Pin Lu

Dynamic properties of flexural beams using a nonlocal elasticity model

In this paper, a nonlocal Bernoulli-Euler beam model is established based on the theory of nonlocal elasticity. Frequency equations and modal shape functions of beam structures with some typical boundary conditions are derived based on the model. The corresponding dynamic properties are presented and discussed in detail, which are shown to be very different from those predicted by classic elasticity theory when nonlocal effects are significant. The results can be applied to modeling and characterization of size-dependent mechanical properties of micro- or nanoelectromechanical system (MEMS or NEMS) devices.

Non-local elastic plate theories

A non-local plate model is proposed based on Eringens theory of non-local continuum mechanics. The basic equations for the non-local Kirchhoff and the Mindlin plate theories are derived. These non-local plate theories allow for the small-scale effect which becomes significant when dealing with micro-/nanoscale plate-like structures. As illustrative examples, the bending and free vibration problems of a rectangular plate with simply supported edges are solved and the exact non-local solutions are discussed in relation to their corresponding local solutions.

Dynamic analysis of axially prestressed micro/nanobeam structures based on nonlocal beam theory

In this article, a nonlocal Euler beam model with axial prestress is established based on the theory of nonlocal elasticity. Frequency equations and modal shape functions of beam structures with axial compressive or tensile prestresses under some typical boundary conditions are derived based on the model. The corresponding dynamic properties are presented and discussed in detail, which are shown to be very different from those predicted by classic elasticity theory. The theoretical model and results presented in this article can be considered as modifications of their counterparts based on classical continuum theory and can be applied to modeling and characterization of size-dependent mechanical properties of micro- or nanobeam-based devices.

An effective method for finding values on and near boundaries in the elastic BEM

Abstract Recent research has paid great attention to the exact calculation of physical values on and near the boundaries of engineering problems. In the boundary element method (BEM), this problem demands special attention because various kinds of singularity may occur when these values are calculated. Despite extensive research, this problem has not yet been solved well. In the present paper, the elimination of various kinds of singular integrals in displacement boundary integral equations and their derivative forms is studied in detail. Firstly, a modified treatment which uses rigid body displacement solutions is introduced to calculate displacements near the boundary. Then derivative formulations of the displacement boundary integral equations are deduced, which form the basis of an investigation of the related hypersingular and nearly singular integrals. Similarly, a modified treatment, which uses the unit displacement derivative solutions together with some general numerical techniques, is proposed for the calculation of displacement derivatives on and near the boundary considered. Finally, strains and stresses are obtained from the calculated displacement derivatives by the use of the compatibility and constitutive equations. Numerical examples show that the proposed method is simple, regular and accurate in treating most singular or nearly singular integrals in the elastic BEM.

Green functions of piezoelectric material with an elliptic hole or inclusion

Abstract In this paper, the Green functions of infinite two-dimensional piezoelectric material containing an elliptic hole or an elliptic piezoelectric inclusion are obtained with the extended Stroh formalism. The results can be used to investigate the mechanical-electric coupling behaviours of infinite piezoelectric material with hole or inclusion acted by a set of generalized concentrated forces, and more importantly as kernels of boundary integral equations in BEM analyses for finite size piezoelectric materials with general forces and boundary conditions.

An alternative derivation of dynamic admittance matrix of piezoelectric cantilever bimorph

In this paper, the derivation method used in (J. Microelectromech. Systems 3 (1994) 105) and the solutions of dynamic admittance matrix of a piezoelectric device derived from the method are reviewed. By solving the problem of dynamic responses of a piezoelectric cantilever bimorph with mode analysis method, an alternative approach in the derivation of the dynamic admittance matrix and other related parameters of a piezoelectric system, which can be expressed explicitly in terms of series resonance characteristics of the structure, is presented. It is shown that this form of solutions may offer some conveniences in studying mechanical and electrical properties of the system in the vicinity of resonance frequencies.

A modified ultrasonic linear motor

A prototype for modified multi-mode ultrasonic linear motor has been developed. In contrast to the other multi-mode ultrasonic linear motors which use single layer piezoelectric ceramics as actuators bonded on the surface of elastic body, it uses actuators made of multi-layer piezoelectric actuators clamped in elastic body with compressive pre-load. With this design, not only peel-off problem that might occur on other multi-mode motors is prevented, but also speed and load are higher.

Extension of the Stroh formalism to the analysis of bending of anisotropic elastic plates

Abstract A new method for the bending analysis of anisotropic elastic plates is developed. It is an extension of Stroh formalism used in generalized plane problems. Some relations concerning the method are discussed. As an application of the method, an anisotropic plate with polygonal holes under uniform bending extension coupling is studied.

Regularized algorithms for the calculation of values on and near boundaries in 2D elastic BEM

It is verified that, under certain continuity conditions, the boundary integral equations (BIEs) of both displacement and displacement derivative can be expressed in a variety of regularized forms with at most weak singularities for any points within the domain or on its boundary. A series of algorithms embedded in the regularized formulations are presented to calculate the field variables within the domain or on its boundary. Detailed numerical results are given to check and compare the validities of the proposed algorithms and some practical effective algorithms are discovered. Due to the character of the at most weak singularities in the formulations, the algorithms require no special numerical treatments, but only the general Gauss quadrature to implement. To the end, the continuity requirements for the field variables and the validities of the algorithms are discussed.

Frequency interference between two quartz crystal microbalances

Multichannel quartz crystal microbalances (MQCM) are very attractive for biosensor applications because these devices can be miniaturized using microelectromechanical systems micromachining technology, leading to substantial reductions in cost, diagnostic time, and sample volumes. However, the miniaturization also brings about frequency interference between adjacent microbalances and the measuring accuracy will thus be affected by the extent of frequency coupling. In this paper, a theoretical analysis of the interference between two QCM on a monolithic quartz crystal is performed. It is found that both the separation between the QCM and the ratio of the electrode widths can significantly affect the frequency interference and mass sensitivity. The frequency interference is particularly strong when the two QCM have the same width or the ratio of the electrode widths is near specific values related to excited overtones. The sensitivity to mass loading decreases significantly when the geometric parameters fall within such strong interference regions. Therefore, the size and separation of the electrode structures must be carefully chosen in the design process for small quartz devices.