Modal analysis is the study of the dynamic properties of linear structures, based on structural testing or finite element analysis-based simulation. These dynamic properties include the resonance frequencies (also called “natural frequencies” or “eigenfrequencies”), and the structural modes (or “eigenmodes”). The dynamic properties are dependent on the mass, stiffness and damping distribution on the structure, and determine the structural vibration behavior when exposed to operational loads. Every deformation of a linear structural system can be expressed as a linear combination of the structural modes, which form an orthonormal vector base.
Modal testing combines data acquisition with further analysis. In an industrial application, the complete process is often referred to as modal testing and analysis, or experimental modal analysis (EMA).
During the data acquisition phase, the structural response is measured on well-defined locations, while the structure is excited by loads with known frequency content. Many excitation methods and setups exist, dependent on the complexity of the structure, but most common are hammer impact excitation and shaker excitation. The resonance frequencies will appear as peaks in vibration response functions on response locations.
During the modal analysis phase, the excitation frequency spectra and the response frequency spectra are used to calculate frequency response functions (FRFs). Those FRFs can theoretically be expressed as a linear combination of modal contributors. As such, they can be used to determine modal parameters using various curve fitting methodologies.
Modal analysis is also a crucial step in structural dynamics simulation. A structural finite element (FE) system consists of a mass, stiffness and damping matrix, and a force vector. Eigenmodes and eigenfrequencies form the fundamental solution of the system, when the force vector is set to zero.
In many cases, for initial analysis, the damping matrix is denied because of the complex nature of the damping property and the extra computational effort it requires. In that case, modal frequencies can be calculated as the square root of the ratio of modal stiffness to modal mass, which can be found on the diagonalized mass and stiffness matrices. These modal frequencies are real numbers, and the corresponding modes are real vectors (also called “real modes” or “normal modes”).
Damping can be accounted for in several ways. In the easiest form, it can be assigned as a factor to individual normal modes, or the damping matrix can be simplified to be proportional to the stiffness matrix. In those cases, the calculated modes will remain normal modes. But in case the damping matrix is fully populated by varying structural damping, the calculation becomes a lot more complicated and leads to complex modes.
Results of modal testing and analysis are used in various simulation and testing applications, including vibration response calculations, root cause analysis of vibration problems and damage detection, but also for adding flexibility to multibody analysis, and to speed up durability and vibro-acoustic simulations. Modal-based calculations are very effective and allow efficient evaluation of structural changes to responses of any kind. Comparing FE modes and test modes in modal correlation analysis can provide a quantitative insight in the quality of the FE model, and can be used to gradually improve an FE model based on test results in model updating.
Benefits of Modal Analysis
Modal analysis performed through either structural testing or finite element analysis-based simulation helps you:
- Understand how a structure vibrates
- Correlate and update simulation models
- Speed up structural, vibro-acoustic and durability calculations
- Include flexibility in multibody simulation models
Modal Analysis Software
Here are examples of software applications that conduct modal analysis, or use modal analysis results to bring efficiency to solvers:
LMS Test.Lab is a complete, integrated solution for test-based engineering, combining high-speed multi-channel data acquisition with a full suite of integrated analysis tools, including many modal parameter estimation methodologies. Designed to make testing more efficient, LMS Test.Lab increases productivity and delivers more reliable results.
LMS Virtual.Lab is an integrated suite of FE and multi-body modeling software which simulates real-life performance of mechatronic systems. It allows you to quickly build complex models and optimize for structural integrity, acoustics, vibration, system dynamics and durability, as well as the correlation between simulation and test models.
LMS Samtech Samcef is a FE solver suite used to simulate critical performance engineering attributes for mechanical systems. It is designed to fulfill precise requirements of applications such as wind turbine development, rotor dynamics, structural and thermal analyses, and composites.
NX Nastran is a finite element solver that analyzes stress, vibration, structural failure/durability, heat transfer, noise/acoustics and flutter/aeroelasticity.
NX CAE is a modern simulation environment that enables engineering teams to reduce modeling time, shorten design-analysis iterations and improve CAE productivity. NX CAE enables engineers to quickly pre- and postprocess FE models for modal analysis, using Siemens PLM Software’s NX Nastran or LMS Samtech Samcef solvers, or popular third-party solvers.
Femap is a CAD and solver independent pre- and postprocessor for FEA, and can be used to build and setup complex engineering models for analysis, as well as results investigation post-analysis.