July 4, 2023 at 7:18 amYohan AhnSubscriber
Hello, I'm leaving a post because I have a question while solving a simple cantliever beam problem. The problem is that the natural frequency calculated at Ansys is less than the theoretical value.
I learned Euler's beam theory, and I was able to get a characteristic equation of a beam that was fixed at one end and free at the other.
< cos(beta*L)*cosh(beta*L)=-1 >
Calculated using the Newton-Raphson method, the value of beta*L was obtained as follows.
< beta1*L=1.8751 >, < beta2*L=4.6941 >, < beta3*L=7.8547575 > ....
When the following properties are applied, the natural frequency value is calculated as follows.
< Properties, Structural Steel: Young's modulus of 200 GPa and density of 7850 kg/m^3
Cross-Section: Rectangular, Length: 0.3m, Wide: 0.03m and Thickness: 0.005m >
Natural frequencies: <45.2987>, <283.8846>, <794.8821>, ....
Ansys model results using beam4 (Number of elements: 40)
Natural frequecies: <45.296>, <283.78>, <794.17>, ...I learned in class that the exact solution at the natural frequency is always the same or less than the approximation. Ansys calculates using approximate solutions, so it must be less than exact solution, so I wonder why this is the result.Are there any additional tools that are reflected on the Ansys? This difference is confirmed that the error increases as the thickness of the beam increases, and the above result is a small difference.cf) Additionally, I wonder if Ansys uses Timoshenko Beam theory for the basic analysis setting of beam modeling.
July 4, 2023 at 9:38 amNanda VerallaAnsys Employee
Yes, you are correct. Both beam elements BEAM188 & BEAM189 elements are based on Timoshenko beam theory which includes shear-deformation effects. The elements can account for unrestrained warping and restrained warping of cross-sections.
The amount of error generally depends on approximations we make in our model. Can you check with both beam elements and check what’s the difference in error. The amount of error you are having is acceptable and doesn’t need to be worried about.
For more information on beam elements, kindly refer to below links:
July 7, 2023 at 7:43 amYohan AhnSubscriber
Thank you, Nanda, for your quick and kind reply.
Currently, the link you attached with my academy license is not accessible, but I checked the information about BEAM4 and BEAM188 you wanted to talk about using Ansys Help. As you answered, very small errors may occur in numerical analysis, etc., and I think it is within an acceptable range.
Lastly, can you check the command using beam 4 that I used in the above problem? The picture below is the command used for the above problem.
Thank you! :)
- You must be logged in to reply to this topic.
Boost Ansys Fluent Simulations with AWS
Computational Fluid Dynamics (CFD) helps engineers design products in which the flow of fluid components is a significant challenge. These different use cases often require large complex models to solve on a traditional workstation. Click here to join this event to learn how to leverage Ansys Fluids on the cloud, thanks to Ansys Gateway powered by AWS.
Earth Rescue – An Ansys Online Series
The climate crisis is here. But so is the human ingenuity to fight it. Earth Rescue reveals what visionary companies are doing today to engineer radical new ideas in the fight against climate change. Click here to watch the first episode.
Subscribe to the Ansys Blog to get great new content about the power of simulation delivered right to your email on a weekly basis. With content from Ansys experts, partners and customers you will learn about product development advances, thought leadership and trends and tips to better use Ansys tools. Sign up here.
- Solver Pivot Warning in Beam Element Model
- Saving & sharing of Working project files in .wbpz format
- Understanding Force Convergence Solution Output
- User manual
- An Unknown error occurred during solution. Check the Solver Output…..
- What is the difference between bonded contact region and fixed joint
- The solver engine was unable to converge on a solution for the nonlinear problem as constrained.
- whether have the difference between using contact and target bodies
- Defining rigid body and contact
- Colors and Mesh Display
© 2023 Copyright ANSYS, Inc. All rights reserved.