Auxiliary mass throw in a tuned and damped vibration absorber

Dynamic vibration absorbers should be tuned and optimally damped to control the amplitudes of vibration of the primary mass over the whole range of exciting frequencies. The lighter the auxiliary mass the greater is the amplitude of its excursions relative to the primary mass. In the case of the tuned system the maximum steady state throw of the auxiliary mass can be easily calculated from the formulas given. These are most elegantly derived by use of a frequency locus technique. It is shown that is the system is also optimally damped the throw of the auxiliary mass has its minimum value which depends only on the mass ratio.     

Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.     

Optimization of a hybrid vibration absorber for vibration control of structures under random force excitation

A recently reported design of a hybrid vibration absorber (HVA) which is optimized to suppress resonant vibration of a single degree-of-freedom (SDOF) system is re-optimized for suppressing wide frequency band vibration of the SDOF system under stationary random force excitation. The proposed HVA makes use of the feedback signals from the displacement and velocity of the absorber mass for minimizing the vibration response of the dynamic structure based on the H₂ optimization criterion. The objective of the optimal design is to minimize the mean square vibration amplitude of a dynamic structure under a wideband excitation, i.e., the total area under the vibration response spectrum is minimized in this criterion. One of the inherent limitations of the traditional passive vibration absorber is that its vibration suppression is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The active element of the proposed HVA helps further reduce the vibration of the controlled structure and it can provide significant vibration absorption performance even at a low mass ratio. Both the passive and active elements are optimized together for the minimization of the mean square vibration amplitude of the primary system. The proposed HVA are tested on a SDOF system and continuous vibrating structures with comparisons to the traditional passive vibration absorber.     

Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads

Optimum design of dynamic vibration absorbers (DVAs) installed on linear damped systems that are subjected to random loads is studied and closed-form design formulas are provided. Three cases are considered in the optimization process: Minimizing the variance of the displacement, velocity and acceleration of the main mass. Exact optimum design parameters for the velocity case, which to the best knowledge of the author do not exist in the literature, are derived for the first time. Exact solutions are found to be directly applicable for practical use with no simplification needed. For displacement and acceleration cases, a solution for the optimum absorber frequency ratio is obtained as a function of optimum absorber damping ratio. Numerical simulations indicate that optimum absorber damping ratio is not significantly related to the structural damping, especially when the displacement variance is minimized. Therefore, optimum damping ratio derived for undamped systems is proposed for damped systems for the displacement case. When acceleration variance is minimized, however, the optimum damping ratio derived for undamped systems is found not as accurate for damped systems. Therefore, a more accurate approximate expression is derived. Numerical comparisons with published approximate expressions at the same level of complexity indicated that proposed design formula yield more accurate estimates. Another important finding of the paper is that for specific applications where all of the response parameters are desired to be minimized simultaneously, DVAs designed per velocity criteria provide the best overall performance with the least complexity in the design equations.     

The effect of a viscously damped dynamic absorber on a linear multi-degree-of-freedom system

The effect of a viscously damped dynamic absorber on the dynamic behaviour of a linear vibration system with many degrees of freedom is investigated. The dynamic absorber is connected to the roof of the primary system. In the sequence, optimal values for the parameters describing the behaviour of the dynamic absorber are determined, in order that the transmissibility of the composite system be minimized over the whole frequency range. As an application, respective types of anti-vibration mountings are proposed.     

On the functional form of a nonlinear vibration absorber

Due to the frequency-energy dependence of nonlinear oscillations, nonlinear dynamical absorbers present interesting properties for mitigating unwanted vibrations in mechanical systems. Unlike the tuned mass damper, the functional form of a nonlinear absorber is not known a priori and must be determined. This short note addresses this issue when a light-weight nonlinear absorber is attached to a nonlinear primary structure. Numerical simulations demonstrate that the determination of an adequate functional form may be directly linked to the frequency-energy dependence of the primary structure.     

Inverse iteration for damped natural vibration

Inverse iteration is extended to internally and/or externally damped natural vibration. Each iteration involves one matrix multiplication and one linear equation solution of order n. The symmetric band form of the original undamped eigenvalue problem is preserved. If the undamped mode is taken as the first approximation, the inverse iteration will converse to the corresponding damped mode in about four iterations. However, the one step method is divergent for heavy damping. Therefore, it is advisible to subdivide the damping into successive steps if inverse iteration does not converge in say five iterations. The method is successful for both discrete systems and distributed systems. The implementation is very simple by means of complex arithmetic which is readily available in many FORTRAN compilers.     

H2 optimization of a non-traditional dynamic vibration absorber for vibration control of structures under random force excitation

The H₂ optimum parameters of a dynamic vibration absorber of non-traditional form are derived to minimize the total vibration energy or the mean square motion of a single degree-of-freedom (sdof) system under random force excitations. The reduction of the mean square motion of the primary structure using the traditional vibration absorber is compared with the proposed dynamic absorber. Under optimum tuning condition, it is shown that the proposed absorber when compared with the traditional absorber, provides a larger suppression of the mean square vibrational motion of the primary system.     

基于磁/电介质混合型基体的宽带超材料吸波体的设计与制备

本文设计了一种基于磁/电介质混合型基体的宽带超材料吸波体, 吸波体基本单元由电阻膜、磁/电介质混合型基体以及金属背板组成. 采用时域有限差分法对超材料吸波体吸波性能进行了仿真, 使用遗传算法优化了反射率小于-10 dB的带宽. 仿真结果表明, 当超材料吸波体厚度为2.5 mm时, 在7.8–18 GHz频率范围内的反射率小于-10 dB, 具有厚度薄、宽带、极化不敏感等优点. 通过等效电路模型对其工作机理进行了分析与讨论. 最后制备样品进行测试, 测试结果与仿真结果一致.     

Design of passive vibration controls for internally damped beams by modal control techniques

Modern modal control techniques are applied to the design of dynamic absorbers for the control of transient vibrations of internally damped thin uniform beams. Parameters and locations of single and dual absorbers are chosen so that the overall system approximates a desired characteristic polynomial.     

Forced vibration of a damped sandwich beam subjected to moving forces

The response of a sandwich beam subjected to moving forces (constant as well as pulsating) is analyzed by the use of Fourier and Laplace transforms and compared with the response of an equivalent elastic beam. The results indicate that the critical speed of force on a sandwich beam is always greater than that on an elastic beam of identical mass per unit length and flexural rigidity, and depends on its geometric and shear parameters. For subcritical speeds, the maximum deflection of a sandwich beam is shown to occur earlier than that of an equivalent elastic beam. An increase in the core shear stiffness is shown to be beneficial in reducing the dynamic magnification of the central deflection of the sandwich beam.     

动力吸振器中库仑阻尼对吸振性能的影响

研究了动力吸振器中库仑阻尼(干摩擦)对吸振性能的影响。给出了库仑摩擦模型,在考虑了吸振器中的库仑阻尼的情况下,分析了库仑阻尼引起的主振动系统与附加质量块的2种相对运动状态(滑移和粘滞)以及它们存在和转换的条件,讨论了因库仑阻尼引起的吸振器自由度冻结现象;用Simulink仿真工具对非线性吸振器进行了数值仿真,研究了谐波和白噪声激励下库仑阻尼对吸振器吸振性能的影响以及库仑阻尼与线性阻尼的等效问题。结果显示:弱激励条件下,非线性吸振器减弱吸振效果,强激励条件下增强吸振效果。     

动力吸振器中库仑阻尼对吸振性能的影响

研究了动力吸振器中库仑阻尼（干摩擦）对吸振性能的影响。给出了库仑摩擦模型,在考虑了吸振器中的库仑阻尼的情况下,分析了库仑阻尼引起的主振动系统与附加质量块的2种相对运动状态（滑移和粘滞）以及它们存在和转换的条件,讨论了因库仑阻尼引起的吸振器自由度冻结现象;用Simulink仿真工具对非线性吸振器进行了数值仿真,研究了谐波和白噪声激励下库仑阻尼对吸振器吸振性能的影响以及库仑阻尼与线性阻尼的等效问题。结果显示：弱激励条件下,非线性吸振器减弱吸振效果,强激励条件下增强吸振效果。     

Design of a varactor-tunable metamaterial absorber

In this paper, we design a varactor-tunable metamaterial absorber （MA）. The tunable MA is based on a mushroom-type high impedance surface （HIS）, in which varactors are loaded between adjacent metal patches to adjust the capacitance and tune the resonance frequency, the primary ground plane is etched as the bias network to bias all of the varactors in parallel, and another ultra-thin grounded film is attached to the bottom. Its absorption characteristics are realized for electrically dielectric loss. The simulated values of a sample indicate that a tunable frequency range from 2.85 GHz to 2.22 GHz is achieved by adjusting the varactor capacitance from 0.1 pF to 2.0 pF, and better than 0.97 absorbance is realized; in addition, the tunable frequency range is expanded from 4.12 GHz to 1.70 GHz after optimization.