A Method of Virtual Design of the Fatigue Life of a Dynamic Structure

A Method of Virtual Design of the Fatigue Life of a Dynamic Structure

В современных инженерных расчетах важное место занимают расчеты усталостной долговечности и оценка надежности динамических систем при их случайном нагружении. При проведении этих расчетов необходимо знать плотность спектра напряжений для исследуемого компонента динамической системы. Современный уров...

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Datum:2015
Hauptverfasser: Zhao, W., Zhou, X., Shena, M.
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Veröffentlicht: Інститут проблем міцності ім. Г.С. Писаренко НАН України 2015
Schriftenreihe:Проблемы прочности
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Zitieren:A Method of Virtual Design of the Fatigue Life of a Dynamic Structure / W. Zhao, X. Zhou, M. Shena // Проблемы прочности. — 2015. — № 3. — С. 162-169. — Бібліогр.: 12 назв. — англ.

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spelling irk-123456789-1733372020-12-01T01:27:20Z A Method of Virtual Design of the Fatigue Life of a Dynamic Structure Zhao, W. Zhou, X. Shena, M. Научно-технический раздел В современных инженерных расчетах важное место занимают расчеты усталостной долговечности и оценка надежности динамических систем при их случайном нагружении. При проведении этих расчетов необходимо знать плотность спектра напряжений для исследуемого компонента динамической системы. Современный уровень развития компьютерных технологий и теорий численного моделирования позволяет моделировать плотность спектра напряжений динамических систем. На основании этого предложен метод численного моделирования для прогнозирования усталостной долговечности динамической конструкции, который базируется на модельных уравнениях для плотности спектра напряжений и усталостной долговечности. В качестве примера выполнен виртуальный анализ усталостной долговечности и надежности большегрузного грузового автомобиля CW-200k. Показаны применимость метода для оценки существующих динамических конструкций и его перспективность для оценки усталостной долговечности разрабатываемых новых конструкций У сучасних інженерних розрахунках важливе місце займають розрахунки втомної довговічності й оцінка надійності динамічних систем при їх випадковому навантаженні. Для проведення цих розрахунків необхідно знати густину спектра напруги для досліджуваного компонента динамічної системи. Сучасний рівень розвитку комп ютерних технологій і теорій числового моделювання дозволяє моделювати густину спектра напруг динамічних систем. На основі цього запропоновано метод числового моделювання для прогнозування втомної довговічності динамічної конструкції, що базується на модельних рівняннях для густини спектра напруг і втомної довговічності. Як приклад виконано віртуальний аналіз втомної довговічності і надійності великовантажного грузового автомобіля CW-200k. Показано застосування методу для оцінки існуючих динамічних конструкцій та його перспективи для оцінки утомної довговічності розроблюваних нових конструкцій. 2015 Article A Method of Virtual Design of the Fatigue Life of a Dynamic Structure / W. Zhao, X. Zhou, M. Shena // Проблемы прочности. — 2015. — № 3. — С. 162-169. — Бібліогр.: 12 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/173337 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
topic Научно-технический раздел
Научно-технический раздел
spellingShingle Научно-технический раздел
Научно-технический раздел
Zhao, W.
Zhou, X.
Shena, M.
A Method of Virtual Design of the Fatigue Life of a Dynamic Structure
Проблемы прочности
description В современных инженерных расчетах важное место занимают расчеты усталостной долговечности и оценка надежности динамических систем при их случайном нагружении. При проведении этих расчетов необходимо знать плотность спектра напряжений для исследуемого компонента динамической системы. Современный уровень развития компьютерных технологий и теорий численного моделирования позволяет моделировать плотность спектра напряжений динамических систем. На основании этого предложен метод численного моделирования для прогнозирования усталостной долговечности динамической конструкции, который базируется на модельных уравнениях для плотности спектра напряжений и усталостной долговечности. В качестве примера выполнен виртуальный анализ усталостной долговечности и надежности большегрузного грузового автомобиля CW-200k. Показаны применимость метода для оценки существующих динамических конструкций и его перспективность для оценки усталостной долговечности разрабатываемых новых конструкций
format Article
author Zhao, W.
Zhou, X.
Shena, M.
author_facet Zhao, W.
Zhou, X.
Shena, M.
author_sort Zhao, W.
title A Method of Virtual Design of the Fatigue Life of a Dynamic Structure
title_short A Method of Virtual Design of the Fatigue Life of a Dynamic Structure
title_full A Method of Virtual Design of the Fatigue Life of a Dynamic Structure
title_fullStr A Method of Virtual Design of the Fatigue Life of a Dynamic Structure
title_full_unstemmed A Method of Virtual Design of the Fatigue Life of a Dynamic Structure
title_sort method of virtual design of the fatigue life of a dynamic structure
publisher Інститут проблем міцності ім. Г.С. Писаренко НАН України
publishDate 2015
topic_facet Научно-технический раздел
url http://dspace.nbuv.gov.ua/handle/123456789/173337
citation_txt A Method of Virtual Design of the Fatigue Life of a Dynamic Structure / W. Zhao, X. Zhou, M. Shena // Проблемы прочности. — 2015. — № 3. — С. 162-169. — Бібліогр.: 12 назв. — англ.
series Проблемы прочности
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AT zhoux methodofvirtualdesignofthefatiguelifeofadynamicstructure
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fulltext UDC 539.4 A Method of Virtual Design of the Fatigue Life of a Dynamic Structure W. Zhao, a,1 X. Zhou, b and M. Shen a a Hangzhou Dianzi University Hangzhou, ZheJiang, China b ZheJiang University, Hangzhou, ZheJiang, China 1 zhaowlcn@163.com ÓÄÊ 539.4 Ìåòîä âèðòóàëüíîãî àíàëèçà óñòàëîñòíîé äîëãîâå÷íîñòè äèíàìè÷åñêîé êîíñòðóêöèè Â. Æàî à , Ê. Æó á , Ì. Øåí à à Õàí÷æîóñêèé óíèâåðñèòåò Äÿíöè, Õàí÷æîó, ×æýöçÿí, Êèòàé á ×æýöçÿíñêèé óíèâåðñèòåò, Õàí÷æîó, ×æýöçÿí, Êèòàé  ñîâðåìåííûõ èíæåíåðíûõ ðàñ÷åòàõ âàæíîå ìåñòî çàíèìàþò ðàñ÷åòû óñòàëîñòíîé äîëãî- âå÷íîñòè è îöåíêà íàäåæíîñòè äèíàìè÷åñêèõ ñèñòåì ïðè èõ ñëó÷àéíîì íàãðóæåíèè. Ïðè ïðîâåäåíèè ýòèõ ðàñ÷åòîâ íåîáõîäèìî çíàòü ïëîòíîñòü ñïåêòðà íàïðÿæåíèé äëÿ èññëå- äóåìîãî êîìïîíåíòà äèíàìè÷åñêîé ñèñòåìû. Ñîâðåìåííûé óðîâåíü ðàçâèòèÿ êîìïüþòåðíûõ òåõíîëîãèé è òåîðèé ÷èñëåííîãî ìîäåëèðîâàíèÿ ïîçâîëÿåò ìîäåëèðîâàòü ïëîòíîñòü ñïåêòðà íàïðÿæåíèé äèíàìè÷åñêèõ ñèñòåì. Íà îñíîâàíèè ýòîãî ïðåäëîæåí ìåòîä ÷èñëåííîãî ìîäåëè- ðîâàíèÿ äëÿ ïðîãíîçèðîâàíèÿ óñòàëîñòíîé äîëãîâå÷íîñòè äèíàìè÷åñêîé êîíñòðóêöèè, êîòîðûé áàçèðóåòñÿ íà ìîäåëüíûõ óðàâíåíèÿõ äëÿ ïëîòíîñòè ñïåêòðà íàïðÿæåíèé è óñòàëîñòíîé äîëãîâå÷íîñòè.  êà÷åñòâå ïðèìåðà âûïîëíåí âèðòóàëüíûé àíàëèç óñòàëîñòíîé äîëãîâå÷- íîñòè è íàäåæíîñòè áîëüøåãðóçíîãî ãðóçîâîãî àâòîìîáèëÿ CW-200k. Ïîêàçàíû ïðèìåíè- ìîñòü ìåòîäà äëÿ îöåíêè ñóùåñòâóþùèõ äèíàìè÷åñêèõ êîíñòðóêöèé è åãî ïåðñïåêòèâíîñòü äëÿ îöåíêè óñòàëîñòíîé äîëãîâå÷íîñòè ðàçðàáàòûâàåìûõ íîâûõ êîíñòðóêöèé. Êëþ÷åâûå ñëîâà: ñèñòåìà ñî ñëó÷àéíûìè êîëåáàíèÿìè, ïëîòíîñòü ñïåêòðà íàïðÿ- æåíèé, ïðîãíîçèðîâàíèå óñòàëîñòíîé äîëãîâå÷íîñòè, âèðòóàëüíûé àíàëèç. Introduction. The fatigue life prediction and reliability analysis of dynamic systems under random excitement are important topics in modern engineering design [1–8]. The vibration characteristics of fatigue damage of beam-type structural components has been researched [9, 10] and a computational and experimental assessment of the sensitivity of structural materials to stress concentration under high-cycle asymmetrical loading has been performed [11]. A numerical calculation of the frequencies of natural vibrations of beams with a cross section varying linearly in height under different conditions of fixing their ends is presented [12]. However, the stress power spectral density of a component in a dynamic system must be known when one predicts its fatigue life and analyzes its reliability. A traditional way is to measure the stress power spectral density, which has played an important role in practice [4]. However, the stress power spectral density of a dynamic system will change with the alteration of the structure and dynamic parameters of a system. So the engineering application in this way is limited. Moreover, one is not able to obtain the stress power spectral density of a new dynamic system before it has been designed. With the rapid development of computer technology and numerical computation theories, it has been possible to simulate stress power spectral density of dynamic systems. Based on this, © W. ZHAO, X. ZHOU, M. SHEN, 2015 162 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 3 the method of simulating stress power spectral density is put forward in this paper, and as an example the fatigue life prediction and reliability analysis of CW-200k [4] vehicle truck are made. Computational Method of Stress Power Spectral Density. Random Response Spectra of Dynamic System Computation [1, 2]. In general, the vibration equation of a linear system can be written in matrix form as M C K F��( ) � ( ) ( ) ( ),z t z t z t t� � � (1) where M, C, and K are N N� symmetric matrices representing the masses, damping, and stiffness of the system, ��( ),z t � ( ),z t and z t( ) are column vectors representing acceleration, velocity, and displacement, respectively, and F( )t is matrix of excitation function. From Eq. (1), the frequency response matrix is obtained by taking the Fourier transform as follows [3]: H F K M C( ) ( )[ ] ,� � � �� � � �2 1j (2) where H z F( ) ( ( ) ( ( )).� � F t F t Therefore, the power spectral density matrix of system can be deduced as G H G Hz T x( ) ( ) ( ) ( ),*� � � �� (3) where H * ( )T � is conjugate transpose matrix of H( )� and Gx ( )� is input power spectral density matrix of a system. If the time difference � exists in the excitation process, according to the time difference property of the Fourier transform, Gx ( )� may be expressed as G Gx x x j j j j j i j ne e e e e ( ) ( )� � �� �� �� �� �� � � � � � 1 1 12 13 1 21 2 � 3 2 1 2 3 1 � � � � � � � e e e e j j j j n n n n � � � � � �� �� �� �� . (4) Similarly, the acceleration amplitude of the system response is given by �� ( ) . min max / z dz� � � � �3 4 1 2 � � � � � G (5) The Unit Load Stress Matrix Computation. In a linear elastic system, the stress state of the structure may be expressed as �( , , , ) ( , , ) ( ),x y z t x y z tT�S b (6) where S( , , )x y z is defined as unit load stress matrix. Vector b( )t is the load state vector. The load state vectors may be expressed as b F M W V J( ) ( ( ), ( )) ( ( ), ( )) ( ),t t t z t z t z t� � � (7) where F F F F( ) ( ( ), ( ), ... , ( ))t t t tn� 1 2 is called the forces in the translation sense, M M M M( ) ( ( ), ( ), ... , ( ))t t t tn� 1 2 is called the moments in rotation, J W V� ( , )T is ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 3 163 A Method of Virtual Design for the Fatigue Life ... called linear operator or coefficients’ matrix, and z t( ) is vector representing the response of each degree of freedom. According to the theory of correlation function [3], the correlation function matrix of stress state of stationary random process can be written as R S Ss T T TE t t x y z E b t b t x y( ) [ ( ) ( )] ( , , ) [ ( ) ( )] ( , ,� � � � �� � � � z )� � � �S J J S S JR( , , ) [ ( ) ( )] ( , , ) ( , , ) ( )x y z E z t z t x y z x y zT T T z� � J S T T x y z( , , ), (8) where E represents mathematical expectation. Therefore, the stress power spectral density matrix can be obtained by taking Fourier transform as G R S J Rs s j z je d x y z e( ) ( ) ( , , ) ( )� � � � � ��� ��� �� �� � � �� �1 2 1 2 ��� � � �d x y zT T� J S ( , , ) �S JG J S( , , ) ( ) ( , , ).x y z x y zz T T� (9) Then the stress square deviation is D R Gs s s d� � �� ��( ) ( ) .0 � � (10) If z t z t z t z tn( ) [ ( ), ( ), ... , ( )]� 1 2 represents response vector matrix of a system, then the response spectra will be of the form G G G G G G G z z z z z z z z z z z z n ( ) ( ) ( ) ( ) ( ) ( ) � � � � � � � 1 1 1 2 1 2 1 2 2 � � 2 1 2 z z z z z z z n n n n n ( ) ( ) ( ) ( ) . � � � � � � � � �G G G � � � (11) Now, the relationship between the response spectra of the system and stress power spectral density of a structure is established. Based on this formulation, one is able to estimate fatigue life and analyze the reliability of the structure. The Fatigue Life Prediction of the CW-200k type Truck. The Stress Power Spectral Density Computation of the CW-200k Type Truck of a Passenger Vehicle. The stress power spectral density of the frame of a truck can be researched in the vertical vibration of six-degree-of-freedom system because in high speed railways track is either straight or has a big radius. The dynamic model of vehicle is as shown in Fig. 1. The equations of motion was obtained as follows: m z C z C z C z K z K z K z J c c c b b c b b c �� � � � ,� � � � � � �2 2 02 2 1 2 2 2 2 1 2 2 �� � � �� � �c c b b c b bC l C lz C lz K l K lz K lz� � � � � �2 22 2 2 1 2 2 2 2 2 1 2 2 1 2 2 1 2 1 2 2 0 2 � � � � � � � � , �� � � ( )� (m z C z C l C C z K z K lb b c c b c c� � 2 1 2 1 1 1 2 1 1 2 2 2 2 K K z C K m z C z C b b b c � � � � � � � � ) (� � ) ( ), �� � � � � � l C C z K z K l K K z C c b c c b � ( )� ( ) (� � � � � � � � � � � � � � 2 21 2 2 2 2 1 2 2 1 3 � � �4 1 3 4) ( ),� � � � � � � � � � � K (12a) 164 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 3 W. Zhao, X. Zhou, and M. Shen J C l K l C l K lb b b �� � (� � ) (� � � � � ���1 1 1 2 1 1 1 2 1 1 1 2 1 1 12 2� � � � � � � � � � � � � � � � � 2 2 1 1 2 2 1 1 2 2 1 1 3 4 12 2 ), �� � (� � )J C l K l C l Kb b b b l1 3 4( ),� �� � � � �� (12b) and Eqs. (12) are written in matrix form as [ ]{��} [ ]{�} [ ]{ } [ ]{�} [ ]{ },M z C z K z C K� � � �� �� � (13) where { }z is displacement vector, { } [ ] ,z z z zc c b b b b T� � � �1 1 2 2 { }� is the input vector, { } [ ] ,� � � � �� 1 2 3 4 T [ ],M [ ],C and [ ]K are 6 6� symmetric matrices representing the mass, damping, and stiffness of a vehicle system, respectively, and [ ]C� and [ ]K � are matrices of coefficients. They correspond to the CW-200k type truck and 25 type passenger rail vehicle. The expression for the track spectrum is given by [4] G� � � � ( ) ( ) ( ) .� � � � Av c r c � � � 2 2 2 2 2 (14) The track spectrum come from the Office for Research and Experiments of the International Union of Railways (ORE B176), the high level ORE parameters are as follows: � c � 08246. rad/m, � r � 00206. rad/m, and Av � � �108 10 6. m rad� . As a result of symmetry of the structure and the force, the whole model of the side frame of truck and the loading model are shown in Fig. 2a and b, respectively. Fig. 1. The vertical vibration model of vehicle. a b Fig. 2. The model of the CW-200k type truck (a); loading model of the CW-200k truck (b). ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 3 165 A Method of Virtual Design for the Fatigue Life ... In figure, P is the vibration force that come from the air rings located between the center of side frame and car body, F is the vibration force that come from spring and damper of axle box, and f1 and f2 represent the distribution loads of the inertial force and inertial moments caused by vibration acceleration. In order to know the position of weak link of the frame, a stress chart (Fig. 3) is derived by locating the unit load (1 kN) in the center of side frame. From the chart, we find the weak link of the side frame, as shown in Fig. 2. According to Eqs. (6) and (7) and Fig. 2b, the stress function of the weak link is obtained as �( ) ( , , ) ( )t S x y z Jz t� 0 0 0 (15) and S x y z T T T T T T T T( , , ) ( , , , , , , , ),0 0 0 1 3 3 2 3 3 3 3� (16) where T L Wz1 1 0� , T L Wz2 2 0� , T L Wz3 0� , L l l l l1 1 2 1 2 24 3� � � , L l l l l2 1 2 1 3 2 34 3�� � � , L l l� �2 1 , and Wz0 is called the section modulus of the weak link, z t z z zb b b b b b T( ) (�� , � , , �� , � , , � , ) ,� 1 1 1 1 1 1 1 1� � � � � (17) J m C K J C l K l C K b b� � � � � � 4 2 2 4 2 2 2 2 1 1 1 2 1 2 1 1 , (18) where mb is the mass of the truck, J b is the moment of inertia of the truck, C1 and K1 are damping and stiffness located on the axle box, respectively. According to Eq. (11), the response spectra of the truck may be written as Fig. 3. The principal stress for unit load. 166 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 3 W. Zhao, X. Zhou, and M. Shen G G G G G G z z z z z z z zb b b b b b b b ( ) �� �� �� � �� �� �� �� � � � 1 1 1 1 1 1 1 1 z z z z z z z z b b b b b b b b b G G G G G 1 1 1 1 1 1 1 1 1 1 1 � �� �� � �� � �� � � � � � � b b b b b b b b b b b G G G G G Gz z z z z z z1 1 1 1 1 1 1 1 1 1 1 1 � � �� � � � � � �� � � � � � � � 1 1 1 1 1 1 1 1 1 1 1 1 1 G G G G G Gz z z z z z z z zb b b b b b b b b b b b �� � �� � G G G G G G z z z z z b b b b b b b b b 1 1 1 1 1 1 1 1 1 1 1 � �� �� �� �� �� �� � � � � � � � � � � � � � � � � b b b b b b b b b G G G G G Gz 1 1 1 1 1 1 1 1 1 1 1 �� � �� �� � �� � �� � � � � �� � � � � �� � � � � � � � � �b b b b b b b b b b bz zG G G G G 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 G G G G G G G b b b b b b b b b b bz z z � �� � �� � � � � � � � � � � � � � � � � � � � � � b b b b b b b G G G G G Gz z z 1 1 1 1 1 1 1 1 1 1 1 1 1 � � �� � � � � �� b b b b b b G G G G G G Gz z z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 � � � � � � �� � � � � � � � � � � � � 1 1 1 1 1 1 1 1 1 1 1 G G G G G b b� � � � � � � � � ���� � � � � � , (19) substituting Eqs. (16), (18), and (19) into Eq. (9) and substitution of the parameters of the truck then numbering computation, the SPSD Gs ( )� of the weak link can be obtained. As an example of stress power spectral density that the train runs at a speed of 180 km per hour is given in Fig. 4. The Fatigue Life Prediction of the Side Frame of The CW-200k Type Truck. After the stress power spectral density are obtained, based on it, the distribution density of stress peak can be deduced as [5, 6] f s R S R R S R ( ) exp ,� � �� �� � � � ! " " 2 2 2 � (20) where R G ds� �� ( ) ,� � 0 ��� � ��R G ds� � �2 0 ( ) , S is random stress when average value is zero. Generally, the fatigue curve can be described by S N Cm � , (21) where S is reversed stress amplitude, N is number of cycles to failure, and m and C are material constants of the structure. Fig. 4. Stress power spectral density (SPSD). G( ) ,� �103 ( )MPa 2/cm�1 �, cm�1 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 3 167 A Method of Virtual Design for the Fatigue Life ... According to the Miner cumulative-damage law [7, 8], the fatigue life computational equation can be obtained as follows: T f S S C dSf m � � � � � � � ( ) . 0 1 (22) From statistics, the fatigue life of structure accords with log normal distribution. In the light of this, the fatigue life equation in different reliabilities can be deduced as N R N R N N N( ) exp ln[ ( )] [ ( )] ln ln[ ( )]� � � � � � � � �1 1 1 2 12 1 2� �# � $ % & , (23) where R N N N N N ( ) ln ln( / ( )) ln( ( )) ,� � � � � � � � 1 1 1 2 2 # � � (24) � � '( )N N N� is called change coefficient, ' N and � N are average value and standard deviation, and N is the life when the reliability is 50%. Its value is equal to T f . In this paper, we computed the fatigue life of a side frame for four reliability, when the train runs at 60 to 200 km/h, as shown in Fig. 5. Conclusions. A method for calculating the stress power spectral density of a general linear dynamic system on the basis of the unit load stress matrix is put forward. The relationship between the stress power spectral density of dynamic components and the response spectra of dynamic system is established, and the corresponding formulas are derived. It is very important for the numerical emulation in dynamic fatigue design and reliability fatigue life prediction by computer. The dynamic response computation and fatigue life prediction of the CW-200k type vehicle truck are developed using the method and the high level ORE track spectrum. The proposed method is suitable not only for the running dynamic system but also for new design dynamic systems. Fig. 5. The fatigue life curve of the side frame of the CW-200k type truck for different reliabilities [(�) P � 50%; (�) P � 90%; (�) P � 99%; (�) P � 99 9. %]. N R( ) ,�106 km V , km/h 168 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 3 W. Zhao, X. Zhou, and M. Shen Acknowledgments. The work is supported by National Natural Science foundation of China (No. 50875070). Ð å ç þ ì å Ó ñó÷àñíèõ ³íæåíåðíèõ ðîçðàõóíêàõ âàæëèâå ì³ñöå çàéìàþòü ðîçðàõóíêè âòîìíî¿ äîâãîâ³÷íîñò³ é îö³íêà íàä³éíîñò³ äèíàì³÷íèõ ñèñòåì ïðè ¿õ âèïàäêîâîìó íàâàí- òàæåíí³. Äëÿ ïðîâåäåííÿ öèõ ðîçðàõóíê³â íåîáõ³äíî çíàòè ãóñòèíó ñïåêòðà íàïðóãè äëÿ äîñë³äæóâàíîãî êîìïîíåíòà äèíàì³÷íî¿ ñèñòåìè. Ñó÷àñíèé ð³âåíü ðîçâèòêó êîìï’þòåðíèõ òåõíîëîã³é ³ òåîð³é ÷èñëîâîãî ìîäåëþâàííÿ äîçâîëÿº ìîäåëþâàòè ãóñòèíó ñïåêòðà íàïðóã äèíàì³÷íèõ ñèñòåì. Íà îñíîâ³ öüîãî çàïðîïîíîâàíî ìåòîä ÷èñëîâîãî ìîäåëþâàííÿ äëÿ ïðîãíîçóâàííÿ âòîìíî¿ äîâãîâ³÷íîñò³ äèíàì³÷íî¿ êîíñò- ðóêö³¿, ùî áàçóºòüñÿ íà ìîäåëüíèõ ð³âíÿííÿõ äëÿ ãóñòèíè ñïåêòðà íàïðóã ³ âòîìíî¿ äîâãîâ³÷íîñò³. ßê ïðèêëàä âèêîíàíî â³ðòóàëüíèé àíàë³ç âòîìíî¿ äîâãîâ³÷íîñò³ ³ íàä³éíîñò³ âåëèêîâàíòàæíîãî ãðóçîâîãî àâòîìîá³ëÿ CW-200k. Ïîêàçàíî çàñòîñóâàííÿ ìåòîäó äëÿ îö³íêè ³ñíóþ÷èõ äèíàì³÷íèõ êîíñòðóêö³é òà éîãî ïåðñïåêòèâè äëÿ îö³íêè óòîìíî¿ äîâãîâ³÷íîñò³ ðîçðîáëþâàíèõ íîâèõ êîíñòðóêö³é. 1. Vijay K. Garg and Rao V. Dukkipati, Dynamics of Railway Vehicle Systems, Academic Press, New York (1984), pp. 1–102. 2. Hu JinYa and Zeng SanYuan, Modern Random Vibration [in Chinese], Railway Book Company of China, Beijing (1989), pp. 38–114. 3. Zhu Weiqiu, Random Vibration [in Chinese], Science Press, Beijing (1998), pp. 21– 69. 4. Running Analyses in ADAMS/Rail (2002), pp. 38–39. 5. S. H. Crandall and W. D. Mark, Random Vibration in Mechanical Systems, Academic Press, New York (1963). 6. N. Willems, J. T. Easley, and S. T. Rolfe, Strength of Materials, McGraw-Hill Book Company, New York (1981), pp. 381–422. 7. V. A. Avakov and R. G. Shomperlen, “Fatigue reliability functions,” J. Vibr. Acoust. Stress Reliab. Des., 111, No. 4, 443–455 (1989). 8. Lu Pengmin, “A probabilistic model of the fatigue accumulation damage for the welded structure in the long life fatigue,” Chinese J. Appl. Mech., 16, No. 1, 100–103 (1999). 9. A. P. Bovsunovskii and V. V. Matveev, “Vibration characteristics of fatigue damage of beam-type structural components,” Strength Mater., 34, No. 1, 35–48 (2002). 10. A. D. Pogrebnyak, M. N. Regul’skii, and A. V. Zheldubovskii, “Assessment of the effect of stress concentration on the fatigue resistance of structural materials under asymmetrical loading,” Strength Mater., 45, No. 1, 82–92 (2013). 11. V. A. Kruts, A. P. Zinkovskii, and E. A. Sinenko, “Influence of a fatigue crack on the vibrations of the simplest regular elastic system,” Strength Mater., 45, No. 3, 308–315 (2013). 12. V. G. Piskunov and R. V. Grynevyts’kyi, “Solution of the problem on the vibrations of beams with a variable cross section using the finite-difference method,” Strength Mater., 44, No. 1, 53–58 (2012). Received 10. 07. 2014 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 3 169 A Method of Virtual Design for the Fatigue Life ...

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