Basing on the theory of one-dimensional wave, authors have studied the problem of longitudinal shock of solid object onto the elastic bar placed on the viscoelastic foundation with constant resistance of a part of the bar side face. | Vietnam Journal of Mechanics, NCNST of Vietnam T. XX, 1998, No 1 {56- 64) LONGITUDINAL SHOCK SOLID OBJECT ONTO THE ELASTIC BAR PLACED ON THE VISCO-ELASTIC FOUNDATION WITH CONSTANT RESISTANCE OF A PART OF THE BAR SIDE FACE r I NGUYEN THUC AN, NGUYEN THI THANH BINH Hanoi Water Resources University 1. Introduction Basing on the theory of one-dimensional wave, authors have studied the problem of longitudinal shock of solid object onto the elastic bar placed on the viscoelastic foundation with constant resistance of a part of the bar side face. The purpose of this paper is to determine stress state of the bar. The diagram of the problem is p(t) t 1 L l 1 X 2. Formulation of the problem . The equation of motion of the part of the side face of the bar with 56 .L constant resistance is determined as a2u -- a2 (a2Uat2 ax2 Kl) with () t > 0; The general solution ofEq.() bounded on the zone la is U1(x,t) = 'PI(at- x) + ~K1x 2 - K1atx. () The general solution of Eq.() on the , lc is {) The general solution of Eq.() on the different zones is U1(x,t) = 'PI(at- x) + I/J1(at + x) + ~K1(L1- x) 2. {) . The equation of motion of the other part of the bar is with L1 S constants. 3. Determination of the wave functions of the bar L1 . Considering wave functions in a limite~ duration 0 :S t :S -a . According to [3] the force of the cap on the shocked head of the bar is () where Basing on () and () the wave function +•" +e f fiL p-aX · . e>+•• rl (0~ 1 (r)- -K.!Z-•L) >+•" 1 +a> , K2 ] \Ou(r) dr. () 1+a>. . . . Basing on the continuous characteristics of function U2(x, t) at the timet = L L a and x = L, we have: tP2 (L, -;;) = 0 and H = Ho = 0, where Ho is integral constant of H in the limited duration L +·• j liLr e~+•> [1-+a>.a>. \Ou(r)1 1 1 K2 +a>. \Ou(r) ] dr. () 0 The wave function 'tj!HZ) at the bar end with L :::; a Z-2L 'tj!l (Z) 2 =_ K2 e J ,!;;, .
