The limiting state of bodies during separation in the case of the general plane problem

Работа посвящена решению общей плоской задачи, связанной с определением предельного состояния тел при отрыве. Уравнения, определяющие условия предельного состояния принимаются функциями, зависящими от среднего давления и направлений отрыва. В результате вычислений были получены характеристические уравнения для двух случаев: при достижении предельных значений отрыва двумя главными напряжениями и при достижении предельного значения отрыва одним главным напряжением. Для двух рассмотренных случаев были получены уравнения характеристик и соотношения вдоль них. The work is devoted to the solution of the general plane problem related to the determination of the limiting state of bodies during separation. The equations defining the conditions for the limiting state are taken as functions that depend on the average pressure and directions of separation. As a result of calculations, the characteristic equations were determined for two cases: when the limiting values of separation by two main stresses are reached and when the limiting value of separation by one main stress is reached. For the two considered cases, equations of characteristics and relations along them were obtained.

Determination of the limiting state of bodies during separation in the case of the general plane problem

The paper considers the general plane problem of determining the limiting state of bodies during separation. The conditions for reaching the limiting state are considered to depend on the average pressure and the direction of separation. The paper defines the characteristic equations for two cases of separation: equality of two principal stresses to the limiting value of separation and equality of one principal stress to the limiting value of separation. Equations of characteristics’ lines and relations along them are determined.

Probabilistic Damage Detection and Identification of Coupled Structural Parameters using Bayesian Model Updating with Added Mass

Damage detection inevitably involves uncertainties originated from measurement noise and modeling error. It may cause incorrect damage detection results if not appropriately treating uncertainties. To this end, vibration-based Bayesian model updating (VBMU) is developed to utilize vibration responses or modal parameters to identify structural parameters (e.g., mass and stiffness) as probability distribution functions (PDF) and uncertainties. However, traditional VBMU often assumes that mass is well known and invariant because simultaneous identification of mass and stiffness may yield an unidentifiable problem due to the coupling effect of the mass and stiffness. In addition, the posterior PDF in VBMU is usually approximated by single-chain based Markov Chain Monte Carlo (MCMC), leading to a low convergence rate and limited capability for complex structures. This paper proposed a novel VBMU to address the coupling effect and identify mass and stiffness by adding known mass. Two vibration data sets are acquired from original and modified systems with added mass, giving the new characteristic equations. Then, the posterior PDF is reformulated by measured data and predicted counterparts from new characteristic equations. For efficiently approximating the posterior PDF, Differential Evolutionary Adaptive Metropolis (DREAM) Algorithm are adopted to draw samples by running multiple Markov chains parallelly to enhance convergence rate and sufficiently explore possible solutions. Finally, a numerical example with a ten-story shear building and a laboratory-scale three-story frame structure are utilized to demonstrate the efficacy of the proposed VBMU framework. The results show that the proposed method can successfully identify both mass and stiffness, and their uncertainties. Reliable probabilistic damage detection can also be achieved.

Mathematical modeling of a MOSFET transistor as modulator in AM transmission

The necessary methodology is presented to characterize the alternating signal transistor in the time and frequency domain and obtain its characteristic equations including its transfer function. The behavior of the transistor gate is studied in different models of manufacturers in alternating signal, therefore the difference between the behavior relationship between the theory and the information obtained in the experimentation is shown. All of the above to have an optimization, control or description of the operation of a real transistor and be used in an electrical / electronic application in general, in this case, for an AM modulation.

Spectral problem for the mean field Hamiltonian

We consider the mean field Hamiltonian HV = κ ΔV + ξ(·) in l2(V ), where V = {x} is a finite set. Characteristic equations for eigenvalues and expressions for eigenfunctions of HV are obtained. Using this result, the spectral representation of the solution of the corresponding ("head transition'') differential equation is derived.

Explicit characteristic equations for integral operators arising from well-posed boundary value problems of finite beam deflection on elastic foundation

<abstract><p>Characteristic equations for the whole class of integral operators arising from arbitrary well-posed two-point boundary value problems of finite beam deflection resting on elastic foundation are obtained in terms of $ 4 \times 4 $ matrices in block-diagonal form with explicit $ 2 \times 2 $ blocks.</p></abstract>