Nowadays the interest of the aerospace and automotive industries on the medium-frequency vibration problems is increasing more and more. The development of software capable of predicting the vibrational behavior in such frequency range is still an open question because the classical methods (i.e. FEM, SEA) are not suitable for the medium-frequency bandwidth. In this context the Variational Theory of Complex Rays (VTCR) [12] is catching on as an ad-hoc method to deal with medium-frequency problems. It is a Trefftz method based on a weak variational formulation which allows great flexibility because any shape function, provided that it satisfies the governing equations, can be used. This work continues the VTCR development introducing the shallow shell approximations to increase flexibility and its effectiveness. Two relevant numerical examples will be presented to show the strategy.
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