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Car-body resting on four coil-springs


The model is a car-body resting on four coil springs and four viscous dampers. The dampers have zero length why their symbols look like small green circles.


This example consists of a car-body named car_1 supported by four springs kmcb11r, kmcb11l, kmcb12r and kmcb12l and four dampers cmcb11r, cmcb11l, cmcb12r and cmcb12l.
The following data are valid:

mc= 50e3 [kg] # Weight of car-body
kzcb= 500e3 [N/m] # Vertical stiffness of coil-springs
czcb= 30e3 [Ns/m] # Damping coefficient in vertical dampers

Eigenfrequency of vertical bounce mode can be calculated as:

Relative damping for the vertical bounce mode can be calculated as:

In current example the vertical bounce mode was found to have an eigenfrequency of 1.01 [Hz] with a relative damping of 19.0 %.

Download the example

Make quasistatic analysis

Make a quasi-static calculation by running file runf/car_body_quasi.quasif in program QUASI.
The coil-springs have only a stiffness in vertical direction and no pre-stress force. Earth gravity makes the car-body to fall until the coil-springs responds with the weight of the car-body. Program QUASI will find the position of the car-body where the forces in all coil-springs equals the weight of the car-body.
In command accel local_all the user defines the magnitude of earth gravity. As default it is set equal to 9.81[m/s2].

On standard output program quasi writes the vertical equilibrium position and the forces in all coil-springs:

Func print06_quasi      kmcb11r.F2z              =  1.22625E+05
Func print06_quasi      kmcb11l.F2z              =  1.22625E+05
Func print06_quasi      kmcb12r.F2z              =  1.22625E+05
Func print06_quasi      kmcb12l.F2z              =  1.22625E+05
Func print06_quasi      car_1.z                  =  2.45250E-01

The weight of the car-body is 50e3*9.81[N]. Distributed on four springs, which gives a vertical load of 122625[N] per spring.

The spring stiffnesses are 500e3[N/m] per spring, which leads to a vertical compression of 0.24525[m] for all springs.

Theory program QUASI

Make time-domain simulation

Make a time-domain simulation by running file runf/car_body_tsim.tsimf in program TSIM.
In runf/car_body_tsim.tsimf the car-body is excited by a sinusoidal motion of the ground.

Make modal analysis

Make a modal analysis of the car-body by running file runf/car_body_modal.modalf in program MODAL. In runf/car_body_modal.modalf the coil-springs are modeled with coupling coupl k3_l_preZ which means that the vertical pre-stress forces are calculated automatically, therefore in this case there is need to make an initial calculation with program QUASI

Theory MODAL

Make frequency-responce analysis

Make a frequency responce analysis by running file runf/car_body_fresp.frespf in program FRESP. In runf/car_body_fresp.frespf the car-body is excited by a white noise spectra from ground.

Theory FRESP