Matlab: transfer function determination

[serbring]

I have a 2 dof vibration system, I have determined the differential equation of the model, can I determine the trasfer function readily with matlab, without using manual algebra operation?
In other word, I have that differential equation system:

[m]x''+[c]x'+[k]x=[f]

where:
[m] mass matrix
[c] damping matrix
[k] stiffness matrix
[f] external forces matrix

through laplace transformation I obtain:

s^[m]x(s)+s[c]x(x)+[k]x(s)=[f]

where s is the laplace variable, how can I find [f]/[x]?
I'm searching a way for estimating readily the transfer function of mechanical system, it is a loss of time to perform the calculation every time

 

[serbring]

may anyone help me?

 

[ddarvil]

You've pretty much got the TF. Rearrange the laplace you've done above so you get f/x = tf (factorise the left side wrt to X). From there, you can use MATLAB to analyse the TF.
MATLAB tools(look in help): tf, bode, ltview.
The time required to manually calculate the TF is trivial for systems like this. You can use dsolve to get a symbolic solution to the ODE but it's not really necessary

 

[serbring]

You've pretty much got the TF. Rearrange the laplace you've done above so you get f/x = tf (factorise the left side wrt to X). From there, you can use MATLAB to analyse the TF.
MATLAB tools(look in help): tf, bode, ltview.
The time required to manually calculate the TF is trivial for systems like this. You can use dsolve to get a symbolic solution to the ODE but it's not really necessary

I know the tf, bode function, but how can I use them when the system has more than one dofs?

 

[blue_raver22]

Yes, you can use Matlab to determine the transfer function of a 2 dof vibration system without having to manually perform algebraic operations. Matlab has built-in functions and tools that can help you solve differential equations and obtain the transfer function of a system.

To find the transfer function, you can use the "tf" function in Matlab. This function takes in the coefficients of the differential equation (mass, damping, and stiffness matrices) and returns the transfer function in the form of a rational function.

For example, if your differential equation is:

[m]x''+[c]x'+[k]x=[f]

You can use the following code in Matlab to find the transfer function:

num = [f]; % coefficients of the numerator
den = [m c k]; % coefficients of the denominator
sys = tf(num, den); % returns the transfer function in the form of a rational function
disp(sys); % displays the transfer function

This way, you can obtain the transfer function without having to manually perform the calculations every time. You can also use other functions in Matlab such as "ss2tf" or "tfdata" to obtain the transfer function from a state-space representation of the system.

In summary, Matlab provides efficient tools and functions for solving differential equations and obtaining the transfer function of a system. This can save you time and effort in manually performing algebraic operations.