Optimal design of damped laminated structures.

Abstract

Vibration problems are a concern for virtually any product with moving parts, and even some structures intended to be stationary (such as buildings in areas prone to earthquakes). Many engineering design hours, and immense cost, are spent trying to deal with vibration problems. Excessive vibration within a structure may result in discomfort for the user, unacceptable noise levels, or premature failure due to fatigue. Damped laminates, where viscoelastic damping layers are applied to the vibrating structure, are effective for reducing vibration for beam and plate structures. These damped laminated structures are the subject of this study. They may be broken up into two different classes: unconstrained damping layers, where a damping layer is bonded to the vibrating structure, and constrained damping layers, where an additional elastic constraining layer is placed on the damping layer. Both of these structures are examined for optimization. The structure is modeled using the ABAQUS commercial finite element code. Continuum elements, based on elasticity theory, are employed. Both beam and plate structures of various dimensions and boundary conditions are examined. The structure is undergoing a transverse forced harmonic excitation. A commercial optimization code is used, which employs a sequential quadratic programming algorithm. The heights of the damping layer elements are the design variables, and the objective is to minimize the peak displacement in the structure. In order to find the peak displacement, the new resonant frequency must be found with each structural change. Results for unconstrained damped laminates show remarkable improvement from the uniform layer structure to the optimal shape. Both bending stress and stress through the thickness are significant in driving the optimal shape. Studies show that recognizing the frequency dependence of the damping material is significant in order to obtain accurate optimization results. Additionally, it is shown that optimizing at one frequency may produce a structure that performs significantly worse at other frequencies. Optimization results for constrained damped laminates also show significant improvement from the original shapes. Generally, the motivating factor behind the optimization process is reducing the height of the damping layer in order to produce higher shearing strains.