Selection of Support System to Provide Vibration Frequency and Stability of Beam Structure - Alexander P. Lyapin; Ilya V. Kudryavtsev; Sergey G. Dokshanin; Andrey V. Kolotov; Alexander E. Mityaev (Modelling)
The current engineering theories on bending vibrations and the stability of beam structures are based on solving eigenvalue problems through similarly formulated differential equations. Solving the eigenvalue problem for engineering calculations is particularly laborious, especially for non-classical supports, where factors like the stiffness of supports, axial forces, or temperature must be considered. In this case, the solution can be obtained only by numerical methods using specially created programs, which makes it difficult to select supports for a given planar beam structure in engineering practice. This work utilizes established solutions from eigenvalue problems in the theory of vibrations and stability of beams, incorporating factors such as axial forces, temperature, and support stiffness. This combined solution is applicable to beam structures of any type and cross-section, as it is determined solely by the selected support conditions (stiffness) and loading (axial force, temperature). Approximation of eigenvalue problem solutions through continuous functions allows the readers to use them for the analytical solution of the design problem of choosing a support system to ensure the frequency of vibrations and stability of the planar beam structure. At the same time, the known solutions given in the reference books on bending vibrations and stability become their particular solutions. This approach is applicable to solving problems of vibrations and loss of stability of various types (torsional, longitudinal, etc.), and is also applicable in other disciplines where solving problems for eigenvalues is required.