Non-linear vibrations of three-layer beams with viscoelastic cores I. Theory |
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| Authors: | MW Hyer WJ Anderson RA Scott |
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| Institution: | Department of Mechanical Engineering and Mechanics, Old Dominion University, Norfolk, Virginia 23508, U.S.A.;Department of Aerospace Engineering, University of Michigan, USA;Department of Applied Mechanics and Engineering Science, University of Michigan, Ann Arbor, Michigan 48104, U.S.A. |
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| Abstract: | Approximate equations of motion are developed for large amplitude motions of three-layer axially restrained unsymmetrical beams with viscoelastic cores. The external force consists of a constant plus an oscillatory term. The combination of this form of forcing and the large amplitude motions cause the beam to respond at multiples of the forcing frequency. This can lead to difficulties in the complex modulus approach to viscoelasticity. These are overcome here through use of hereditary integrals and their relationships with complex moduli. Theoretical results on the frequency response of clamped, symmetrical beams are compared with earlier experimental work. On the whole, reasonable agreement is found. |
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