PROBLEM3: Assume that the mass and stiffness of the system of Fig3 are: m = 1000 kg, k = 1000 kN/m, and that it is undamped. If the initial displacement is u(0) = 4cm, and the displacement at t = 1.2sec is also 4cm, determine: (a) the displacement at t = 2.4sec (b) the amplitude of free vibration uo

PROBLEM3: Assume that the mass and stiffness of the system of Fig3 are: m = 1000 kg, k = 1000 kN/m, and that it is undamped. If the initial displacement is u(0) = 4cm, and the displacement at t = 1.2sec is also 4cm, determine: (a) the displacement at t = 2.4sec (b) the amplitude of free vibration uo

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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FEA for Dynamic Problems

Finite element analysis or FEA is a computational tool that evaluates the approximate solution for a particular engineering problem. The tools provided by FEA help to evaluate the solutions of partial differential equations (PDEs) computationally following a numerical approach. Solutions of the PDEs can also be performed by following traditional algebraic approaches, but when the problem gets towards the complex side, it becomes very tedious and almost impossible to arrive at the solutions. In such cases, the FEA fulfills the purpose by evaluating the equations following multiple time steps and iterations. The more the time steps and iterations, the more accurate the solution. The solution plotted by FEA analysis and mathematical approaches varies asymptotically.

Question

PROBLEM3:
Assume that the mass and stiffness of the system of Fig3 are: m = 1000 kg , k = 1000 kN/m, and that
it is undamped. If the initial displacement is u(0) = 4cm, and the displacement at t = 1.2sec is also 4cm,
determine:
(a) the displacement at t = 2.4sec
(b) the amplitude of free vibration uo
[1
ooooo
k
m
-v(t)
p(t)
fø(1)
fs(1)
fr(1)
- v(t)
p(1)
(a)
(b)
Figure 3-Idealized SDOF system: (a) basic components; (b) forces in equilibrium

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