Modal Analysis using pre-stress from static nonlinear analysis

It is possible to solve for the modal behavior of a structure with non-linear material properties using pre-stress options in some finite element software. However, the specific capabilities of the software and the ability to use pre-stress options for non-linear material modal analysis will depend on the software package you are using.

In general, non-linear material properties are usually considered in static analyses, such as non-linear static, non-linear dynamic, or explicit dynamic analysis. These analyses allow you to consider the non-linear behavior of a material under a specific set of loading conditions. In contrast, modal analysis focuses on the natural frequencies and mode shapes of a structure and typically assumes linear material properties.

However, some advanced software can solve non-linear material model by using a linearized modal analysis with pre-stress. In this method, an initial pre-stress is applied to the structure, and modal analysis is performed on the deformed structure. This method can give a good approximation to the natural frequencies and mode shapes of the structure with non-linear material properties.

It is important to note that to use this method you need to have a good understanding of the material model, and you will also require a good initialization of pre-stress state which is not always an easy task. It is also worth noting that if you are using pre-stress, it can be applied in some various ways like applying to structure or applying to elements, it also depends on the software you are using and the type of pre-stress you want to apply.

Alternative Ways to Solve Modal Analysis with Non-Linear Material Properties

there are other ways to solve modal analysis of structures with non-linear material properties, here are a few examples:

1. Non-linear static analysis with a reduced-integration element: This method uses a reduced-integration element to model the non-linear behavior of the material, and then the eigenvalues and eigenvectors are extracted from the solution of the non-linear static analysis.
2. Harmonic balance method: This method is based on the assumption that the system’s response is a sum of harmonic functions with different frequencies, with the same amplitude and phase. In this method, a non-linear equation of motion is solved for each frequency of interest, and then a linear eigenvalue problem is solved on the result.
3. Direct integration method: This method is based on the direct integration of the equation of motion of the structure. Non-linearities are taken into account through the use of explicit time integration, and the system’s response is calculated for different frequency of interest, and then the modal properties are extracted from the time history.
4. Continuation methods: This method is based on solving the non-linear problem multiple times while varying certain parameters. One common example is solving a problem at different levels of pre-stress or loading to determine a response under different conditions.

It’s worth noting that the choice of method will depend on the specific material model, the structure, and the level of accuracy required. Non-linear material models are often more computationally intensive to solve and may require more memory and computational resources. Also, it’s worth noting that, for some non-linearities, the modal properties of the system may not be constant and may vary with loading conditions.

The most common way to solve modal analysis of structures with non-linear material properties is using a linearized modal analysis with pre-stress. This method is widely used in practice as it can provide good approximations to the natural frequencies and mode shapes of the structure with non-linear material properties, even with a relatively simple model, and it’s relatively easy to implement and interpret the results. It’s also widely available in commercial and open-source finite element software packages.

The other methods I mentioned, such as the non-linear static analysis with a reduced-integration element, harmonic balance method, direct integration method, and continuation methods, are more advanced and typically require a more sophisticated mathematical formulation and more computational resources. They are not as widely available in commercial software, and their usage may depend on the specific application and the expertise of the user.

It is important to note that these methods are not mutually exclusive and they can be used in combination or in a complementary way to optimize the results. A good practice is to try different methods and compare the results, considering the trade-offs between accuracy, computational cost, and the complexity of the problem.