Dynamic response of beam type structures subjected to bi-directional excitation

Engineering structures are subjected to complex dynamic loadings in various practical operating environments. Conventionally, the research on the response analysis of such structures focuses on uni-directional excitation. However, such structures may experience bi-directional as well as multi-directional excitations, which significantly affect their dynamic response. In this regard, the present study investigates the effects of bi-directional excitation on beam type structures to explore and predict their dynamic behaviour under such conditions. In this work, a mathematical model based on the energy method is developed to calculate and predict a more accurate response of the beam under bi-directional excitation. The excitation is considered from axial as well as from base excitation in transverse direction. In the mathematical model, one excitation (axial excitation) is considered within the framework of time dependent stiffness. The model is validated against experimental data and applied to different beam configurations considering different sizes and material properties. The results reveal that bi-directional excitation leads to significantly different dynamic responses compared to uni-directional excitation, particularly in terms of complex vibrational modes. Limiting values for axial excitation parameters are reported after which the response is dominated by axial excitation. The study highlights the necessity of incorporating bi-directional excitation scenarios in the design and analysis of beams to ensure structural integrity and reliability.