Approximate study of the free vibrations of a cantilever anisotropic plate carrying a concentrated mass

• Published in: Journal of sound and vibration Vol. 302; no. 3; pp. 621 - 628
• Main Authors: Ciancio, P.M., Rossit, C.A., Laura, P.A.A.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 08.05.2007; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Free vibration; Epoxy resin; Anisotropic material; Function approximation; Modeling; Natural frequency; Boron; Added mass; Cantilever plate; Rectangular plate; Ritz method; Principal stress; Structural analysis
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2006.11.027

This study is concerned with the vibration analysis of a cantilevered rectangular anisotropic plate when a concentrated mass is rigidly attached to its center point. Based on the classical theory of anisotropic plates, the Ritz method is employed to perform the analysis. The deflection of the plate is approximated by a set of beam functions in each principal coordinate direction. The influence of the mass magnitude on the natural frequencies and modal shapes of vibration is studied for a boron-epoxy plate and also in the case of a generic anisotropic material. The classical Ritz method with beam functions as the spatial approximation proved to be a suitable procedure to solve a problem of this analytical complexity.