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By extending the pseudo-Stroh formalism to multilayered one-dimensional orthorhombic quasicrystal plates, we derive an exact closed-form solution for simply supported plates under surface loadings. The propagator matrix method is introduced to efficiently and accurately treat the multilayered cases. As a numerical example, a sandwich plate made of quasicrystals and crystals with two different stacking sequences is investigated. The displacement and stress fields for these two stacking sequences are presented, which clearly demonstrate the importance of the stacking sequences on the induced physical quantities. Our exact closed-form solution should be of particular interest to the design of one-dimensional quasicrystal laminated plates. The numerical results can be further used as benchmarks to various numerical methods, such as the finite element and finite difference methods, on the analysis of laminated composites made of one-dimensional quasicrystals.

By using the generalized Stroh formalism, the electric-elastic eld induced by a straight dislocation parallel to a periodic axis of a one-dimensional quasicrystal is obtained. The derivation is concise and the solution is in an exact closed form. As an illustration, the electric-elastic elds around a straight dislocation in a one-dimensional hexagonal quasicrystal are studied. Besides the interesting numerical results presented, the generalized Stroh formalism can be applied to more complicated dislocation problems in quasicrystals.

An exact closed-form solution for the three-dimensional free vibrational response of a simply-supported and multilayered magneto-electro-elastic plate considering the nonlocal effect is presented. The solution is derived using the pseudo-Stroh formulation and propagator matrix method. Various numerical examples are presented for a homogeneous elastic plate, piezoelectric plate, magnetostrictive plate, and sandwich plates made of piezoelectric and magnetostrictive materials. The natural frequencies and the corresponding mode shapes of the multilayered plates show the influence of stacking sequence and the important role that the nonlocal effect plays in dynamic analysis of nanostructures. This exact solution is useful for it provides benchmark results to assess the accuracy of nonlocal thin plate models and finite element formulations.