The Research of SOL Treated Cantilever Beam Based on Analytical Methods and ANSYS

Abstract

SOL (stand-off layer) damping treatment is the most effective method to improve the damping characteristics of the base structure compared with unconstrained and constrained layer damping treatment. In this case, the viscoelastic layer is sandwiched between the SOL and the constraining layer. During vibration, the SOL acts as a strain magnifier which magnifies the shear strain in the viscoelastic layer by increasing the distance between the viscoelastic layer and the neutral axis of the base structure thus dissipates more vibration energy. The equations of motion root in kinematic equations, constitutive equations and equilibrium equations of force and moment, and constitute one variable (lateral deflection) with order differential equation and two variables (axial deflections of the base beam and the constraining layer) with order differential equation of motion. Together with the boundary conditions, the transfer function method and the finite element method are adopted to analyze the damping characteristics of the composite structure. In distributed function method, the equations are transferred to state space form. In finite element method, the lateral deflection is interpolated by Hermite interpolation function and the axial deflections of the base layer and the constraining layer are interpolated by Lagrange interpolation function. At last, the predictions of the two analytical methods are validated against the commercial software ANSYS. Close agreements are found among the three methods. To achieve the expected effect, the SOL must have high shear stiffness and low bending stiffness so it does not significantly influence the flexural rigidity of the base structure but does not absorb the shear stress desired to be passed on to the viscoelastic layer. This paper is focus the application of SOL damping treatment on cantilever beam model, but it is essential to note that the model can be extended to complex structures such as plates and shells. We can select the slotted SOL damping treatment which could effectively avoid the increase in bending stiffness but also maintain high shear stiffness as the substitute.