Free vibration in 2DOF spring mass systems

In summary, free vibration in two-degree-of-freedom (2DOF) spring-mass systems involves the analysis of the system's natural frequencies and mode shapes. The behavior of such systems can be described using equations of motion derived from Newton's second law or Lagrange's equations. The system's configuration, characterized by the arrangement of springs and masses, influences the coupling between the degrees of freedom. The eigenvalue problem that arises from the system's characteristic equation reveals the natural frequencies, while the corresponding eigenvectors indicate the mode shapes. Understanding these dynamics is crucial for applications in engineering and design, particularly in ensuring stability and resilience in structures subjected to dynamic loads.
  • #1
M2H37
1
0
Homework Statement
Identify the experimental value of the natural frequencies and mode shapes using the graphs obtained from the experimental data
Relevant Equations
Unsure
I am completely new to this subject and I am trying to find out how I read data off a displacement vs time graph to find the natural frequencies and mode shapes. Lecturer hasn't provided any materials on graphs, just looking for some help and where to go so I can understand it. Thank you
 
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  • #2
Hello @M2H37 ,
:welcome: ##\qquad ##!​

You've come to the right place for help !
For good assistance, it's best to ask answerable questions: we need you to point us in the direction of assistance that is useful for you. The more specific, the better.

In this case: find a typical exercise with a "displacement vs time graph" and point out what it is you don't undestand.

You're new to the subject, so I don't expect a highbrow mathematical approach is appropriate at this point.

##\ ##
 
  • #3
The statement does not mention anything about displacement versus time graphs. Why do yo think that such graphs are relevant to the question? Is the assignment statement as given in the OP or there is more to it?
 

FAQ: Free vibration in 2DOF spring mass systems

What is a 2DOF spring-mass system?

A 2DOF (two degrees of freedom) spring-mass system consists of two masses connected by springs and possibly dampers, allowing movement in two independent directions. These systems can model various physical scenarios where two masses interact with each other and external forces.

How do you derive the equations of motion for a 2DOF spring-mass system?

To derive the equations of motion, you apply Newton's second law to each mass. Identify the forces acting on each mass, including spring forces and damping forces, and set up the differential equations that describe the system. Typically, this results in a set of coupled second-order differential equations.

What are the natural frequencies and mode shapes of a 2DOF system?

Natural frequencies are the frequencies at which the system tends to oscillate in the absence of external forces or damping. Mode shapes describe the relative motion of the masses at these frequencies. These can be found by solving the characteristic equation derived from the system's equations of motion, resulting in eigenvalues (natural frequencies) and eigenvectors (mode shapes).

How do you solve for the response of a 2DOF system to initial conditions?

To solve for the response, you can use the system's natural frequencies and mode shapes. Express the initial conditions in terms of the system's modal coordinates, then solve the resulting uncoupled differential equations for these coordinates. Finally, transform back to the physical coordinates to get the time response of the system.

What is meant by "free vibration" in the context of a 2DOF system?

Free vibration refers to the motion of the system when it is displaced from its equilibrium position and then allowed to vibrate without any external forces acting on it. The system's response is solely due to its initial conditions and inherent properties like mass and stiffness.

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