Finite Element Analysis / Structural Analysis

In summary, to calculate the velocity of oscillation for a system of two bars connected to a common node, you can use the equations of motion and initial conditions to determine the constants A and B, and then use the equations x(t) and v(t) to find U(t) and V(t), respectively. The angular frequency of the oscillation can be calculated using the stiffness and mass of the system.
  • #1
pitBull7
1
0
Homework Statement
Finite Elements Analysis / Structural Analysis
Relevant Equations
NO
Hello engineer's community !

I got a problem. If i got a truss frame with 2 bars and an initial nodal displacement for the common node , then how can i calculate the velocity of the oscillation as function of time ? (the 2 bars have different length , same elasticity modulus , same density and different angle with the horizontal line and they are connected to a common node as i said
YMQm-1584216453565.jpg
)

I would be glad if you help me !
1584216749187.png

1) Supports are fixed , the bars can only rotate .

2)I don't have numerical values of the data , i try to solve it using variables and create a general formula

3)Yes , the connecting joint has an initial displacement . I don't have any other data about magnitude or direction , i only know that i have displaced the connecting joint and later i let it move freely ( from zero velocity) and an oscillation takes place ( on x , y axis) due to elasticity .

4)If "U" is the horizontal velocity and "V" the vertical velocity of the connecting joint then i want to find how these 2 velocities change during the oscillation/time . I want to find the formulas for U(t),V(t) (t=time) . But yes oscillation frequency is needed for these equations .

5)I consider only axial deformation , and the maximun degrees of freedom for each node should be 2 ( moving vertically , moving horizontally)
 
Physics news on Phys.org
  • #2
The velocity of the oscillation can be calculated using the equations of motion for a system of two bars connected to a common node. The equations of motion can be written as mx" + kx = 0where m is the mass of the system, x is the displacement of the node from its initial position and k is the stiffness of the system. The solution to this equation is given by x(t) = Acos(wt) + Bsin(wt)where A and B are constants determined by the initial conditions of the system and w is the angular frequency of the oscillation given by w = sqrt(k/m)The velocity of the oscillation can then be calculated as v(t) = -wAcos(wt) + wBsin(wt) The constants A and B can be determined from the initial displacement and velocity of the node. I hope this helps!
 

1. What is Finite Element Analysis (FEA) and how does it work?

Finite Element Analysis (FEA) is a computer-based numerical method used to solve complex engineering problems by dividing a structure into smaller, simpler parts called elements. These elements are connected at specific points called nodes, and the behavior of each element is described by mathematical equations. FEA works by using these equations to calculate the behavior of each element and then combining them to determine the overall behavior of the structure.

2. What is the difference between linear and nonlinear FEA?

Linear FEA assumes that the material properties and behavior of the structure are constant and do not change with applied loads. Nonlinear FEA takes into account changes in material properties and behavior under varying loads, making it more accurate for complex structures and materials.

3. What are the main applications of FEA in structural analysis?

FEA is commonly used in structural analysis to predict the behavior of structures under different loading conditions, such as stress and strain analysis, vibration analysis, and thermal analysis. It can also be used to optimize designs, evaluate failure points, and simulate real-world conditions.

4. What are the benefits of using FEA in structural analysis?

FEA offers several benefits, including the ability to analyze complex structures that would be difficult or impossible to analyze using traditional methods. It also allows for quick and efficient design iterations, reducing the time and cost of product development. FEA can also provide more accurate results compared to hand calculations or physical testing.

5. What are the limitations of FEA in structural analysis?

While FEA is a powerful tool, it does have some limitations. It requires a significant amount of computational resources and expertise to set up and run simulations. FEA also relies on accurate input data and assumptions, so the results may not be entirely accurate if these are not properly accounted for. Additionally, FEA is only as accurate as the underlying mathematical models and assumptions used, so it is important to validate the results with physical testing when possible.

Similar threads

Engineering Struggling with a Structural Analysis Problem?
    • Engineering and Comp Sci Homework Help
Replies
1
Views
863
Engineering Question about Truss Analysis (Statics)
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Engineering Current density calculation in anisotropic ferromagnetic film
    • Engineering and Comp Sci Homework Help
Replies
7
Views
726
The 8 Mode Shapes of a plane finite element
    • Mechanical Engineering
Replies
2
Views
851
B Incorporating boundary conditions in the Finite Element Method (FEM)
    • Differential Equations
Replies
4
Views
755
Hi I'm Jayvhie, Mechanical Engineer from PH
    • New Member Introductions
Replies
1
Views
56
Oblique soccer shot calculation task
    • Introductory Physics Homework Help
2
Replies
38
Views
1K
Random Vibration Fatigue Analysis
    • Mechanical Engineering
Replies
3
Views
210
B In uniform acceleration, mean velocity ##\bar v = \frac{v_0+v}{2}##?
    • Classical Physics
Replies
23
Views
1K
Studying Finite element analysis for Electromagnetism
    • STEM Academic Advising
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top