MODAL ANALYSIS OF MULTI-SPAN TIMOSHENKO BEAMS CONNECTED OR SUPPORTED BY RESILIENT JOINTS WITH DAMPING
✍ Scribed by S.-W. HONG; J.-W. KIM
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 214 KB
- Volume
- 227
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
The present paper proposes an exact modelling and modal analysis method for non-uniform, multi-span beam-type structure supported and/or connected by resilient joints with damping. To this end, an exact dynamic matrix for a Timoshenko beam element is derived by means of the spatial domain Laplace transform. A generalized modal analysis method is also proposed and applied to the derivation of frequency response and time response formulas for general beam structures. Three examples are provided for validating and/or illustrating the proposed method. In the "rst numerical example, the proposed method is compared with FEM. The second example deals with a three-stepped beam structure supported by joints with damping property. In the "nal example, a dynamic analysis of a multi-span beam under moving load is demonstrated. The numerical study proves that the proposed method is useful for the dynamic analysis of multi-span beam-type structures.
where u and are the transverse and angular displacements of the beam and F and M are the corresponding force and moment respectively. , G and E are the density, shear modulus and Young's modulus respectively. A and I B are the area and the diametral moment of inertia respectively, and k is the shape factor that is dependent on the cross-sectional shape.
Laplace transformation of equation ( 1) with respect to time, with zero initial conditions, leads to
*M* *x "F*# I B s* . Here, the asterisk represents the Laplace transform of the corresponding state variable, s being the Laplace variable for time. Equation (2) can be rewritten, in a simple matrix form, as * (x, s) *x "B(s) (x, s), (3) MODAL ANALYSIS OF DISTRIBUTED PARAMETER BEAM SYSTEM