How to solve 3DOFs using ECP system?

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It may be helpful to select the unknowns that are most relevant to the problem at hand, such as the masses and stiffnesses, to focus on when solving the equations. In summary, the equations of motion for a 3DOF system can be obtained and solved using various techniques to find the unknowns and calculate the amplitudes of vibrations at different frequencies.
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equations of motions for 3DOFs obtained.
but how do i solve for e 6 unknows: m1 m2 m3 k1 k2 k3 using the ECP system?

Equations formulated as below:


[A] { m1 }
{ m2 }
{ m3 } = [F]
{ k1 }
{ k2 }
{ k3 }

where [A] is a 6 by 9 matrix: first 3 rows at freq w1, next 3 rows at w2, last 3 rows at w3
[F] (1 by 9 matrix) : is the applied force for each sinosindual excitation under 3 diff frequencies.

Natural freq of this 3DOFs was obtained and excited with sinosindual by input-ing at each of these 3 natural frequency (hence able to find amplitude of these vibrations, but so many amplitudes, which 1 to select?). And how should I go about solving the 6 unknowns?
Can anyone help me?
Thanks.
 
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The solution process is the same for any system of equations with unknowns. You can solve this system of equations using a variety of techniques, such as Gaussian elimination, Cramer's rule, or matrix inversion. After you have solved the system of equations for the 6 unknowns, you can use the solution to calculate the amplitudes of the vibrations at each of the 3 natural frequencies.
 

1. What is a 3DOF system?

A 3DOF (degree of freedom) system is a mechanical or structural system that has three independent variables or parameters that determine its motion or behavior. In other words, it is a system that can move or rotate in three different directions.

2. How does an ECP system work?

ECP (electrochemical polishing) is a process that uses an electrical current to remove material from a metal surface, resulting in a smooth and polished finish. In the context of solving 3DOF systems, an ECP system is used to selectively remove material from specific areas of a structure in order to balance or control its motion.

3. What are the benefits of using an ECP system for solving 3DOF systems?

Using an ECP system allows for precise and controlled removal of material, which can help to optimize the behavior and performance of a 3DOF system. It also offers a non-intrusive and reversible method of adjusting the structure, making it a valuable tool for experimental research and testing.

4. Are there any limitations to using an ECP system for 3DOF solutions?

While ECP is a powerful method for solving 3DOF systems, it does have some limitations. It is most effective for structures made of conductive materials, and the size and complexity of the structure can also impact the success of the solution. Additionally, the process may be time-consuming and require specialized equipment.

5. How can I determine if an ECP system is the best solution for my 3DOF problem?

The decision to use an ECP system for solving 3DOF systems should be based on the specific needs and goals of your project. It is important to evaluate the feasibility, cost, and potential benefits of using this method compared to other techniques. Consulting with an expert in the field can also help guide this decision.

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