Damping ratio maximization in thickness direction using viscoelastic and structural materials based on constrained layer damping

Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA) is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an invaluable design tool.

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Evaluation Principles and Applications of Dynamic Elastic Modulus and Damping Ratio of Structural Materials Using the IET Method

Transactions of the Korean Society of Mechanical Engineers A ◽

10.3795/ksme-a.2019.43.4.261 ◽

2019 ◽

Vol 43 (4) ◽

pp. 261-266

Author(s):

Sun A Yoon ◽

Jung Kwon Lee ◽

Chang Soon Lee ◽

Tae Hwan Lim ◽

Chul Woon Han ◽

...

Keyword(s):

Elastic Modulus ◽

Damping Ratio ◽

Structural Materials ◽

Dynamic Elastic Modulus

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Topology Optimization for Minimizing the Resonant Response of Plates with Constrained Layer Damping Treatment

Shock and Vibration ◽

10.1155/2015/376854 ◽

2015 ◽

Vol 2015 ◽

pp. 1-11 ◽

Cited By ~ 10

Author(s):

Zhanpeng Fang ◽

Ling Zheng

Keyword(s):

Sensitivity Analysis ◽

Topology Optimization ◽

Damping Ratio ◽

Optimization Method ◽

Constrained Layer Damping ◽

Resonant Response ◽

Optimal Layout ◽

Analysis Method ◽

Topology Optimization Problem ◽

Sensitivity Analysis Method

A topology optimization method is proposed to minimize the resonant response of plates with constrained layer damping (CLD) treatment under specified broadband harmonic excitations. The topology optimization problem is formulated and the square of displacement resonant response in frequency domain at the specified point is considered as the objective function. Two sensitivity analysis methods are investigated and discussed. The derivative of modal damp ratio is not considered in the conventional sensitivity analysis method. An improved sensitivity analysis method considering the derivative of modal damp ratio is developed to improve the computational accuracy of the sensitivity. The evolutionary structural optimization (ESO) method is used to search the optimal layout of CLD material on plates. Numerical examples and experimental results show that the optimal layout of CLD treatment on the plate from the proposed topology optimization using the conventional sensitivity analysis or the improved sensitivity analysis can reduce the displacement resonant response. However, the optimization method using the improved sensitivity analysis can produce a higher modal damping ratio than that using the conventional sensitivity analysis and develop a smaller displacement resonant response.

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Viscoelastic Damping of Ortho-Planar Springs

Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2008-49862 ◽

2008 ◽

Cited By ~ 2

Author(s):

Sterling Anderson ◽

Brian D. Jensen

Keyword(s):

Damping Ratio ◽

Spring Constant ◽

Viscoelastic Damping ◽

Viscous Damping ◽

Constrained Layer Damping ◽

Equivalent Viscous Damping ◽

Background Theory ◽

Modal Damping ◽

Damping Treatments ◽

Equivalent Viscous Damping Ratio

This paper presents the design of a damped ortho-planar spring that uses viscoelastic constrained-layer damping to reduce the free response oscillations of the spring and suppress modal resonances in that response. Background, theory, and applications surrounding fully-compliant ortho-planar springs and viscoelastic damping treatments are first discussed. Next, the effect of various constrained layer thickness on the spring constant, damping ratio, equivalent viscous damping ratio, modal frequencies, and modal damping ratios are compared, and trends discussed. The results show that the equivalent viscous damping co-efficient of the viscoelastically-damped spring can be increased to nearly 2.5 times that of the reference configuration without significantly changing the size of the constraining layer or the spring constant of the ortho-planar spring. Viscoelastically-damped ortho-planar springs are also shown to successfully remove mechanical noise from a contact resistance test stand.

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Vibration Analysis and Control of a Rotating Flexible Arm With ACLD Treatment

Adaptive Structures and Materials Systems ◽

10.1115/imece2002-33981 ◽

2002 ◽

Author(s):

E. H. K. Fung ◽

D. T. W. Yau

Keyword(s):

Vibration Suppression ◽

Damping Ratio ◽

Equations Of Motion ◽

Gravitational Effect ◽

Transverse Displacement ◽

Complex Eigenvalue ◽

Constrained Layer Damping ◽

Rotating Speed ◽

Centrifugal Stiffening ◽

And Control

In this paper, the vibration behavior and control of a clamped-free rotating flexible cantilever arm with fully covered Active Constrained Layer Damping (ACLD) treatment is investigated. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The stress-strain relationship for the viscoelastic material (VEM) is described by a complex shear modulus while the shear deformations in the two piezoelectric layers are neglected. Hamilton’s principle in conjunction with finite element method (FEM) is used to derive the nonlinear coupled differential equations of motion and the associated boundary conditions that describe the rigid hub angle rotation, the arm transverse displacement and the axial deformations of the three-layer composite. This refined model takes into account the effects of centrifugal stiffening due to the rotation of the beam and the potential energies of the VEM due to extension and bending. Active controllers are designed with PD for the piezo-sensor and actuator. The vibration frequencies and damping factors of the closed-loop beam/ACLD system are obtained after solving the characteristic complex eigenvalue problem numerically. The effects of different rotating speed, thickness ratio and loss factor of the VEM as well as different controller gain on the damped frequency and damping ratio are presented. The results of this study will be useful in the design of adaptive and smart structures for vibration suppression and control in rotating structures such as rotorcraft blades or robotic arms.

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Attenuation of Free Vibration Using Particle Impact Damper

Volume 9: Mechanical Systems and Control, Parts A, B, and C ◽

10.1115/imece2007-42731 ◽

2007 ◽

Author(s):

Hamid R. Hamidzadeh

Keyword(s):

Free Vibration ◽

Damping Ratio ◽

Particle Impact ◽

Constrained Layer Damping ◽

Equivalent Viscous Damping ◽

Impact Damper ◽

Equivalent Damping ◽

Vibrating System ◽

Damping Characteristics ◽

Moving Particle

The particle impact damper is an effective vibration damping treatment that can be used in the cases where visco-elastic constrained layer damping fails due to excessive surrounding temperature. In this type of passive damping, particles move in a container attached to the vibrating system resulting in plastic impact with the container. In the presented theoretical study, the damping characteristics of free oscillation for a vertical system with an initial displacement are considered and a governing equation for the system under free vibration with a particle damper is derived. To evaluate the damping characteristics for the free vibrating system, the equivalent damping ratio is determined by considering both kinematics and kinetics of the particle motion and its impacts with the container. The presented solution concludes that in general damping effectiveness can be enhanced by increasing the mass of the particle in comparison with total mass of the system. Mathematical optimum clearance for the moving particle and the equivalent viscous damping ratio are determined for the best performance of the particle impact damper.

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