State-space approach to thermoelastic interactions in generalized thermoelasticity type III

The present work is attempted to formulate the state-space approach to the problems of thermoelastic interactions with energy dissipation on the basis of the theory of generalized thermoelasticity type-III, recently developed by Green and Naghdi. The formulation is then applied to solve a boundary value problem of an isotropic elastic half space with its plane boundary subjected to two different types of boundary conditions: (1) sudden increase in temperature and zero stress and (2) sudden increase in load and zero temperature change. Integral transform method is applied to obtain the solution of the problem. The short time approximated solutions for the field variables have been constructed analytically for both the cases. The problem is illustrated with the help of different graphs of numerical values of the field variables.     

Continuum modelling of piezoelectromechanical truss beams: an application to vibration damping

Summary We call piezoelectromechanical (PEM) truss beam a truss modular beam coupled with a transmission electrical line when the coupling is obtained by piezoelectric actuators which act as bars in the module and as capacitances in the electrical line. The truss module length is assumed negligible with respect to the considered wave lengths. The transmission electrical line is assumed continuously distributed along the truss beam. Applying the method of virtual power as expounded in [2] we formulate a continuum model for PEM truss beams and we prove that there exists a critical value for the transmission electrical impedance in the neighborhood of which the electromechanical modal coupling is maximum and the possible electrical dissipation of mechanical energy is relevant. Accepted for publication 1 June 1997     

可观测度的探讨及其在捷联惯导系统可观测性分析中的应用

可观测度是为了分析线性系统中组合状态的可观测程度而提出来的,在卡尔曼滤波的滤波效果分析中得到了应用。文中先对已有的两种可观测度分析方法进行了简述,并且分析了两种方法的等价性;然后从理论上分析了此描述方法的不全面性。通过典型例子说明了理论分析的结果,给出了一种更全面的描述系统可观测组合状态可观测度的方法,并且用新的描述方式分析了捷联惯导系统的各状态可观测度。结果表明,该数值刻画方式能够定量的给出系统状态可观测的程度,是解析分析方法的很好的补充。     

亏损系统振动模态的可控可观性

利用奇异值分解方法来讨论系统广义模态的可控可观性的量度问题,得到了亏损系统广义模态可控可观性的量度指标,同时用实例说明了本文方法是有效的。     

The method of subregions in coupled thermoelasticity

Summary There are at present only a few exact solutions of rather simple problems in coupled thermoelasticity. For many problems important from a practical point of view no exact solutions are known. The present paper deals with a convenient method of approximate solutions of these problems. As guideline in the use of this method for the solutions of quasistatic, thermoelastic-coupled problems a numerical example is presented, where the effect of coupling is demonstrated.

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Übersicht Bisher sind nur wenige und relativ einfache thermoelastische Probleme unter Berücksichtigung der Verkopplung von Wärmeleitungsgleichung und der Gleichung für die elastischen Verschiebungen gelöst worden. Viele praktisch interessierende Probleme konnten noch nicht exakt gelöst werden. Zu ihrer näherungsweisen Lösung wird hier ein geeignetes und einfaches Verfahren angegeben. An einem numerisch ausgerechneten Beispiel wird der Einfluß der Verkopplung der beiden Ausgangsgleichungen untersucht.

     

Numerical-analytical solution of plane problems in thermoelasticity

The scaled-boundary method is used as a numerical-analytical method to solve problems of thermoelasticity. As an example, the stress intensity factor for a heated thin circular orthotropic disk with an internal crack is evaluated __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 122–126, December 2007.     

Failure mode transitions in RC beams: A cohesive/overlapping crack model application

The analysis of reinforced concrete beams in flexure taking into account the nonlinear behaviour of concrete is addressed by a numerical approach based on the Cohesive-Overlapping Crack Model. An extensive experimental research has been proposed by Bosco and Carpinteri (Scale effects and transitional phenomena of reinforced concrete beams in flexure. ESIS Technical Committée 9 Round Robin proposal, 1993), Bosco et al. (Scale effects and transitional failure phenomena of reinforced concrete beams in flexure. Report to ESIS Technical Committée 9, 1996) and El-Khatieb (Transizione di scala duttile-fragile per le travi in calcestruzzo armato. PhD Thesis, 1997) in order to obtain a rational explanation for failure transitional phenomena of RC beams by varying steel percentage and/or beam slenderness and/or beam size-scale. In the present paper, collapse mechanisms due to concrete tensile cracking, concrete compressive crushing and steel yielding and/or slippage are analysed and a numerical vs. experimental comparison is presented in order to validate the proposed model.     

Energy and dissipation of inhomogeneous plane waves in thermoelasticity

Inhomogeneous small-amplitude plane waves of (complex) frequency ω are propagated through a linear dissipative material. For thermoelasticity we derive an energy-dissipation equation that contains all the quadratic dependence on the field quantities, see Eq. (10). In addition, we derive a new energy-dissipation equation (Eq. (22)) involving the total energy density which contains terms linear in the field quantities as well as the usual quadratic terms. The terms quadratic in the small quantities in the energy density, energy flux and dissipation give rise to inhomogeneous plane waves of frequency 2ω and to (attenuated) constant terms. Usually these quadratic quantities are time-averaged and only the attenuated constant terms remain. We derive a new result in thermoelasticity for these terms, see Eq. (54). The present innovation is to retain the terms of frequency 2ω, since they are comparable in magnitude to the attenuated constant terms, and a new result, see Eq. (44), is derived for a general energy-dissipation equation that connects the amplitudes of the terms of the energy density, energy flux and dissipation that have frequency 2ω. Furthermore, for dissipative waves or inhomogeneous conservative waves the (complex) group velocity is related to these amplitudes rather than to the attenuated constant terms as it is for homogeneous waves in conservative materials.     

Comparative asymptotic analysis of coupled and uncoupled thermoelasticity

The asymptotic solution of the three-dimensional dynamic of coupled thermoelasticity problem (with the mutual influence of the strain and temperature fields taken into account) for an isotropic rectangular plate is used to perform a comparative analysis of the results obtained according to this theory and the theory of temperature stresses. The parameters whose values affect the applicability of these theories and of the applied theory used to solve quasistatic problems of thermoelasticity are obtained.     

Exact dynamic solutions to piezoelectric smart beams including peel stresses I: Theory and application

This work presents exact dynamic solutions to piezoelectric (PZT) smart beams including peel stresses. The governing equations of partial differential forms are firstly derived for a PZT smart beam made of the identical adherends, and then general solutions of the governing equations are studied. The analytical solutions are applied to a cantilever beam with a partially bonded PZT patch to the fixed end. For the given boundary conditions, exact solutions of the steady state motions are obtained. Based on the exact solutions, frequency spectra, natural frequencies, normal mode shapes, harmonic responses of the shear and peel stresses are discussed for the PZT actuator. The details of the numerical results and sensing electric charges will be presented in Part II of this work. The exact dynamic solutions can be directly applied to a PZT bimorph bender. To compare with the classic shear lag model whose numerical demonstrations will be given in Part II, the related equations are also derived for the shear lag rod model and shear lag beam model.     

Impossibility of localization in linear thermoelasticity with voids

In this note we prove the impossibility of the localization in time of the solutions of the linear thermoelasticity with voids. This means that the only solution for this problem that vanishes after a finite time is the null solution. From a thermomechanical point of view, this result says that the combination of the thermal and porous dissipation in the linear theory is not sufficiently strong to guarantee that the thermomechanical deformations will vanish after a finite time. The main idea to prove this result is to show the uniqueness of solutions for the backward in time problem.