In this paper, the free vibration of magnetoelectro-elastic (MEE) nanoplates is investigated based on the nonlocal theory and Kirchhoff plate theory. The MEE nanoplate is assumed as all edges simply supported rectangular plate subjected to the biaxial force, external electric potential, external magnetic potential, and temperature rise. By using the Hamilton's principle, the governing equations and boundary conditions are derived and then solved analytically to obtain the natural frequencies of MEE nanoplates. A parametric study is presented to examine the effect of the nonlocal parameter, thermo-magneto-electro-mechanical loadings and aspect ratio on the vibration characteristics of MEE nanoplates. It is found that the natural frequency is quite sensitive to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the thermal loading.

Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory

Damage detection techniques for wind turbine blades: A review

This paper investigates the free vibration of magneto-electro-elastic (MEE) nanobeams based on the nonlocal theory and Timoshenko beam theory. The MEE nanobeam is subjected to the external electric potential, magnetic potential and uniform temperature rise. The governing equations and boundary conditions are derived by using the Hamilton principle and discretized by using the differential quadrature (DQ) method to determine the natural frequencies and mode shapes. A detailed parametric study is conducted to study the influences of the nonlocal parameter, temperature rise, external electric and magnetic potentials on the size-dependent vibration characteristics of MEE nanobeams.

Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory

Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory

This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

Wave propagation in non-homogeneous magneto-electro-elastic plates

In engineering practice, failures due to fatigue cracks in metallic structures have always been difficult to predict. In our study, nonlinear Lamb wave-mixing was applied in the detection of micro-cracks in plates. The analysis of the nonlinear interaction of these waves with cracks of various lengths and widths was performed using finite-element simulations. The simulation results showed that the sideband at the sum frequency provide a sensitive means for micro-crack detection. Moreover, the sideband amplitudes show a monotonic increase with micro-crack length, but a decrease with micro-crack width. Experiments using Lamb wave-mixing were conducted on plates with fatigue cracks. The experimental results show that a proposed acoustic nonlinearity parameter related to the sideband at the sum frequency is sensitive to micro-cracks in plate, and is well correlated with the damage degree.

Nonlinear Lamb wave-mixing technique for micro-crack detection in plates

Based on linear three-dimensional piezoelasticity, the Legendre orthogonal polynomial series expansion approach is used for determining the wave characteristics in hollow cylinders composed of the functionally graded piezoelectric materials (FGPM) with open circuit. The displacement and electric potential components, expanded in a series of Legendre polynomials, are introduced into the governing equations along with position-dependent material constants so that the solution of the wave equation is reduced to an eigenvalue problem. Dispersion curves for FGPM and the corresponding non-piezoelectric hollow cylinders are calculated to show the piezoelectric effect. The influence of the ratio of radius to thickness is discussed. Electric potential and displacement distributions are used to show the piezoelectric effect on the flexural torsional mode. The influence of the polarizing direction on the piezoelectric effect is illustrated. For the radial and axial polarization, the piezoelectric effect reacts mostly on the longitudinal mode. For circumferential polarization, the piezoelectric effect reacts mostly on the torsional mode. In the FGPM hollow cylinder, piezoelectricity can weaken the guided wave dispersion.

Wave characteristics in functionally graded piezoelectric hollow cylinders

Traditional acoustic source location techniques are greatly affected by the threshold value of the acoustic signals. Based on the theory of modal acoustic emission, acoustic signals have characteristics indicative of multi-mode, broad band and dispersion. One-dimensional acoustic source location theory is developed to incorporate these characteristics. The arrival times and wave velocities needed for source location are influenced by mode and frequency. Based on the number of sensors used, two universal source location techniques have been investigated. To obtain the arrival time of one mode at certain frequency, the Gabor wavelet transform is applied to the analysis of acoustic signals. One-dimensional acoustic source location experiments in a thin plate have been performed using a lead break as acoustic source. The acoustic source location techniques have been greatly improved and the accuracy of these acoustic source location methods has been verified. Copyright © 2007 John Wiley & Sons, Ltd.

Wu Bin

Papers

Wave propagation in non-homogeneous magneto-electro-elastic plates

Nonlinear Lamb wave-mixing technique for micro-crack detection in plates

Wave characteristics in functionally graded piezoelectric hollow cylinders

Acoustic emission source location methods using mode and frequency analysis

Characteristics of guided waves in graded spherical curved plates