Static response of functionally graded multilayered one-dimensional quasicrystal cylindrical shells

In one-dimensional hexagonal piezoelectric quasi-crystals, there exist the phonon–phason, electro–phonon, and electro–phason couplings. Therefore, the phonon–phason coupling and piezoelectric effects on axial guided wave characteristics in one-dimensional hexagonal functionally graded piezoelectric quasi-crystal (FGPQC) cylinders are investigated by utilizing the Legendre polynomial series method. The dispersion curves and cut-off frequencies are illustrated. Wave characteristics in three hollow cylinders with different quasi-periodic directions are comparatively studied. Some new wave phenomena are revealed: the phonon–phason coupling and piezoelectric effects on the longitudinal and torsional phonon modes ( N = 0) vary as the quasi-periodic direction changes; the phonon–phason coupling effect on flexural–torsional modes in the r-, z-FGPQC hollow cylinders, and on flexural–longitudinal modes in ϑ-FGPQC hollow cylinders increases as N increases. The corresponding results obtained in this work lay the theoretical foundation for the design and manufacture of piezoelectric transducers with high resolution and energy-conversion efficiency.

“…The relationship of the displacement-strain and electric field-electric potential in the phonon and phason fields can be written as follows [25,32]:…”

Section: The Z-direction Cylindermentioning

confidence: 99%

Axial guided wave characteristics in functionally graded one-dimensional hexagonal piezoelectric quasi-crystal cylinders

Zhang¹,

Wang

Elmaimouni

et al. 2021

“…Hosseiniu et al [15] analyzed the elastodynamic responses of a hollow cylinder with decagonal QC properties via meshless approximation. In addition, the shear fracture [16], micromechanics [17], and the static response [18] in QC cylindrical composites have been analyzed.…”

Section: Introductionmentioning

confidence: 99%

Electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal circular plates with simply supported or clamped boundary conditions

Huang

Zhao

Feng

2021

A three-dimensional (3D) electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal (QC) circular plates with simply supported or clamped boundary conditions is presented through a state vector approach. Both perfect and imperfect bonds between the layers are considered by adjusting the parameter sets in the model. Governing equations for the plates subjected to electric or elastic load on the bottom surfaces are derived using the state equations and the propagator matrix method. We explicitly obtain the analytical solution by writing the physical variables as Bessel series expansions and polynomial functions with respect to the radial coordinate. The solution is validated by comparing the numerical results with the 3D ﬁnite element analysis. The basic physical quantities of the plates in the phonon, phason, and electric fields are computed in the numerical examples. Result shows that the QC layers as coatings decrease the deflection in the phonon and phason fields of plates. The phonon–phason coupling elastic modulus and piezoelectric constant produce positive and negative effects on the magnitudes of stresses. Besides, compliance coefficients of the weak interface in the phonon field contribute more to the variations than those in the phason field.

“…They considered materials are linear elastic transversely isotropic, and the exponential variation of properties along the depth of each layer was assumed in order to model the effect of inhomogeneity. Li et al [20] and Gupta and Bhengra [21] reviewed other types of analysis pertaining to such materials.…”

Section: Introductionmentioning

confidence: 99%

Rocking forced displacement of a rigid disc embedded in a functionally graded transversely isotropic half-space

Kalantari

Khaji

Eskandari‐Ghadi

2020

Recent studies have confirmed that rockable structures have beneficial effects in earthquakes due to uniform dynamic behavior of the structure. For these kinds of structures, an equivalent static analysis is accurate enough, as the rocking motion is the dominant mode of their interaction with the surrounding soil (i.e. soil–structure interaction problem). In this study, the soil–structure interaction problems are extended to consider the effect of elastic non-homogeneities as well as changing the elasticity constants with depth in an exponential manner for the rocking loads. This paper analytically investigates the mixed boundary value problem regarding the forced rocking interaction of a rigid foundation embedded in a finite depth of an exponentially graded transversely isotropic half-space. The potential function method accompanied by Hankel integral transforms is applied to solve the system of the equations of motion of the media. Due to integral transforms used in the solving procedure, the mixed boundary value problem raised may be apt to be transformed to dual integral equations, which in turn, could be reduced to Fredholm integral equation of the second kind. To evaluate the solution of the integral equations, a robust numerical procedure has been developed for different anisotropic materials. Regarding the complicated integrand functions, the integrals are numerically and graphically presented to cover the effect of degree of change of material properties that plays a key role.