Tetragonal barium titanate nanoparticles (BTNPs) have been exploited as nanotransducers owing to their piezoelectric properties, in order to provide indirect electrical stimulation to SH-SY5Y neuron-like cells. Following application of ultrasounds to cells treated with BTNPs, fluorescence imaging of ion dynamics revealed that the synergic stimulation is able to elicit a significant cellular response in terms of calcium and sodium fluxes; moreover, tests with appropriate blockers demonstrated that voltage-gated membrane channels are activated. The hypothesis of piezoelectric stimulation of neuron-like cells was supported by lack of cellular response in the presence of cubic nonpiezoelectric BTNPs, and further corroborated by a simple electroelastic model of a BTNP subjected to ultrasounds, according to which the generated voltage is compatible with the values required for the activation of voltage-sensitive channels.

Piezoelectric Nanoparticle-Assisted Wireless Neuronal Stimulation

The Green's function (GF) method, which makes use of GFs, is an important and elegant tool for solving a given boundary-value problem for the differential equation from a real engineering or physical field. Under a concentrated source, the solution of a differential equation is called a GF, which is singular at the source location, yet is very fundamental and powerful. When looking at the GFs from different physical and/or engineering fields, i.e. assigning the involved functions to real physical/engineering quantities, the GFs can be scaled and applied to large-scale problems such as those involved in Earth sciences as well as to nano-scale problems associated with quantum nanostructures. GFs are ubiquitous and everywhere: they can describe heat, water pressure, fluid flow potential, electromagnetic (EM) and gravitational potentials, and the surface tension of soap film. In the undergraduate courses Mechanics of Solids and Structural Analysis, a GF is the simple influence line or singular function. Dropping a pebble in the pond, it is the circular ripple traveling on and on. It is the wave generated by a moving ship in the opening ocean or the atom vibrating on a nanoscale sheet induced by the atomic force microscopy. In Earth science, while various GFs have been derived, a comprehensive review is missing. Thus, this article provides a relatively complete review on GFs for geophysics. In section 1, the George Green's potential functions, GF definition, as well as related theorems and basic relations are briefly presented. In section 2, the boundary-value problems for elastic and viscoelastic materials are provided. Section 3 is on the GFs in full- and half-spaces (planes). The GFs of concentrated forces and dislocations in horizontally layered half-spaces (planes) are derived in section 4 in terms of both Cartesian and cylindrical systems of vector functions. The corresponding GFs in a self-gravitating and layered spherical Earth are presented in section 5 in terms of the spherical system of vector functions. The singularity and infinity associated with GFs in layered systems are analyzed in section 6 along with a brief review of various layer matrix methods. Various associated mathematical preliminaries are listed in appendix, along with the three sets of vector function systems. It should be further emphasized that, while this review is targeted at geophysics, most of the GFs and solution methods can be equally applied to other engineering and science fields. Actually, many GFs and solutions methods reviewed in this article are derived by engineers and scientists from allied fields besides geophysics. As such, the updated approaches of constructing and deriving the GFs reviewed here should be very beneficial to any reader.

https://iopscience.iop.org/article/10.1088/1361-6633/ab1877/pdf

Green’s functions for geophysics: a review

Three-dimensional static analysis of multi-layered piezoelectric hollow spheres via the state space method

Recent advances in smart structures technology have lead to a resurgence of interest in piezoelectricity, and in particular, in the solution of fundamental boundary value problems. In this paper, we develop an analytic solution to the axisymmetric problem of an infinitely long, radially polarized, radially orthotropic piezoelectric hollow circular cylinder rotating about its axis at constant angular velocity. The cylinder is subjected to uniform internal pressure, or a constant potential difference between its inner and outer surfaces, or both. An analytic solution to the governing equilibrium equations (a coupled system of second-order ordinary differential equations) is obtained. On application of the boundary conditions, the problem is reduced to solving a system of linear algebraic equations. The stress distribution in the tube is obtained numerically for a specific piezoceramic of technological interest, namely PZT-4. For the special problem of a uniformly rotating solid cylinder with traction-free surface and zero applied electric charge, explicit closed-form solutions are obtained. It is shown that for certain piezoelectric solids, stress singularities at the origin can occur analogous to those occurring in the purely mechanical problem for radially orthotropic elastic materials.

The stress response of radially polarized rotating piezoelectric cylinders

A new four-node bilinear shell element with full piezoelectric coupling is presented. It can be used for the analysis of light-weight smart structures (adaptive structures), i.e. laminated composite structures with piezoelectric patches attached to its surface or embedded within the laminated layers. The piezoelectric patches can be both passive (sensors) or active (actuators). The element has been successfully integrated into ANSYS 7.1 and thus can take full advantage of all capabilities of this commercial package, e.g. the connection to electric circuit elements, so far within the scope of linear problems.
The element is a continuum-based degenerated solid shell element based on the Reissner-Mindlin theory of plates. It uses the modification of the enhanced assumed strain (EAS) theory for the in-plane strains together with the discrete shear gap method for the transverse shear strains, hence it is free of both membrane locking and shear-locking in bending. It has six mechanical degrees of freedom at each node without difficulties in the drilling rotations, and up to six voltage degrees of freedom. A special logic has been implemented so as to allow for a natural description of the electric interconnections between the piezoelectric layers.
The element passes the structural patch tests from the standard set of tests proposed by MacNeal and Harder (Finite Element Anal. Design 1985; 1:3-20) including warped geometry problems. The piezoelectric behaviour was verified by comparing it with analytical solutions for plannar and curved geometry. A further validation was made by comparison with experimental measurements of harmonic response of actuated beam having both active and passive piezoelectric patches. A good agreement of the results was achieved. It can be concluded that the combination of the theories used makes this element robust and reliable. Copyright © 2006 John Wiley & Sons, Ltd.

Yu-Ching Wu

Papers

Electroelastic fields in layered piezoelectric spheres