Abstract
AbstractA new state-space model is formulated for the dynamic analysis of sandwich beams that are made of two thin elastic layers continuously joined by a shear-type viscoelastic (VE) core. The model can accommodate different boundary conditions for each outer layer and accounts for the rate-dependent constitutive law of the core through additional state variables. The mathematical derivation is presented with the Standard Linear Solid (SLS) model (i.e., a primary elastic spring in parallel with a single Maxwell element) and then extended to the generalized Maxwell (GM) model. The kinematics equations are developed by means of Galerkin-type approximations for the fields of axial and transverse displacements in the outer layers, and imposing the pertinent compatibility conditions at the interface with the core. Numerical examples demonstrate the accuracy and versatility of the proposed approach, which endeavors to represent the effects of the VE memory on the vibration of composite beams.
Highlights
Beams and panels with viscoelastic (VE) damping are widely used in state-of-the-art engineering structures, allowing to achieve improved safety, increased durability, and noise and vibration control, as well as reduced costs during the through-life manufacturing, operation, and maintenance of the structural systems (e.g., Lockett 1972; Soong and Dargush 1997; Zhang and Soong 1992; Lee 1997; Rao 2003)
A different computational strategy consists of defining the dynamic stiffness matrix for the composite beam (Howson and Zare 2005), but this requires the solution of a transcendental eigenvalue problem with the so-called Wittrick-Williams algorithm (Williams and Wittrick 1983)
A new state-space formulation has been developed and numerically validated for the dynamic analysis of sandwich beams consisting of two parallel Euler-Bernoulli elastic beams continuously connected by a shear-type VE layer
Summary
Beams and panels with viscoelastic (VE) damping are widely used in state-of-the-art engineering structures, allowing to achieve improved safety, increased durability, and noise and vibration control, as well as reduced costs during the through-life manufacturing, operation, and maintenance of the structural systems (e.g., Lockett 1972; Soong and Dargush 1997; Zhang and Soong 1992; Lee 1997; Rao 2003).
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