A Validation Study for the Computation of Nonlinear Modal Frequency using a Hamiltonian Reduced Order Model

Abstract

A common structural design verification is to conduct modal analysis and to ensure that the vibration modes of the structure do not get harmonically excited during operation. Since the modal frequencies are dependent on the mass and stiffness properties of the structure, they are an influencing factor in the design optimization. Modal frequencies are obtainable using eigenvalue analysis after linearization approximations in the restoring force terms of the governing equation of motion. While this approximation is valid for lower loads, it is not acceptable for strong nonlinear vibrations. A measurable shift in the modal frequency is observable when the amplitude of vibrations is in the order of the thickness of the vibrating structure. This phenomenon is more pronounced in thin walled and flexible structures where the vibration amplitudes can exceed the linear threshold relatively more easily. A credible approach in computation of nonlinear modes is the utilization of parametric continuation schemes for generating nonlinear frequency-amplitude response. However, utilization of this scheme with a large degree of freedom model is a computationally intensive approach which necessitate the development of reduced order models. A model reduction method in the finite element framework, termed as Hamiltonian Reduced Order Model (ROM), has been recently developed at Delft University of Technology. The present study is conducted for the experimental validation of the ROM. Governing equations of motion of a stiffened plate have been derived using the Hamiltonian ROM and the nonlinear frequency response has been generated using a continuation scheme. For validation, experiments have been conducted using the Laser Doppler Vibrometer to obtain similar frequency response curves. A comparison of the numerical and the experimental results shows excellent agreement. Furthermore, accurate numerical response is obtainable using only a single degree of freedom in the reduced order model which proves the effectiveness of the Hamiltonian ROM. The results also demonstrate the necessity of a nonlinear damping model for obtaining comparable results.Aerospace Engineerin