Rapid developments in system dynamics and control, areas related to many other topics in applied mathematics, call for comprehensive presentations of current topics. This series contains textbooks, monographs, treatises, conference proceedings and a collection of thematically organized research or pedagogical articles addressing dynamical systems and control.The material is ideal for a general scientific and engineering readership, and is also mathematically precise enough to be a useful reference for research specialists in mechanics and control, nonlinear dynamics, and in applied mathematics and physics.

The paper is concerned with a thin beam and a thin plate made of a transversally isotropic linearly elastic material heterogeneous in the thickness direction. The ordinary Kirchhoff–Love and Timoshenko–Reissner models are known to be unacceptable for a strongly heterogeneous material or for a multilayered material with large ratio between the Young moduli of layers. A generalized Timoshenko–Reissner model is proposed for bending and free vibrations of such beams/plates. A multilayered beam/plate is reduced to one‐layer one with the equivalent elastic parameters. The range of application of such a model is very wide.

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