MATLAB code for ADOF Beam model

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Damage can be defined in the context of structural health monitoring as a change in the properties of a structure, such as mass and/or stiffness, which would be analogous to the development of fatigue cracking, corrosion, joints loosening, or other similar mechanisms. As a result of these changes, the dynamic characteristics (i.e. mode shapes, frequencies, and damping) will be impacted and, consequently, the dynamic response of the system will change. Structural health monitoring methods make use of this change in the system dynamics to compare two states of the structure, before and after damage occurs, to attempt to identify the presence, location, and severity of the damage. The  sensitivity of dynamic characteristics to damage is critical – characteristics with a high sensitivity to damage and a low sensitivity to noise or other variable conditions are ideal.

Preventative inspection and testing is a common structural health monitoring approach to identify progression of fatigue damage prior to structural failure. For many structures, damage is typically not externally evident. Traditional non-destructive inspection techniques include acoustic and ultrasonic methods, eddy current methods, radiography, and others , all of which require access to the structure and either prior knowledge of damage locations or detailed, time consuming inspection of all potential failure points of the structure. In many cases, such inspections are time consuming and costly , and do not provide opportunities for ongoing structural health monitoring.

Dynamic testing methods have been investigated for application to structural health monitoring, allowing more efficient testing and monitoring of structures to identify and localize damage. Previous work demonstrated damage characterization capabilities based on modal characterization methods. These methods evaluate changes in experimentally measured mode shapes, frequencies, and damping characteristics of a structure to identify damage, localize the damage, and in some methods, predict the magnitude of the damage. 

Methods of particular interest focus oh strain energy based approaches which evaluate differences in modal strain energy distributions of the damaged and undamaged structures. These methods, while showing promise in a variety of simplified cases, are limited by the constraints imposed by practical application in an experimental setting. 

Measurements are generally restricted to a limited number of locations, modal characteristics provide a limited set of information from which to draw conclusions, and variability in measurements and environmental conditions over time affect measured modal characteristics used in the assessment.


The MATLAB finite element model is initially developed at an equivalent NDOF to the FEMAP model, providing the same resolution along the length of the beam with 0.5-inch elements. This model is then reduced using SEREP to a set of ADOF corresponding to the limited measurement locations on the physical beam structure. The reduced mass and stiffness matrices are then projected into modal space using the analytical mode shapes and the transient response of the structure is calculated for each mode. The linear summation of the individual modal responses is then projected back to physical space to provide the analytical structural response. An example of the MATLAB scripts for the finite element model and response simulation are included in this code. 



This code has a document (196 pages) which describe the algorithm in detail.



This project provides an example of the codes which generate the ADOF MATLAB beam models mass and stiffness matrices which are used to calculate the ADOF system response. The main MATLAB code and all additional function codes are included in this project.

This project contains many MATLAB code with following tasks :

MATLAB code generates the ADOF mass and stiffness matrices of the undamaged beam.

MATLAB code generates the ADOF mass and stiffness matrices of the damaged beam.

MATLAB code assembles individual mass and stiffness elements into system mass and stiffness matrices.

MATLAB code conducts an eigensolution on a system given by a mass and stiffness matrix, calculating mode shapes and frequencies.

MATLAB code generates individual stiffness elements based on provided material and geometric properties.

MATLAB code generates individual mass elements based on provided material and geometric properties.

MATLAB code converts a given node number in the beam model to the corresponding DOF.

MATLAB code converts a given damage location in the ADOF beam model to the corresponding DOF.

MATLAB code is used for System Equivalent Model Reduction Expansion Process (SEREP) model reduction of a set of system mass and stiffness matrices.

MATLAB code calculates the transient response of a given set of mass and stiffness matrices given prescribed forcing and initial conditions. This code is the primary response calculation code used for this project.

MATLAB code applies the Analytical Model Improvements (AMI) technique to a given mass and stiffness matrix and target mode shapes and frequencies. The code updates the matrices such that the eigensolution of the updated matrices results in frequencies and mode shapes matching the target frequencies and mode shapes.

MATLAB code is a subfunction which is utilized calculate the transient response of the beam model. This code is adapted from previous work, which evaluated the nonlinear contact of a beam with a fixed surface. A large gap is imposed between the beam and the surface to prevent contact.

MATLAB code is a subfunction and is utilized calculate the transient response of the beam model using a Newmark solution.

1 review for MATLAB code for ADOF Beam model

  1. Maxim

    A fantastic project! You are obviously very experienced.

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