Damped Vibrational Response of Beams on Multi-Parametric Foundations: A Computational and Analytical Approach
摘要
This investigation presents a novel computational and analytical approach to finding the undamped, underdamped, and overdamped frequencies and the vibrational response of Euler Bernoulli, shear, and Timoshenko beams placed on two (visco–Winkler (VW)) and three (visco–Pasternak (VP)) parametric foundations. The scientific innovation combines eigenvalue-based dispersion relations with an improved separation of variables technique to provide a novel spatial matrix formulation for displacements, slopes, and corresponding derivatives. This approach enhances precision and reliability, particularly when simulating complex vibrational behavior with shear, rotary inertia, and damping coefficient effects. To provide a shear-locking free solution, the study also incorporates the Galerkin finite element method (GFEM), to demonstrate convergence to accurate results. To accurately analyze the response of damped systems, the study also presents the use of state-space formulation (SSF) alongside the Runge-Kutta method (RK4). The results are verified and shown under various damping circumstances using a thorough comparison of analytical and finite element approaches, offering valuable insights regarding the design and optimization of structures with viscous supports. As rotary inertia and shear effects are incorporated into EBB, key findings show that damped frequencies decrease by 29