Linear Analysis of Cantilever Beam using MATLAB

Introduction

MATLABSolutions demonstrate In this particular task, This example illustrates how to develop a structural model of a beam and determine its time and frequency response when subjected to an impulse force. In this scenario, we consider a steel cantilever beam with a point load applied at its tip. The Partial Differential Equation Toolbox™ is required to build the structural model.

The steel beam is deformed by applying a 100 N external load at its tip and then releasing it. Since no additional loading is applied, the tip's displacement oscillates with an amplitude equal to the initial displacement caused by the applied force. The process involves three steps:

Construct a structural model of the beam.

Linearize the structural model to obtain a sparse linear model of the beam.

Analyze the time and frequency response of the linearized model.

Structural Model of Beam

Using Partial Differential Equation Toolbox, build a structural model and compute the impulse response. For an example of modeling a cantilever beam, see Dynamics of Damped Cantilever Beam (Partial Differential Equation Toolbox).

First construct the beam and specify the Young's modulus, Poisson's ratio, and mass density of steel. Specify the tip of the beam using the addVertex function.