orthotropic layers has been analyzed. The numerical investigation carried out and comparison with earlier results has concluded that:
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The possibility of describing a priori interlaminar continuous transverse normal stress XX makes the mixed theories more attractive with respect to other available modelling.
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Any re"nements of classical models are meaningless, unless the e!ects of interlaminar continuous transverse shear and normal stresses are both taken into account in a multilayered shell theory.