英语翻译140954614.doc

b=12tyi+1-yi-1 c=yiand using yi=d2ydt2t =ti=d2yd2 =0=2awe obtain yi=1t2-2yi+yi-1then we can get Eq.(2.64). We must know yi-1, yi and at first ,in order to get yi+1 from Eq.(2.64);the RI should be known to get yi, mean the yi and yp,i-1must be knew. So, we can the yi+1 of the moment of ti+1, if we can get the displacement yi-1and yi,and yp,i-1.According to the conditions of both initial displacement and the initial velocity are the 0, we can get the y0, y1, R0 and yp0y0=R0= yp0=0y1=y0+y0t+y02t2=y02t2 (2.65)Example 2.9 Sought to the change rule of single-degree-of-freedom system by a shock load, that is P(t)=0, t0 P-t curve and the corresponding P-t curve as shown in Fig. 2.31(b)(c) Figure 2.3 1Table 2.3 Example 2.9 Elastic-plastic vibration calculate tableNumberTimeDisplacementXRIypiyiityi=2yi-1-yi-2+yi-1(t)2x=yi-yp,i-11)ypiyp,i-1yi-xx yi=Pi-RI000-000.7-0=0.710.50.7(0.5)2/2=0.08750.0875-010.087500.61252120.0875-0+0.61250.52=0.32860.328-010.328600.371431.520.3286-0.0875+0.37140.25=0.660.66-0111.001-1=0.001-0.352.521.001-0.66+-0.30.25=1.2671.267-0.001111.267-1=0.267-0.36321.267-1.001+-0.30.25=1.4581.458-0.267111.458-1=0.458-0.373.521.458-1.267+-0.30.25=1.5741.574-0.458111.574-1=0.574-0.38421.574-1.458+-0.30.25=1.6151.615-0.574111.615-1=0.615-0.394.521.615-1.574+-0.30.25=1.5811.518-0.61510.9660.615-0.26610521.581-1.615+-0.2660.25=1.4811.481-0.61510.8660.615-0.166115.521.481-1.581+0.1660.25=1.3401.340-0.61510.7250.615-0.02512621.340-1.481+-0.0250.25=1.1931.193-0.61510.5780.6150.122136.521.193-1.340+0.1220.25=1.0711.071-0.61510.4560.6150.24414721.071-1.193+0.2440.25=1.0101.010-0.61510.3950.6150.305157.521.010-1.071+0.3050.25=1.0251.025-0.61510.4100.6150.29016821.025-1.010+0.290.25=1.1121.112-0.61510.4970.6150.230 SOLUTION: All the calculation process as shown in Table2.3. Choosing t=0.5. By calculating the order is down by line, and in each row by item from left to right. The first line,t=0, from the first equation of Eq.2.65,we can gety0=R0= yp0=0from the Eq.2.63, we can calculate y0=P0-R0=0.7. Then the second line, t=0.5.First,from the second equation of Eq.2.65,we can get y1=y02t2=0.720.52=0.0875According to the recursive formula to calculate, mean that from Eq.2.60 to obtain x, from Eq.2.62 to obtain ypi, from Eq.2.63 to obtain yi,then turn to the next line ,from Eq.2.64 to get yi+1.Repeated computation until t=0.8.The date of table2.3 is illustrated in Fig.2.32, where graph of y(t) are shown for the response of elasto-plastic dynamic. The curve can be divided into three stages(1) Initial elastic stage, before t=1.5,Ri1, no plastic deformation(2) Plastic stage, when t=2.0,then Ri=1,the system into plastic stage, the plastic deformation yp get 0.615 maximum till t=4.0. the dotted line is the stage in the figure.(3) Rebound stage, after t=4.5, Ri1, the system no longer occur new plastic deformation, so yp0.615.In order to facilitate comparison, we also can find the Elastic dynamic displacement curve and Static displacement curve in the figure. 1.615、1.4、0.7respectively of the maximum displacement of the three curves. Elastic-plastic system and elastic system dynamic coefficients respectively： 1.6150.7=2.31 1.40.7=2Figure 2.32 Example 2.9 Elastic-plastic vibration dynamic displacement curveQuestions2.1 Why the natural cycle is inherent in the structure？Which inherent quantity of structure is relevant to it？2.2 In order to calculate the displacement of mass point of vibrating freely in any time , what must be known besides initial displacement and initial velocity ？2.3 Try to give a few examples of free vibration of single degree of freedom（Horizontal movement, vertical movement or rotation）2.4 Try to deduce the differential equation of free vibration of Example 2.3 with flexibility method.2.5 What is the reason that damping be created in the process of vibration?2.6 What is critical damping? What is damping ratio? How to measure the damping ratio of system in the process of vibration?2.7 How will the damping vibration cycle changes, if damping numerical get greaten?2.8 What is the dynamic coefficient? What factors is relevant to the size of dynamic coefficient? Whether the dynamic coefficient of single-degree-of-freedom system and the dynamic coefficient of internal force are the same or not?2.9 What is the difference between and t in Duhamel Integral ? And how to apply to solve the problem of dynamic displacement under the action of arbitrary dynamic loa