Dimensional reduction of a piezoelectric composite rod

In the present paper, a new generalized Timoshenko model is constructed for a composite rod with embedded or attached piezoelectric materials. This model is applicable to composite rods without prescribed electric potential along the lateral surfaces. The Variational-Asymptotic Method (VAM) is applied as a mathematical tool to carry out the dimensional reduction process. The present reduced model captured the effects of dielectric as well as the polarization of the piezoelectric material, which justifies its coupled electromechanical nature. First, the three-dimensional electromechanical enthalpy is asymptotically approximated by VAM using the slenderness of the rod as the small parameter and subsequently an equivalent one-dimensional electromechanical enthalpy is developed. Energy terms, which are asymptotically correct up to the second order are kept in the approximate enthalpy expression. For engineering applications, the approximate enthalpy is then transformed into a generalized Timoshenko model which has the traditional six mechanical degrees of freedom along with an extra one-dimensional electric degree of freedom.     

Stress singularities near the apex of a cylindrically polarized piezoelectric wedge

Summary In this paper, the stress singularities for a cylindrically polarized piezoelectric wedge are investigated. The characteristic equations are derived analytically by using the extended Lekhnitskii formulation. The piezoelectric material (PZT-4) is polarized in the radial, circular or axial direction, respectively. Similar to the rectilinearly polarized piezoelectric problem, the inplane and antiplane stress fields are uncoupled. The results show the variations of the singularity orders with the changes of the wedge angle, material constants, polarized direction, and the boundary conditions.     

A modulus gradient model for an axially loaded inhomogeneous elastic rod

A new gradient elasticity formulation is proposed for a one-dimensional linear elastic inhomogeneous rod. In the new formulation, similar to the differential relation between the local strain and the gradient enhanced strain in the classical models of gradient elasticity, a differential relation is proposed for the Young’s modulus. Analytical and finite element solutions of the proposed formulation are derived. Results of the proposed model are compared with a classical model of gradient elasticity for a model problem of carbon nanotube reinforced polymer composite.     

Wave propagation in a piezoelectric rod of 6 mm symmetry

The wave propagation in a piezoelectric rod of 6 mm symmetry is investigated by applying a 3-D piezoelectric elastic model. A self-adjoint method is introduced to solve this problem, this method avoids calculating the generalized eigenvalue equation, it completely draws the dispersion curves in the forms of Quasi-P wave, Quasi-SV wave and Quasi-SH wave under the self-adjoint boundary condition, and it can evaluate the dispersion curves of all kinds of boundary conditions. As an example, the dispersion curves of PLT-5H are completely drawn, we also found the Quasi-SV wave has standing wave phenomenon in the PLT-5H rod. In addition the relation of dispersion curves among different boundary conditions is discussed, and an experiment method is introduce to decide the dispersion curves for another boundary conditions.     

A proposed method of measuring the complex modulus of a thick viscoelastic layer

A simple, non-destructive method of measuring the complex modulus of a layer of viscoelastic material is proposed. The method relies upon an analysis of the frictionless contact of a rigid smooth indentor and the layer. The contact is maintained by means of a fluctuating normal load. The total load (or the indentation) is required to vary in a simple sinusoidal way. The complex modulus may then be determined from the results of observations made when the contact area is maximum (or minimum).     

A method for determining ultrahigh temperatures

The problem of determining high and ultrahigh temperatures is urgent in connection with mastering the technology of new high-power energy sources. The known methods of measuring temperatures by using thermocouples, ultrasound, or optical devices can either be used only over limited temperature ranges or are very difficult to apply in practice. The present article describes a method of determining temperature based on the phenomenon of rethermalization of neutrons. The neutron is used as an agent interacting with the hot medium. When neutrons are scattered by atoms of a hot medium there is a change in their energy spectrum which is uniquely related to the kinetic temperature of the medium. In principle there is no apparent upper limit of the temperatures which can be measured by this method.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 8–11, May–June, 1979.The authors thank G. A. Ilyasova and M. Ya. Bankrashkova for their kind assistance in calculating the neutron energy spectra.     

Effect of variability of the modulus of elasticity on the thermoelastic stresses associated with the pulsed heating of a rod

In the practical utilization of thermal shock in a rod with a load at the end in accordance with the method of [1] as a means of studying the stability of the rod and the dynamic modulus of elasticity of elevated temperatures, it is necessary under certain conditions to take into account the effect of the variability of the modulus of elasticity on the thermoelastic forces. This is the subject of the present article.     

简支梁中截面挠度计算的一种简易方法

介绍了一种首先利用简支梁的对称性找出等价悬臂梁, 然后利用叠加法求出等效悬臂梁自由端的挠度, 从而得到一般载荷作用下简支梁中间截面挠度的方法.