QUESTION 6 The vibrating of the beam under external force is subjected to shear force (elastic force), o'xt), the viscou

[answerhappygod]

Question 6 The Vibrating Of The Beam Under External Force Is Subjected To Shear Force Elastic Force O Xt The Viscou 1 (156.26 KiB) Viewed 43 times

QUESTION 6 The vibrating of the beam under external force is subjected to shear force (elastic force), o'xt), the viscous damping force and the external force, F(t). The ordinary differential equation of the displacement of the beam is given by dan + 2 y + oʻx= F() with the boundary conditions, *(0)=0, x(10) = 2. The terms, a represents a positive damping constant and is a constant of proportionality. (1) Suppose 2 = 0.5, o = 2 and F() is periodic such that F(t) = F, sin(21) with Fo = 0.8 and 2 = 0.4. Perform discretisation process for the second order ordinary differential equations by dividing the time interval into four equal subintervals. (7 Marks) Use the discretisation output in (i) to write the displacement, x, at each interior nodes, 1. Then, transform your system of linear equations into tridiagonal system. (8 Marks) (iii) Find the approximate solution of the displacement in (ii) by using Thomas algorithm method. (12 Marks)