Numerical and Experimental Studies on Local and Global Instability of Slender System Subjected to a Specific Load

K. Sokół Częstochowa University of Technology, J.H. Dąbrowskiego 73, 42-201 Częstochowa, Poland

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The paper contains the results of theoretical, numerical, as well as experimental investigations on local and global instability of slender system subjected to a specific load. The phenomenon of local and global instability can be found when nonlinear slender systems are studied. The mentioned instability regions are defined during a comparative analysis on the bifurcation load of a geometrically nonlinear structure to a critical load of a corresponding linear one (generally, the linear system is a simplification of a nonlinear one). In the numerical simulation one focuses on an influence of the parameters of the system on vibration frequency and loading capacity on the basis of which the instability regions are plotted. The investigated structure has a defect in the form of a reduced cross-sectional area. The presence of the notch affects both investigated parameters. The studied slender system is loaded by the specific load that leads to the divergence-pseudoflutter shape of the characteristic curve. The differential equations of motion and natural boundary conditions are obtained with the use of the Hamilton principle. The problem is solved with the small parameter method. The main goal of this research is to obtain the global and local instability regions and to decide when to use nonlinear system or to substitute is with the corresponding linear one. Finally, the numerical calculations are compared to the experimental tests.

DOI:10.12693/APhysPolA.138.207 topics: vibrations, stability, piezoceramic, vibration control