Transient Response of a Spring-mass System

Sanjeet Kumar Singh

A system containing two masses, m1 and m2, and two springs of stiffness k1 and k2. Determine the displacement response of the system for the load history

E = 2e11 Paγ = 0.3ρ = 0.25 kg/m3k2 = 6 N/mk1 = 16 N/mm2 = 2 kgm1 = 2kg

F(t)

F(t)

t

Fo=50N

Calculate the response x1 , m (@ t = 1.3s) X 2, m (@ t = 1.3s) X1, m (@ t = 2.4s) X2, m (@ t = 2.4s)

td=1.8 sec

2 Blocks = 2m x 2m x 2m

Length of L1 spring = 6mLength of L2 spring = 7m

Fixed End

The step drop is modeled as F0 = 50 N @ t = 1.8 sec and F0 = 0 N @ t = 1.80001 sec.

Results Target ANSYS Workbench

X1, m (@ t = 1.3s)

14.48 14.17

X2, m (@ t = 1.3s)

3.99 3.8297

X1, m (@ t = 2.4s)

18.32 18.68

X2, m (@ t = 2.4s)

6.14 6.2584

Results Comparison