tailieunhanh - On the parametric transverse vibrations of continuous beam on intermediate elastic supports under the action of moving body

In this text the method of substructures is applied for establishing the vibration equation of beam under the action of moving body. Later an algorithm is built to solve the vibration equation received. From this algorithm a computer program is set up with TURBO PASCAL language | T\'P chf Ca h9c Journal of Mechanics, NCNST of Vietnam T. XVII, 1995, No 4 (42 - 48) ON THE PARAMETRIC TRANSVERSE VIBRATIONS OF CONTINUOUS BEAM ON INTERMEDIATE ELASTIC SUPPORTS UNDER THE ACTION OF MOVING BODY DO XUAN THO- NGUYEN VAN KHANG Hanoi University of Technology SUMMARY, In this text the method of substructures [2J is applied for establishing the vibration equation of beam under the action of moving body. Later an algorithm is built to solve the vibration equation received. From this algorithm a computer program is set up with TURBO PASCAL language 1. INTRUDUCTION Parametric transverse vibration of continuous beam with intermediate elastic supports under the action of moving body has been mentioned in some works such as [1, 3, 4]. In this text the method of substructures [2] is applied for establishing the vibration equation of beam under the action of moving body. Later an algorithm is built to solve the vibration equation received. From this algorithm a computer program is set up with TURBO PASCAL language. 2. SETTTING UP THE VIBRATION EQUATION Consider a continuous beam with ng intermediate elastic supports and span f Suppose that its mass of length unit is pF and bending rigidity EJ is constant on all of its length. Here p is mass density, F cross sectional area, E . . elastic module, J .moment of inert~a. Ci and l;, are called (i = 1, . , ng) respectively rigidity and coordinate of intermediate elastic supports i. The body consists of mass m attached to the spring system with rigidity k and a damper system d directly proportional with velocity. Body moves with velocity v and bears the action of force G sin flt caused by the disequilibrium mass which rotates with angle speed fl. Here G is amplitude of force. Besides it is supposed that during all the moving time, body is not separated from the beam (fig. ). . t i v m z k{,,_t d ( ,f~ ~. " '1 = vt .ft -t w Fig. 42 ,; j l •X To divide the system