Yue-Sheng Wang

Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory

Thermoelectric-mechanical vibration of the piezoelectric nanobeams is first investigated in this paper based on the nonlocal theory and Timoshenko beam theory. The governing equations and boundary conditions are derived by using the Hamilton principle. The differential quadrature (DQ) method is employed to determine the natural frequencies of the piezoelectric nanobeams with different boundary conditions. The influences of the nonlocal parameter, temperature change, external electric voltage and axial force on the thermoelectric-mechanical vibration characteristics of the piezoelectric nanobeams are discussed in detail. It is found that the nonlocal effect is significant for the natural frequencies of the nanobeams. This study also reveals that the natural frequencies of the nanobeams are quite sensitive to the thermoelectric-mechanical loadings. The results should be relevant to the design and application of the piezoelectric nanodevices.

Effects of material parameters on elastic band gaps of two-dimensional solid phononic crystals

In this paper we study the influences of the material parameters on phononic band gaps of two-dimensional solid phononic crystals. The analysis begins with the basic wave equations and derives the material parameters directly determining band gaps. These parameters include the mass density ratio, the shear modulus ratio, and Poisson’s ratios of the scatterer and host materials (or equivalently, the wave velocity ratio, the acoustic impedance ratio, and Poisson’s ratios). The effects of these parameters on phononic band gaps are discussed in details for phononic crystals with different filling fractions and lattice forms for both antiplane and in-plane wave modes. Band gaps are calculated by the plane wave expansion method. The results show that for the antiplane mode, the mass density ratio predominantly determines the band gap, while that for the in-plane mode, both mass density ratio and shear modulus ratio play equally important roles. The maximum band gap will appear at both large density ratio and sh...

Buckling and post-buckling of size-dependent piezoelectric Timoshenko nanobeams subject to thermo-electro-mechanical loadings

Buckling and post-buckling behaviors of piezoelectric nanobeams are investigated by using the nonlocal Timoshenko beam theory and von Karman geometric nonlinearity. The piezoelectric nanobeam is subjected to an axial compression force, an applied voltage and a uniform temperature rise. After constructing the energy functionals, the nonlinear governing equations are derived by using the principle of minimum total potential energy and discretized by using the differential quadrature (DQ) method. A direct iterative method is employed to determine the buckling and post-buckling responses of piezoelectric nanobeams with hinged-hinged, clamped-hinged and clamped-clamped end conditions. Numerical examples are presented to study the influences of the nonlocal parameter, temperature rise and external electric voltage on the size-dependent buckling and post-buckling responses of piezoelectric nanobeams.

Large bandgaps of two-dimensional phononic crystals with cross-like holes

In this paper we study the bandgap properties of two-dimensional phononic crystals with cross-like holes using the finite element method. The influence of the geometry parameters of the holes on the bandgaps is discussed. In contrast to a system of square holes, which does not exhibits bandgaps if the symmetry of the holes is the same as that of the lattice, systems of cross-like holes show large bandgaps at lower frequencies. The bandgaps are significantly dependent upon the geometry (including the size, shape, and rotation) of the cross-like holes. The vibration modes of the bandgap edges are computed and analyzed in order to clarify the mechanism of the generation of the lowest bandgap. It is found that the generation of the lowest bangdap is a result of the local resonance of the periodically arranged lumps connected with narrow connectors. Spring-mass models are developed in order to predict the frequencies of the lower bandgap edges. The study in this paper is relevant to the optimal design of the b...

Effects of inclusion shapes on the band gaps in two-dimensional piezoelectric phononic crystals

In this paper, the elastic wave propagation in piezoelectric phononic crystals with several inclusion shapes is investigated by taking the electromechanical coupling into account. The band structures for five different shapes of scatterers (regular triangle, square, hexagon, circle, and oval) with square lattice are calculated using the plane-wave expansion method. The effects of the inclusion shapes on the normalized band width are discussed. The largest complete band gap is obtained by selecting the scatterers with the same symmetry of lattice for the first band gap, but this rule is not valid for the second band gap.

Vibration control of beams with active constrained layer damping

An analytical methodology is presented to study the active vibration control of beams treated with active constrained layer damping (ACLD). This analytical method is based on the conventional theory of structural dynamics. The process of deriving equations is precise and easy to understand. Hamiltons principle with the Rayleigh–Ritz method is used to derive the equation of motion of the beam/ACLD system. By applying an appropriate external control voltage to activate the piezoelectric constraining layer, a negative velocity feedback control strategy is employed to obtain the active damping and effective vibration control. From the numerical results it is seen that the damping performances of the beam can be significantly improved by the ACLD treatment. With the increase of the control gain, the active damping characteristics are also increased. By equally dividing one ACLD patch into two and properly distributing them on the beam, one can obtain better active vibration control results than for the beam with one ACLD patch. The analytical method presented in this paper can be effectively extended to other kinds of structures.

The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells

Based on the nonlocal Loves shell theory, this paper develops an embedded magneto-electro-elastic (MEE) cylindrical nanoshell model. This model incorporates effects of the small scale parameter and thermo-electro-magnetic loadings. The surrounding elastic medium is described as the Winkler model characterized by the spring. By using this model and the Hamilton principle, the governing equations and boundary conditions are derived for free vibration of the embedded MEE cylindrical nanoshells. The Naviers method is first utilized to obtain the analytical solution for the simply supported MEE nanoshell. Then, numerical solutions for MEE nanoshells under various boundary conditions are obtained by using the differential quadrature (DQ) method. A detailed parametric study is conducted to highlight the influences of the nonlocal parameter, temperature rise, external electric potential, external magnetic potential, spring constant, radius-to-thickness ratio and length-to-radius ratio on natural frequencies of MEE nanoshells.

Multi-objective optimization of two-dimensional porous phononic crystals

In this paper, we show that it is possible to design two-dimensional (2D) porous phononic crystals (PnCs) with a simultaneously maximal bandgap width (BGW) and the minimal mass through multi-objective optimization (MOOP) by using the non-dominated sorting-based genetic algorithm II. Compared with the single-objective optimization, the optimized structures from the MOOP can achieve a balance between the relative BGW and mass of PnCs. For the combined out-of-plane and in-plane wave modes, we present an optimized design with the relatively big BGW, which breaks the record value of 2D porous PnCs.

Nonlinear vibration of nonlocal piezoelectric nanoplates

This paper presents an analytical study on the nonlinear vibration of rectangular piezoelectric nanoplates resting on the Winkler foundation. The piezoelectric nanoplate is assumed to be simply supported on all four edges and is subjected to an external electric voltage and a uniform temperature rise. Based on von Karman nonlinear strain-displacement relations and the nonlocal constitutive relations, the nonlinear governing equations and corresponding boundary conditions are derived by employing Hamiltons principle. The Galerkin method is used to obtain the nonlinear ordinary equation, which is then solved by the direct integration method. An extensive parametric study is conducted to examine the effects of the nonlocal parameter, external electric voltage, temperature rise and Winkler parameter on the nonlinear vibration characteristics of piezoelectric nanoplates.

Fretting Contact of Two Dissimilar Elastic Bodies with Functionally Graded Coatings

A two-dimensional fretting contact problem involving normal and tangential loading of two dissimilar elastic bodies with functionally graded coatings is analyzed. The bodies are first brought into contact by a monotonically increasing normal load and then a cycled tangential load is applied with the normal load held constant. Friction with a finite coefficient is assumed between the contact surfaces. The linear multi-layered model is used to model functionally graded coating with arbitrarily varying shear modulus and constant Poissons ratio under plane strain deformation. With the use of the transfer matrix method and Fourier integral transform technique, the problem is reduced to a set of Cauchy singular integral equations which are solved numerically. An iterative method is developed to determine the stick/slip region and contact tractions. The numerical results show that the functionally graded coating on the harder body can lower the fretting contact stresses and thus improve the resistance to the fretting contact damage, and that in comparison with a homogeneous coating, a functionally graded coating can eliminate the interfacial stress concentration induced by material property mismatch.