Liao-Liang Ke

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.

Flexural Vibration and Elastic Buckling of a Cracked Timoshenko Beam Made of Functionally Graded Materials

Free vibration and elastic buckling of beams made of functionally graded materials (FGMs) containing open edge cracks are studied in this paper based on Timoshenko beam theory. The crack is modeled by a massless elastic rotational spring. It is assumed that the material properties follow exponential distributions along beam thickness direction. Analytical solutions of natural frequencies and critical buckling load are obtained for cracked FGM beams with clamped-free, hinged-hinged, and clamped-clamped end supports. A detailed parametric study is conducted to study the influences of crack depth, crack location, total number of cracks, material properties, beam slenderness ratio, and end supports on the free vibration and buckling characteristics of cracked FGM beams.

Dynamic Stability of Functionally Graded Carbon Nanotube-Reinforced Composite Beams

This article presents a dynamic stability analysis of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to vary in the thickness direction and are estimated through the rule of mixture. The differential quadrature method is employed to convert the governing differential equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotins method. Free vibration and elastic buckling are also discussed as subset problems. A parametric study is conducted to investigate the influences of nanotube volume fraction, slenderness ratio, and end supports on the dynamic stability characteristics of FG-CNTRC beams. Numerical results for composite beams reinforced by uniformly distributed carbon nanotube are also provided for comparison.

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.

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.

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.

Frictionless contact analysis of a functionally graded piezoelectric layered half-plane

This paper investigates the frictionless contact problem of a layered half-plane made of functionally graded piezoelectric material (FGPM) in the plane strain state under the action of a rigid punch whose shape may be flat, triangular or cylindrical. It is assumed that the punch is a perfect electrical insulator with zero electric charge distribution. The electroelastic properties of the FGPM layer vary exponentially along the thickness direction. By using the Fourier integral transform technique, the problem is reduced to a Cauchy singular integral equation which is then numerically solved to determine the contact pressure, contact region, maximum indentation depth, normal stress, electrical potential and electric displacement fields. The stress intensity factor is also given to quantitatively characterize the singularity behavior of the contact pressure at the ends of a flat and triangular punch. Numerical results show that both the material property gradient of the FGPM layer and the punch geometry have a significant influence on the contact performance of the FGPM layered half-plane.

Flexural vibration of an atomic force microscope cantilever based on modified couple stress theory

This paper is concerned with the flexural vibration of an atomic force microscope (AFM) cantilever. The cantilever problem is formulated on the basis of the modified couple stress theory and the Timoshenko beam theory. The modified couple stress theory is a nonclassical continuum theory that includes one additional material parameter to describe the size effect. By using the Hamiltons principle, the governing equation of motion and the boundary conditions are derived for the AFM cantilevers. The equation is solved using the differential quadrature method for the natural frequencies and mode shapes. The effects of the sample surface contact stiffness, length scale parameter and location of the sensor tip on the flexural vibration characteristics of AFM cantilevers are discussed. Results show that the size effect on the frequency is significant when the thickness of the microcantilever has a similar value to the material length scale parameter.

Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory

ABSTRACT This article investigates the nonlinear vibration of piezoelectric nanoplate with combined thermo-electric loads under various boundary conditions. The piezoelectric nanoplate model is developed by using the Mindlin plate theory and nonlocal theory. The von Karman type nonlinearity and nonlocal constitutive relationships are employed to derive governing equations through Hamiltons principle. The differential quadrature method is used to discretize the governing equations, which are then solved through a direct iterative method. A detailed parametric study is conducted to examine the effects of the nonlocal parameter, external electric voltage, and temperature rise on the nonlinear vibration characteristics of piezoelectric nanoplates.