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1

Improvement of the graphical method for plotting the shear and moment diagrams for members subjected to linearly varying loads

Husain Muhammed Abbas, Ali Abdulkhaliq Salim

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 1

46--66

EN

This study presents an improvement of the graphical method for plotting the shear and moment diagrams for the structural members under linearly varying loads (triangular and trapezoidal loads). Based on the parabolic nature of the shear function, when the loading varies linearly, and on the relations among load, shear, and moment, a mathematical equation is developed to locate the zero-shear point, while a geometric technique is presented to calculate the parabolic shear area. Five comprehensive examples of beams loaded with linearly varying loads are selected to illustrate the steps of the solution for the proposed techniques. The results demonstrated the applicability of the presented method, and gave exact diagrams compared with the basic graphical method. It is concluded that the proposed improved method is generally more convenient, less time-consuming, and has less computational efforts because it does not require sectioning, solving equilibrium equations, and quadratic formulas compared with the basic graphical method.

2

Thermoelastic response of nanobeam resonators subjected to exponential decaying time varying load

Abouelregal A. E., Zenkour A. M.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

937—948

EN

This work investigates the vibrational response of thermoelastic nanobeam resonators induced by ramp-type heating and subjected to exponential decaying time varying load via Euler-Bernoulli beam theory. Governing equations are derived in the context of nonlocal generalized thermoelasticity theory with dual phase lags. The nonlocal nanobeam theory incorporates a nonlocal parameter to capture the small scale effect. Using the Laplace transform technique, an analytical solution has been attained. and inversions of the transformed solutions have been carried out by means of calculus of residues. The effects of nonlocal, point load and ramping-time parameters on all studied fields of the nanobeam are investigated and discussed.

3

Construction of integral equations describing limit equilibrium of cylindrical shell with a longitudinal crack under time-varying load

Makhorkin M., Nykolyshyn M

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2016

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Vol. 5, No 3

141--146

EN

The problem on limit equilibrium of a closed infinite cylindrical shell with a longitudinal crack under the action of time-varying load by the exponential law has been considered. According to presented conditions the expressions for the field of the stress-free deformations along the crack are presented in the form [wzory] are the operators identical to those given in [7] for the case of static load [wzory] and , are the operators that take into account the dependence of load on time. Using the same transformations that in the case of static load [7, 11], the key functions [wzory] are determined, and the clarification of the shell's stress-state is reduced to solving the system of singular integral equations (SIE). Its general form is similar to the same system constructed for static load [7], and the kernels of SIE have the form [wzory], where is a singular part [wzory], is a regular part in which the component [wzory] takes into account the time dependence of load [wzory], are described by the expressions similar to the same given in [7].

4

Identyfikacja warunków eksploatacyjnych na potrzeby diagnostyki przekładni planetarnej do napędu koła czerpakowego

Bartelmus W., Zimroz R.

Diagnostyka

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2006

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nr 1(37)

151-158

PL

Niniejsza praca stanowi kontynuację rozpoznania problemu diagnostycznego i określenia właściwości sygnałów diagnostycznych generowanych przez przekładnię planetarną będącą elementem układu napędowego koła czerpakowego w koparce kołowej pracującej w polskim przemyśle wydobywczym. Obiekt diagnozowania wyposażony jest w nowoczesny, skomplikowany, wielokanałowy system diagnostyczny pracujący w trybie on-line z możliwością sterowania i diagnozowania przez Internet. Z diagnostycznego punktu widzenia system nie spełnia oczekiwania użytkowników. Jest to związane z jego złożonością (wymaga wykwalifikowanych służb do zarządzania systemem, interpretacji wyników itp.) oraz wyjątkowo trudnymi warunkami eksploatacyjnymi, w jakich pracuje koparka. Zauważono, że w czasie pracy systemu diagnostycznego dochodzi w pewnych przypadkach do generowania tzw. fałszywych alarmów - czyli zostaje wygenerowana informacja o przekroczeniu progów alarmowych świadczących o wystąpieniu uszkodzenia - mimo, że obiekt jest nadal w dobrym stanie technicznym. Wydaje się uzasadnione powiązanie faktu generowania fałszywych alarmów z warunkami eksploatacyjnymi, w jakich pracuje maszyna (a ściślej warunkami urabiania organu urabiającego). Z punku widzenia diagnostyki jest to analiza wpływu czynnika eksploatacyjnego, który wpływa na postać sygnału diagnostycznego. W pracy wykazano zmienny charakter obciążenia przekładni (zmienność zgodna z teoretycznym przebiegiem obciążenia koła czerpakowego) i wpływ tej zmienności na postać sygnału diagnostycznego (zmienność amplitudy i struktury częstotliwościowej widma).

EN

The paper gives continuation of introductory problem recognition of vibration signal properties generated by planetary gearbox that is the part of the driving system of a bucket wheel excavator used in the polish extractive industry. The object is diagnosed is by a modern elaborate multi-channel diagnostic system that work on-line with possibility to control and diagnosing by an Internet. From diagnostic point of view the does not fulfill its user expectations. It is related with system complexity and user qualification to manage it, and result interpretation, and hard digging condition of a bucket wheel excavator. It have been noticed at some condition the diagnostic system generates false alarms - its generated the information about limit exceeding that should give evidence on driving system faults but actually the planetary gearbox is in good condition. It seems to be that false alarms are related to exploration condition of a bucket wheel. From diagnostic point of view it is a diagnostic factor which is connected with outer load variability which have influence the diagnostic signal and the diagnostic signal analysis way. In the paper has shown that the identified load variability is compatible with theoretical one and it has influence on diagnostic signal (its amplitudes and a spectrum frequency composition).