Simscape modeling of thin bar vibration
バージョン 1.0.1 (1.74 MB) 作成者:
Stephen Thompson
The Simscape Foundation Mechanical domain has components that are sufficient to model the transverse vibration of thin bars.
Much of this work was done by Carter J. Childs as part of his PhD research work at Penn State University.
The Simscape Foundation Mechanical domain has components that are sufficient to model the transverse vibration of thin bars. The theory behind these components is in the paper by Childs and Thompson that is included in this submission. Figure below is an example of the Simscape components described in the theory. The figure shows a bar with three segments. Each segment is a bar-spring element surrounded in cascade by mass elements. Material parameters for these parts are described in the referenced paper. Each bar-apring element has two Simscape conserving ports at each end. The upper port at each end in the figure is a Translational Mechanical domain port that models displacement normal to the top surface of the bar. The lower port at each end is a Rotational Mechanical domain part that models the rotation due to bending of the bar.The bar-aprings are connected in cascade so that the vertical displacement and rotation angle are both continuous across the boundary. An external driving force could be added at any of the mass connections. ![Segmented bar with three segments](data:image/png;base64,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The file bar10_example.slx is a 10-segment bar as described above. In addition to the bar, this model includes a driving force, and a set of measurement components that allow the bar motion to be recorded. The driving force is a sinusoidal force applied to the second mass from the clamped left end. Measurement components are included to record the position of each of the masses along the bar.
The first calculation performed is a frequency domain calculation of the bar displacement to obtain the mechanical resonance frequencies of the clamped-free bar. The chosen example is an aluminum bar that is 1 cm wide, 5 mm wide and 50 cm total length. Figure belowshows the frequency response of the magnitude of the driving point displacement. The first three resonance frequencies are calculates as 16.3 Hz, 102 Hz and 289 Hz, which match the analytically calculated frequencies to three significant figures.
The next calculation is to drive the bar at one of its resonance frequencies and calculate the displacement of the bar. The result for the first three modes is shown in the Figure below Note that the Simscape model calculates the displacement only at the nodes in the model. The figure uses straight line interpolation between the nodes, which is clear at least in the second and third mode shapes. A better interpolation function would be a curve that matches the displacement and slope at the two ends of the segment. That upgrade will be made at a future time.
The included paper describes the means to upgrade the model to that of the Timoshenko bar, and to include internal longitudinal stress. The first would provide a more accurate model and one that can be expanded to a two dimensional thin plate. The second would allow an especially thin bar to model a thin tensioned wire like that on a guitar or piano, and include a small amount flexural rigidity. All of those are features and models are anticipated in the future.
引用
Stephen Thompson (2024). Simscape modeling of thin bar vibration (https://www.mathworks.com/matlabcentral/fileexchange/122982-simscape-modeling-of-thin-bar-vibration), MATLAB Central File Exchange. 取得済み .
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