CONSTITUTIVE EQUATIONS OF METAL-CORE PIEZOELECTRIC FIBERS

Metal-core piezoelectric fibers （MPFs） are one of the new type piezoelectric devices. To investigate the piezoelectricity and the mechanical properties of the piezoelectric fibers, the constitutive equations are established. It can describe the response of piezoelectric fibers subject to an axial force and an external voltage. A cantilever bar subject to a tip axial force and an external voltage on the electrodes is considered. The internal energy density in thermodynamic equilibrium is obtained. The total internal energy is calculated by integrating over the entire volume of the bar. The generalized displacement of the tip axial force is the tip elongation δ, and the generalized displacement of the voltage is the electrical charge Q on the electrodes. In the established constitutive equations, the excitation （input） parameters are the axial force and the external voltage, the response （output） parameters are the tip elongation and the electric charge. And the response parameters are related to the excitation parameters by a 2× 2 piezoelectric matrix. Finally, two experiments using MPF as a sensor or an actuator are performed to verify the constitutive equations. And experimental results are compared with analytical ones.

Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core

The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The field of displacements is for- mulated using the classical broken line hypothesis and the proposed nonlinear hypothesis that generalizes the classical one. Using both hypotheses, the strains are determined as well as the stresses of each layer. The kinetic energy, the elastic strain energy, and the work of load are also determined. The system of equations of motion is derived using Hamilton＇s principle. Finally, the system of three equations is reduced to one equation of motion, in particular, the Mathieu equation. The Bubnov-Galerkin method is used to solve the system of equations of motion, and the Runge-Kutta method is used to solve the second-order differential equation. Numerical calculations are done for the chosen family of beams. The critical loads, unstable regions, angular frequencies of the beam, and the static and dynamic equilibrium paths are calculated analytically and verified numerically. The results of this study are presented in the forms of figures and tables.

Vibration and Buckling Analyses of Sandwich Plates Containing Functionally Graded Metal Foam Core

In the present work,free vibration and buckling analyses of sandwich plates with various functionally graded foam cores are carried out.Foam cores are assumed to be made of metal,and three different configurations of the porous distribution in the core layer are taken into consideration.To carry out a comparative study between the distributions of pores in the core foam,the mass of foam in all three cases is kept the same.The vibration and buckling behaviors of skew plates are also analyzed as a part of the current investigation.The principle of minimization of potential energy and Hamilton’s principle are used for the derivation of the governing equations,while a C-0 finite element-based higher-order zigzag formulation is developed to solve the free vibration and buckling problems.The influences of gradation laws,boundary conditions,skew angle and geometry of plates are studied in detail for the dynamic and stability characteristics.It is found that both the non-dimensional natural frequency and buckling load decrease with the increase in the thickness of the metal foam cores,while they show an increasing trend as the skew angle of the plate increases.

The modification toward excited-state dynamics and catalytic activity by isomeric Au_(44)clusters

The structure determination of metal nanoclusters protected by ligands is critical in understanding their physical and chemical properties,yet it remains elusive how the metal core and ligand of metal clusters cooperatively contribute to the observed performances.Here,with the successful synthesis of Au_(44)TBPA_(22)Cl_(2)cluster(TBPA=4-tert-butylphenylacetylene),the structural isomer of previously reported Au_(44)L_(28)clusters(L denoted as ligand)is filled,thereby providing an opportunity to explore the property evolution rules imparted by different metal core structures or different surface ligands.Time-resolved transient absorption spectroscopy reveals that the difference in the core structure between Au_(44)TBPA_(22)Cl_(2)and Au_(44)L_(28)can bring nearly 360 times variation of excited-state lifetime,while only 3–24 times differences in excited-state lifetimes of the three Au_(44)L_(28)nanoclusters with identical metal core but different ligands are observed,which is due to much stronger impact of the metal core than the surface ligands in the electronic energy bands of the clusters.In addition,the Au_(44)clusters protected by alkyne ligands are shown to be highly effective toward the electrochemical oxidation of ethanol,compared to the Au_(44)clusters capped by thiolates,which is ascribed to smaller charge transfer impedance of the former clusters.We anticipate that the study will enhance the process in controlling the nanomaterial properties by precisely tailoring metal core or surface patterns.