vehicle dynamics week 10c

Question:

The sprung parts of a passenger car weigh 11.12 kN (2500 Ib) and the unsprung parts weight 890 N (200 lb). The combined stiffness of the suspension springs is 45.53 kN/m (260 lb/in.) and that of the tires is 525.35 kN/m (3000 lb/in.) (use the mass and stiffness as is – no need to divide)

1. Determine the two natural frequencies of the bounce motions of the sprung and unsprung masses. (5+5 points)
2. Calculate the amplitudes of the sprung and unsprung parts if the car travels at a speed of 48 km/h (30 mph) over a road of a sinewave form with a wavelength of 9.15 m (30 ft) and an amplitude of 5 cm (2 in.) (10 points)

Answer:

Matlab code:

clear all

close all

clc

ms = 11120/9.81; % converting N to kg

mus = 890/9.81; % converting N to kg

ks = 45530; %N-m

kt = 525350;

zo=0.05

v=48/3.6

wl=9.15

ws=sqrt(((ks*kt)/(ks+kt))/ms)

wus=sqrt((ks+kt)/mus)

f=v/wl

w=2*pi*f

num_zs=ks*kt

den_zs=ms*mus*((w)^4)+ks*mus*((w)^2)+ms*((w)^2)*ks+ms*((w)^2)*kt+ks*kt

num_zus=ms*kt*((w)^2)+ks*kt

den_zus=ms*mus*((w)^4)+ks*mus*((w)^2)+ms*((w)^2)*ks+ms*((w)^2)*kt+ks*kt

zs=(num_zs/den_zs)*zo

zus=(num_zus/den_zus)*zo

steps:

-Inputs are declared

-Natural frequency of sprung mass is calculated using:ws=sqrt ((ks*kt)/(ks+kt)/ms)

-then Natural frequency of unsprung mass is calculated using:ws=sqrt ((ks+kt)/mus)

-then frequency of the bumb is calculated using f=v/l

-then omega is calculated using w=2*pi*freq

-then amplitude is calculated with c=0 using:

Numerator of z sprung =zs=ks*kt

Denominator of z sprung =ms*mus*((w)^4)+ks*mus*((w)^2)+ms*((w)^2)*ks+ms*((w)^2)*kt+ks*kt

Numerator of z us prung:

num_zus=ms*kt*((w)^2)+ks*kt

denemorator of z unsprung:

den_zus=ms*mus*((w)^4)+ks*mus*((w)^2)+ms*((w)^2)*ks+ms*((w)^2)*kt+ks*kt

-then to calculate z sprung and z unsprung the numerator and denemorator is devided over each other and then multiplied by the given z0

Results:

sprung mass natural frequency ws =6.0797 rad/s

unsprung mass natural frequency wus =79.3253 rad/s

bumb frequency w=9.15 rad/s

zs/z0=0.301

zus/z0=0.931

zs = 0.0151 m

zus =0.0466 m

files:

https://drive.google.com/file/d/1oePlrtXVOvpq_3WwJwD_V8yWBIQNjK43/view?usp=sharing