Longitudinal Vibrations of Piezoceramic Rods

The nature of the coupled field is investigated for certain cases of longitudinal waves propagating in thin, infinitely long, piezoceramic rods, whose axes are parallel to the poling axis (z axis).     

Nonlinear Behavior of Piezoceramic Actuators

Nonlinear behavior of piezoceramics is a well-known phenomenon. For large stresses and/or strong electric fields it is described by various hysteresis curves. Quasi-static experiments exhibited hysteresis relations between excitation voltage and strain as well as between excitation voltage and electric displacement. This behavior can be modeled by using the classical Preisach model. On the other hand, typical nonlinearities of Duffing type such as jump phenomena, multiple stable amplitude responses at the same excitation voltage and frequency, and the presence of superharmonics in response spectra can be observed when piezoceramic actuators are excited near resonance, even at weak electric fields. In this paper, different experimental results for both quasi-static and dynamic nonlinear behavior and corresponding models are presented and compared. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterisation and Modelling of Piezoceramic Actuator Hystereses

Piezoelectric ceramics are often used as actuators in smart structures technology. In the vast majority of papers dealing with this topic only linear constitutive relations are used. However, the electric field-strain relations of such actuators show hysteretic behaviour, which means that the piezoelectric coupling coefficient is not constant. In this study the hysteresis of a mechanically unconstrained actuator is obtained using the Michelson interferometry. The hysteretic behaviour is modelled by a Preisach model. Using these experimental data, for the modelling of an active structure with embedded piezoelectric actuators the actual coupling coefficient can then be determined with the help of the Preisach model. With this procedure the actuation strain of an embedded actuator, including the physical nonlinearities, can be calculated using the material characteristics obtained for an unconstrained actuator. For an experimental validation of the method outlined above, a Lead Zirconate Titanate (PZT) actuator is characterised experimentally and then glued to a cantilever beam. Then, the tip displacement of the actuated beam is determined experimentally and simulated numerically using the above method. The experimental and numerical results agree reasonably well if the shear lag due to the bonding layer between the actuator and the structure is taken into consideration. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Atomic Vibrations in Solids

This paper is an introductory survey of the basic theory ofatomic vibrations in solids. Crystalline solids, solids withdefects, and disordered materials are considered both generallyand by means of illustrative models. The emphasis throughoutis on a unified approach, using the formalism and theorems ofmatrix algebra.     

Vibrations of isotropic viscoelastic shells

It is shown that the boundary value problems for viscoelastic and elastic shells coincide. The natural and forced vibrations of shells are investigated by the averaging method.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 157–163, January–February, 1971.     

Vibrations of thin tolerance-periodic plates

In this contribution, linear-elastic thin plates with a tolerance-periodic structure in planes parallel to the plate midplane are considered. It is assumed that their averaged (macroscopic) properties are described by continuous, slowly-varying functions. Hence, plates of this kind can be treated as plates with a functionally graded structure. Here, free vibrations frequencies of a plate band are calculated within the proposed averaged model using the finite differences method. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Matrices and Molecular Vibrations

The flexibility matrix of a system is described and the normal modes of vibration of various simple ‘molecules’ are derived. Matrices which describe the geometrical symmetries of the molecules are shown to commute with the flexibility matrix, and this property assists the quick calculation of normal modes. Symmetry gives rise to degeneracy in the frequency spectrum, and this suggests practical ways of deciding which of various possible configurations a molecule actually has. The treatment is as simple as possible so that it can be used in the classroom.     

粘弹性杆的某些问题

本文利用[3]所提出的方法讨论了粘弹性杆的几种线性和非线性问题.对于线性情形,[1]的结果在这里得到较为初等和简明的印证,同时还论述了有阻尼项的线性问题和有非线性强迫作用项Pu3的幂非线性问题,从而建立了一些新的结果.     

Solitary-Wave Interactions in Elastic Rods

The propagation of longitudinal deformation waves in an elastic rod is modelled by the nonlinear partial differential equation with p = 3 or 5. This equation is first derived under a range of possible constraints. We then show that this equation and even certain generalizations do not pass the Painlevé test, and hence are probably not completely integrable. Finally, we study the head-on collision of two equal solitary waves numerically and also asymptotically for small and large amplitude.     

Concentration of Mechanical Stresses near a Hole in a Piezoceramic Layer

A new procedure for solving three-dimensional mixed antisymmetric problems of elasticity theory for a layer weakened by through tunnel holes is proposed. The boundary-value problem is reduced to a system of one-dimensional singular integral equations consisting of 3k (k = 1, 2, ...) equations. The calculation results for characteristic stresses are presented.     

Vibrations of a fractal elastic string

We construct the solution of the fractional space-time equations that describe the vibrations of a quasi-one-dimensional fractal elastic string. We give the solution of the Cauchy problem for fractional differential equations with initial conditions. We carry out a numerical analysis and construct the graphic variation of the displacement function of a fractal elastic string. Three figures. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 142–147     

Efficient Calculation of Tread Block Vibrations

A model is presented that allows to calculate the dynamics of tyre tread blocks. The numerical efficiency is achieved by the combination of static and important modal ansatz functions, also known as Hurty/Craig/Bampton transformation. Nonlinear single point contacts provide the contact forces and consider the surface roughness. The non-smooth friction characteristic is approximated an arctan function and a parameter study of the slope parameter is conducted. Typical stickslip limit cycles of the tread block are shown. These phenomena can have a part in the tyre/road noise. Experimental results qualitatively agree with the modelled tread block vibrations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flexural Vibrations of Shafts with Delaminations

The purpose of this theoretical work is to present a general model of laminated rotating shaft with circumferential delaminations. The shaft is treated as a thin‐walled composite cylindrical shell. The delamination of constant width is parallel to the shell reference surface and it covers the entire circumference. The edge delamination is modeled by changing the effective reduced stiffnesses of debonded parts. The stabilizing effect of external damping and destabilizing effect of internal damping are taken into account in the dynamic stability analysis. The influence of the relative delamination length and configuration on the critical angular velocity of shaft is shown.     

Fundamental Solutions of Electroelasticity Equations for a Piezoceramic Layer in R3

Coupled electroelastic fields in a piezoceramic layer under the action of force and electric sources are determined analytically. The Fourier coefficients of the displacement and electric potential vectors and of the stress tensor are expressed in terms of the Macdonald cylindrical functions in a closed form. The solutions obtained can be used to consider the boundary-value problems of electroelasticity for a piezoceramic layer with tunnel heterogeneities.