Prediction of Lateral-Vibration Responses of A Full Size Cantilever Beam by Using Those of Its Scale Models

The main objective of this article is to study and calculate lateral vibration responses of the cantilever beam by using a scale model and the associated scaling laws. Lateral vibration responses of a cantilever beam are analyzed theoretically and to validate results using a method of finite element to calibrate vibration response of a similar beam. We get the results and then we had compared both scale model and full-size cantilever beam model. Initially derive the solution of free response and steady-state response for the full and scaled model. Later, the scaling-laws for all the applicable parameters concerning the cantilever beam in the size of full and its scale beam of free vibration are get from the Euler’s equation of motion of the last two systems. Next, by dimensional analysis find the scaling factors for applicable dimensions and properties of required two systems. And in Finite element method introduce property matrices and equations of motion of cantilever beam system and also systematic procedure to get element property matrices of the beam is shown. In the end it is solved by Method of Eigen value problem with the help of Mat lab software. Lastly the impact of specimen dimensions on the similarity basis, natural frequencies of cantilever beam specimen is investigated.