# Summary

In this course, we discussed about the Mode Superposition method used to solve Transient Analysis problems, as well as the key factors that influence the accuracy of the solution. Let us summarize the key takeaways from each lesson.

Introduction to Mode Superposition Transient Analysis – Lesson 1

• Transient Analysis is used to study the change in a system's behavior over a specific time period, by considering the temporal effects of inertia and damping. Transient Analysis can be solved using two methods, the Full Solution Method, and the Mode Superposition Method.
• The Full Solution method solves the coupled equations of motion directly using full mass, stiffness, and damping matrices. Since it solves the coupled equations directly with no assumptions, the solution is relatively expensive for each time step.
• The Mode Superposition Method transforms the governing equation of motion into an alternate form using modal coordinates and a linear combination of mode shapes. It is more efficient than the Full Solution method since it converts coupled equation of motion into modal form.
• But as the MSUP method is linear, it does not permit inclusion of nonlinearities introduced by contact, plasticity, and large deflection.
• Modal Analysis is a prerequisite for the MSUP method, and it should be connected to the Transient Analysis.

Predicting Transient Vibrations in Ansys Mechanical – Lesson 2

• When a system is excited by a sudden, non-periodic excitation, transient vibrations will usually arise.
• The mode-superposition method is an efficient way to predict a structure's response to these types of loadings.
• It can be used to answer questions such as, “What will be the response's peak amplitude?”, “When will it occur?”, as well as “How long does it take for the response to decay?”
• MSUP method allows most load types, and as the solution is conducted in generalized coordinates displacement and acceleration loads are valid only when only when applied as base excitation.
• In the MSUP Method, inputs are excitations consisting of loads that are a function of time and they can be defined as a) constant over time b) based upon closed form mathematical functions c) can vary according to values input in tabular data.

Obtaining Accurate Results with MSUP Transient – Lesson 3

• MSUP Transient is a computationally efficient solution method, but in order to obtain accurate results we should be aware of four key considerations.
• The first factor which influences the accuracy of Transient solution is the mesh density. If we use a coarse mesh, then we cannot accurately capture the higher frequencies of the structure. Thus, higher the mesh density, more accurate is the Transient solution.
• The second factor to consider is the time step size used to solve the Transient Analysis; it should be small enough to accurately capture the transient response of the system. When a large time step size is used, peak responses can be missed, and the higher order frequencies in the vibration won’t be resolved.
• But using fine mesh density and small time step size come at the cost of computational expense, which is why it is necessary to strike a balance between numerical accuracy and computational expense.
• The third key consideration for numerical accuracy is the number of modes included in the Modal solution. A sufficient number of modes should be included in the Modal solution to avoid mode truncation error.
• But in some cases, despite including a high number of modes, it can still be difficult to capture a localized response. In such cases, Residual vectors can be used to capture the accurate response, despite including fewer modes in the Modal solution.