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Purpose: The free vibration of three-dimensional angle-interlock woven composite (3DAWC) cantilever beam is studied. Methods: Through tensile, bending and compression test, the material properties of 3DAWC are obtained. A two-dimensional cantilever beam model for 3DAWC is established. The state space method and differential quadrature method are combined to solve the natural frequencies and mode shape of 3DAWC. The present results are in good agreement with the previous methods. The influence of material coefficient and stacking sequence on the mode shape is considered in numerical examples. Results: The results indicate that the 3DAWC displays a better dynamic performance than the traditional fabric biaxial warp-knitted composite (BWKC), which is helpful for 3DAWC applications in wind turbine blades. [ABSTRACT FROM AUTHOR]

A two-dimensional (2D) layered deep beam model for one-dimensional (1D) quasicrystal (QC) materials is proposed under various boundary conditions. The free vibration and static bending of homogeneous and two sandwich QC deep beams with a rectangular cross section are studied by combining the state space method with the differential quadrature method. According to the basic equation of 1D QCs, the state equations in the 2D coordinate system are derived, and then the differential quadrature method is used to solve the state equations for various boundary conditions of QC beams including simply supported (S–S) beam, cantilever (C–F) beam, clamped-simply supported (C–S) beam and clamped-clamped (C–C) beam. The phonon and phason displacements for bending deformation, and the natural frequencies and mode shape for free vibration of homogeneous and layered QC beams are obtained effectively. The natural frequencies and maximum defection of beams obtained by the present 2D model are in good agreement with those from the previous methods and theories. Furthermore, the effects of various boundary conditions, geometric parameter and stacking sequence on the vibration response and the bending deformation of 2D layered deep beams made of 1D QC materials are analyzed in numerical examples, which are useful in the application of QC materials as beam structures. [ABSTRACT FROM AUTHOR]

A mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire. [ABSTRACT FROM AUTHOR]

The modified couple stress theory has been applied in many nanomaterials except for nano-quasicrystals. In this paper, the modified couple stress theory is firstly adopted to analyze the static bending deformation of multilayered one-dimensional (1D) hexagonal quasicrystal (QC) nanoplates under surface loadings. The general solutions for the extended displacement and traction vectors in a simply supported and homogeneous QC nanoplate are derived by solving an eigenvalue problem reduced from the governing equations. Utilizing the propagator matrix method, the analytical solutions of multilayered 1D QC nanoplates are then obtained by assuming that the layer interfaces are continuous. Numerical examples for some kinds of nanoplates made up of QC and crystal ( BaTiO 3 ) are provided to illustrate the effects of the material length parameter, the number of layers and the stacking sequence of nanoplates on the phonon and phason fields, which is helpful for the application of QCs to surface coating and solar energy selective absorber. [ABSTRACT FROM AUTHOR]

Quasicrystals (QCs) are sensitive to the piezoelectric (PE) effect. This paper studies static deformation of a multilayered one-dimensional (1D) hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal (PQC) plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures. [ABSTRACT FROM AUTHOR]