Alexander K. Belyaev

Shaping of Piezoelectric Sensors/Actuators for Vibrations of Slender Beams: Coupled Theory and Inappropriate Shape Functions

Flexural vibrations of smart slender beams with integrated piezoelectric actuators and sensors are considered. A spatial variation of the sensor/actuator activity is achieved by shaping the surface electrodes and/or varying the polarization profile of the piezoelectric layers, and this variation is characterized by shape functions. Seeking shape functions for a desired purpose is termed a shaping problem. Utilizing the classical lamination theory of slender composite beams, equations for shaped sensors and actuators are derived. The interaction of mechanical, electrical and thermal fields is taken into account in the form of effective stiffness parameters and effective thermal bending moments. Self-sensing actuators are included. From these sensor/actuator equations, shaping problems with a practical relevance are formulated and are cast in the form of integral equations of the first kind for the shape functions. As a practical interesting aspect of these inverse problems, shape functions which fail to measure or to induce certain structural deformations are investigated in the present paper. Such inappropriate shape functions are termed nilpotent solutions of the shaping problems. In order to derive an easy-to-obtain class of such nilpotent solutions, the homogeneous versions of the integral equations for the shaping problems are compared to orthogonality relations valid for redundant beams. Hence, by analogy, the presented nilpotent solutions are shown to correspond to solutions of the basic theory of thermoelastic structures, namely to thermally induced static bending moment distributions. This result beautifully reflects the close connection between the theory of thermally loaded structures and the theory of smart structures. A particular result for a nilpotent shape function previously investigated in the literature is explained in the context of the present theory, and examples of nilpotent shape functions for various structural systems are presented.

Dynamics of mechanical systems with variable mass

A rational treatment of the relations of balance for mechanical systems with a time-variable mass and other non-classical supplies. - Systems with mass explicitly dependent on position. - Dynamics of the mass variable body. - Mechanics of multi-component media with exchange of mass and non-classical supplies. - Modeling of fluid-structure interaction: effects of added mass, damping and stiffness. - Dynamics and stability of engineering systems with moving continua.

Advanced Dynamics and Model-Based Control of Structures and Machines

The seismic collapse capacity of highly inelastic non-deteriorating single-degree-of-freedom (SDOF) systems, which are vulnerable to the destabilizing effect of gravity loads (P-delta effect), is evaluated. The collapse capacity based on different definitions of the intensity measure is discussed. In particular, collapse capacity spectra are derived utilizing sets of Incremental Dynamic Analyses (IDAs) involving 44 recorded ground motions.

Propagation of sound waves in stressed elasto-plastic material

Acoustoelasticity approach is a method of non-destructive testing and it is based upon the theory of propagation of ultrasonic longitudinal and transverse waves of different polarization in solids. This approach is able to uniquely determine the value of the principal stress in the case of no plastic deformation. An elastoplastic material with hardening is taken and the problem of propagation of a plane acoustic wave in a homogeneous prismatic elastic-plastic body that is uniaxially prestressed in the direction perpendicular to the wave propagation direction is solved. The sound velocities for the transverse and longitudinal waves are obtained for different approximations in terms of the first and second order of smallness. A strong dependence of the velocities from the hardening factor and component of the deviatoric stress tensor was detected. The study provides a number of closed-form expressions required for solving the practical problem of technical diagnostics of structures exposing plasticity.

Comparative study of various approaches to stochastic elastic wave propagation

SummaryThree approaches to the problem of 1-D wave propagation in media with random elastic and mass properties are studied: (i) method of integral spectral decomposition, (ii) the Fokker-Plank-Kolmogorov equation, and (iii) the Dyson integral equation. Merits and shortcomings of each approach are discussed. It is shown that the approaches cover actually all possible problems of the harmonic wave propagation in heterogeneous or stochastic media, hence, by means of a preliminary analysis of a particular problem and bearing in mind the strong and weak sides of each approach, one can choose an appropriate solution strategy.

Versuchsgestützte Modellierung von Kfz-Stoßdämpfern für die dynamische Mehrkörpersimulation (MKS)

ZusammenfassungIm vorliegenden Beitrag wird ein aussagekräftiges Stoßdämpfermodell vorgestellt, welches erlaubt, fahrdynamische und komfortrelevante Untersuchungen am Gesamtfahrzeug mit Hilfe der Mehrkörper-Software ADAMS wirklichkeitsnahe durchzuführen. Das neue Modell ist so einfach wie möglich gehalten, basiert aber auf hydrodynamischen Betrachtungen; im Gegensatz zu herkömmlichen Beschreibungen wird bei der neuen Formulierung aufgrund einer robusten und zutreffenden physikalischen Modellierung ein weiter Amplituden- und Frequenzbereich abgedeckt. Zur Parameteridentifikation und Verifikation des Modells wurden umfangreiche Messungen an fahrzeugtypischen Dämpfern durchgeführt.AbstractThis paper is concerned with a more detailed shock absorber model to increase the quality of full vehicle models for dynamic and comfort computations in the multi-body systems software ADAMS. The new model is based on hydrodynamic consideration. Compared with conventional damper models it is able to cover a wide amplitude and frequency range due to a simple but robust physical modeling. For parameter identification and verification of the damper model measurements of typical car dampers were realized.

Thermodynamic derivation of dynamic boundary value problem and heat conduction equation for polarised thermoelastic materials

SummaryIt is shown that the dynamic boundary value problem and the heat conduction equation for simple piezoelectric materials with time-dependent properties result from the first and second law of thermodynamics. It is also shown that the conventional form of the heat conduction equation for geometrically nonlinear anisotropic thermoelastic media does not satisfy the principle of material frame indifference. A new form of the heat conduction equation is proposed.

Nonlinear Wave Propagation in Complex Structures Modelled by Random Media with Self-Stresses

General modelling for complex engineering structures is proposed. In order to describe such intrinsic properties of complex structures as vibration localisation and parameter uncertainty, complex structures are modelled by random media with self-stresses, the role of the latter being played by the internal degrees of freedom of structural members. The rheological model is composed of an infinite number of elastic-plastic elements in parallel. The Dyson integral equation is applied to solve the problem of wave propagation in essentially heterogeneous random media. It is shown that the considerable spatial decay of the propagating wave is caused by (i) dispersion and scattering, (ii) resonant absorption in secondary systems attached to the primary structure and (iii) nonlinear material damping and dry friction between the structural members. The latter causes various nonlinear effects, e.g. the vibration saturation in complex structures. Structures are also shown to exhibit another nonlinear effect, namely, maximum distance which the wave propagates down the structure.

Thermodynamic derivation of the heat conduction equation and the dynamic boundary value problem for thermoelastic materials and fluids

SummaryIt is shown that the dynamic boundary value problem and the heat conduction equation for some simple materials are derivable from the first and second laws of thermodynamics. The dynamic boundary value problem, the heat conduction equation and two variational principles are derived for thermoelastic materials with time-dependent properties, for the case when the volume and surface forces are not “dead”, and when the free energy of the material depends upon the temperature. It is also shown that the conventional form of the heat conduction equation for geometrically nonlinear anisotropic elastic media does not satisfy the principle of material frame indifference. A new form of the heat conduction equation is offered. The heat conduction equation for the Navier-Stokes fluid and the dynamic boundary value problem for an elastic fluid are obtained. The elastic fluid is proved to be the only simple fluid without “memory”.

Combined integral and FE analysis of broad-band random vibration in structural members

The paper addresses a new approach for the description of broad-band random vibrations of components in complex structures. Random vibrations at low frequencies are determined by methods of computational structural dynamics. Vibrations at high frequencies are described in an integral form, i.e. by means of combination of the Bolotin method of integral estimates and the methods of high-frequency dynamics. The fuzzy intermediate range between the upper frequency bound of efficient numerical computations and the lower bound of the high frequency approach is examined by means of an example. The methodology essentially reduces the computing costs without noticeable loss of information in the high frequency domain. Further, the approach enables one to indicate a frequency domain wherein the vibration localisation within structural members occurs. The applicability of the concept is demonstrated by computing the broad band random vibrations of a thin-walled cover of an engine head.