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Car-body resting on four coil-springs

• Introduction
• Download the example
• Make quasistatic analysis
• Make time-domain simulation
• Make modal analysis
• Make frequency-responce analysis

Introduction

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:

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

• Download the tar-file intro_tutor_2_car-body.tgz
• List the contents of the tar-file with "tar tvfkz intro_tutor_2_car-body.tgz"
• Extract the contents of the tar-file with "tar xvfkz intro_tutor_2_car-body.tgz"

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].

• Double-click file runf/car_body_quasi.quasif and select open->run with the right mouse button.
• As output the following files will be produced:

  id/car_body_quasi.id	MPdat-file for plotting in MPLOT
  gp/car_body_quasi.gp	GPdat-file for animation in GPLOT

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.

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.

• Double-click file runf/car_body_tsim.tsimf and select open->run with the right mouse button.
• As output the following files will be produced:

  id/car_body_tsim.id	MPdat-file for plotting in MPLOT
  gp/car_body_tsim.gp	GPdat-file for animation in GPLOT

• Animate the results in postprocessor GPLOT
  • Double-click file runf/car_body_tsim.tsimf in the file text area.
  • Press the Gplot–pushbutton
  • Open file gp/car_body_tsim.gp by selecting File->read_GPdat in the pulldown menu bar
  • Select View->show_1_diag from the pulldown menu bar and set the deformation scale to 100 approx.
  • Start the animation by pressing the Fwd–pushbutton.
  • Close the GPLOT window
• Show the results in postprocessor MPLOT
  • Double-click file mplotf/tsim.mplotf in the file text area
  • Select open->run with the right mouse button
  • In the pop-up menu select ident car_body_tsim
  • Change page with the radio buttons at the top
  • Close the MPLOT window and the associated terminal window in the background
  
  Theory program TSIM

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

• Double-click file runf/car_body_modal.modalf and select open->run with the right mouse button.
• As output the following files will be produced:

  id/car_body_modal.id	MPdat-file for plotting in MPLOT
  gp/car_body_modal.gp	GPdat-file for animation in GPLOT
  calcmod/car_body_modal.mode	mode-file containing all eigenvalues
  calcmod/car_body_modal.modf	modf-file containing all eigen forms
  calcmod/car_body_modal.modjac	modjac-file for linear analysis

• Animate the results in postprocessor GPLOT
  • Double-click file runf/car_body_modal.modalf in the file text area.
  • Press the Gplot–pushbutton
  • Open file gp/car_body_modal.gp by selecting File->read_GPdat in the pulldown menu bar
  • Start the animation by pressing the Fwd–pushbutton.
  • Change eigen mode by pressing the Next or Prev –pushbutton.
  • Close the GPLOT window

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.

• Double-click file runf/car_body_fresp.frespf and select open->run with the right mouse button.
• As output the following files will be produced:

  id/car_body_fresp.id	MPdat-file for plotting in MPLOT
  calcmod/car_body_modal.modjac	modjac-file for linear analysis

• Show the results in postprocessor MPLOT
  • Double-click file mplotf/fresp.mplotf in the file text area
  • Select open->run with the right mouse button
  • In the pop-up menu select ident car_body_fresp
  • Page number one shows the following curves:

    ground.z	Real part of the vertical position, body ground
    ground.vz	Imaginary part of the vertical position, body ground
    car_1.z	Real part of the vertical position, body car_1
    car_1.vz	Imaginary part of the vertical position, body car_1

  • Change page with the radio buttons at the top
  • Page number two shows the following curves:

    ground.bz	Absolute value of the vertical position, body ground
    ground.pz	Phase angle of the vertical position, body ground
    car_1.bz	Absolute value of the vertical position, body car_1
    car_1.pz	Phase angle of the vertical position, body car_1

• Close the MPLOT window and the associated terminal window in the background