Search

Based on the nonlocal theory, this paper develops the Kirchhoff nanoplate and Mindlin nanoplate models for the wave propagation analysis of piezoelectric nanoplates. The effects of small scale parameter and thermo-electro-mechanical loads are incorporated in the nanoplate models. The Hamilton's principle is employed to derive the governing equations of the nanoplate, which are solved analytically to obtain the dispersion relation for piezoelectric nanoplates. The results show that the nonlocal parameter, temperature change, mechanical load and external electric potential have significant influence on the wave propagation characteristics of the piezoelectric nanoplates. The cut-off wave number is observed to exist for piezoelectric nanoplates subjected to positive electric potential, axial tensile force and temperature rise. [ABSTRACT FROM AUTHOR]

In this paper, thermal buckling properties of a nanoplate with small-scale effects are studied. Based on the nonlocal continuum theory, critical temperatures for the nonlocal Kirchhoff and Mindlin plate theories are derived. The thermal buckling characteristics are presented with different models. The influences of the scale coefficients, half-wave numbers, width ratios, and the ratios of the width to the thickness are discussed. From this work, it can be observed that the small-scale effects are significant for the thermal buckling properties. Both the half-wave number and width ratio have influence. The nonlocal Kirchhoff plate theory is valid for the thin nanoplate, and the nonlocal Mindlin plate theory is more appropriate for simulating the mechanical behaviors of the thick nanoplate. [ABSTRACT FROM AUTHOR]

Periodic structures have great scientific potential because of their superior structural dynamic properties. The aim of this study is to analyze the dynamic behavior of periodic plate structures using the spectral element method (SEM). The spectral equations of the plate elements with two parallel sides that are simply supported are established. Then, the spectral dynamic stiffness matrix of the whole periodic plate structure is assembled. The frequency responses are obtained by the calculation of the spectral equations to illustrate the characteristics of the band gaps. From the results, it is seen that the SEM can be effectively applied to study the vibration properties of the periodic structures. Compared with the results calculated by the finite element method, it can be observed that more accurate results in high-frequency ranges can be achieved by the SEM. These results indicate that the band gap characteristics depend on both the material properties and unit cell numbers. Furthermore, the effects of the structure damping and type on the frequency responses are investigated. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the bending behaviors of the nanoplate with small scale effects are investigated by the nonlocal continuum theory. The governing equations for the nonlocal Mindlin and Kirchhoff plate models are derived. The expressions of the bending displacement are presented analytically. The difference between the two models is discussed and bending properties of the nanoplate are illustrated. It can be observed that the small scale effects are obvious for bending properties of the nanoplate. The half wave numbers, width ratios and elastic matrix properties also have significant influence on bending behaviors. [Copyright &y& Elsevier]

Abstract: In this paper, the thermal effects on the vibration properties of the double-layered nanoplates are studied. Based on the nonlocal continuum theory, the governing equations are derived and the expressions of the natural frequencies are presented. The axial stress caused by the thermal effects is considered. The influences of the small scale coefficient, the room or low temperature, the high temperature, the half wave numbers, the temperature change and the ratio of plate widths are discussed. Numerical results show that the small scale effects are significant for larger half wave numbers. The vibration properties can be obviously tuned by the thermal effects, the ratio of the nanoplate widths and the half wave numbers. The influences on the vibration behaviors are usually different for mode I and mode II. [Copyright &y& Elsevier]

Abstract: In this paper, the propagation characteristics of the longitudinal wave in nanoplates with small scale effects are studied. The equation of the longitudinal wave is obtained using the nonlocal elastic theory. The phase velocity and the group velocity are derived, respectively. The dispersion relation is analyzed with different wave numbers and scale coefficients. It can be observed from the results that the dispersion properties of the longitudinal wave are induced by the small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. Furthermore, the characteristics for the group velocity of the longitudinal wave in nanoplates can also be tuned by these factors. [Copyright &y& Elsevier]