Modified Reynolds Equation for Squeeze-Film Air Damping of Slotted Plates in MEMS Devices

A differential equation for calculating squeeze-film air damping in slotted plates is developed by modifying the Reynolds equation. A term is added to account for the effect of airflow through the slots on the air damping of the plate. The end effect of the airflow in the slots is also treated by substituting an effective channel length for the geometric channel length （i. e. the thickness of the plate）..The damping pressure distribution, damping force, and damping force coefficient of the slotted plates can be found by solving the equation under appropriate boundary conditions. With restrictions on the thickness and the lateral dimensions of the slotted plate removed,the equation provides a useful tool for analysing the squeeze-film air damping effect of slotted plates with finite thickness and finite lateral dimensions. For a typical slotted plate structure, the damping force coefficient obtained by this equation agrees well with that generated by ANSYS.

Influence of active constrained layer damping on the coupled vibration response of functionally graded magneto-electro-elastic plates with skewed edges

This article makes the first attempt in assessing the influence of active constrained layer damping(ACLD)treatment towards precise control of frequency responses of functionally graded skew-magneto-electroelastic(FGSMEE)plates by employing finite element methods.The materials are functionally graded across the thickness of the plate in terms of modest power-law distributions.The principal equations of motion of FGSMEE are derived via Hamilton’s principle and solved using condensation technique.The effect of ACLD patches are modelled by following the complex modulus approach(CMA).Additionally,distinctive emphasis is laid to evaluate the influence of geometrical skewness on the attenuation capabilities of the plate.The accuracy of the current analysis is corroborated with comparison of previous researches of similar kind.Additionally,a complete parametric study is directed to understand the combined impacts of various factors like coupling fields,patch location,fiber orientation of piezoelectric patch in association with skew angle and power-law index.

Experimental Study and System Identification of Hydrodynamic Force Acting on Heave Damping Plate

Although Morison equation is often applied for simulating hydrodynamic force of marine structure, it may give poor results when non-linear behavior is severe or random wave is encountered. This leads to some modifications of Morison equation or other methods for predicting hydrodynamic force. One of them is the system identification technique. In this paper, NARMAX model theory is firstly used to identify the hydrodynamic system of heave damping plates, which are commonly installed on spar platform. Both linear and non-linear models are obtained. The comparisons between the predieted results and measured data indicate that NARMAX model can predict hydrodynamic force of a heave damping plate very well. The measured data for identification originate from forced oscillation tests, which are random records with given spectrum. The forced oscillation forms in experiment also contain simple harmonic, multi-frequency ones.

THE DYNAMIC PLASTIC BEHAVIOR OF A SIMPLY SUPPORTED CIRCULAR PLATE IN A DAMPING MEDIUM WITH FINITE-DEFLECTIONS

A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. Analytical solutions of every moving stage under both medium and high loads are developed.

Effect of porosity on active damping of geometrically nonlinear vibrations of a functionally graded magneto-electro-elastic plate

This paper investigates the effect of porosity on active damping of geometrically nonlinear vibrations(GNLV)of the magneto-electro-elastic(MEE)functionally graded(FG)plates incorporated with active treatment constricted layer damping(ATCLD)patches.The perpendicularly/slanted reinforced 1-3 piezoelectric composite(1-3 PZC)constricting layer.The constricted viscoelastic layer of the ATCLD is modeled in the time-domain using Golla-Hughes-Mc Tavish(GHM)technique.Different types of porosity distribution in the porous magneto-electro-elastic functionally graded PMEE-FG plate graded in the thickness direction.Considering the coupling effects among elasticity,electrical,and magnetic fields,a three-dimensional finite element(FE)model for the smart PMEE-FG plate is obtained by incorporating the theory of layer-wise shear deformation.The geometric nonlinearity adopts the von K arm an principle.The study presents the effects of a variant of a power-law index,porosity index,the material gradation,three types of porosity distribution,boundary conditions,and the piezoelectric fiber’s orientation angle on the control of GNLV of the PMEE-FG plates.The results reveal that the FG substrate layers’porosity significantly impacts the nonlinear behavior and damping performance of the PMEE-FG plates.

A Theoretical Analysis of Thermoelastic Damping Model in Laminated Trilayered Circular Plate Resonators

Thermoelastic damping of the axisymmetric vibration of laminated circular plate resonators is discussed in this paper. Based on the classical laminated plate theory assumptions, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of trilayered circular plate. The analytical expression for thermoelastic damping is obtained and the accuracy is verified through comparison with finite element analysis results. Then some simplifications are made on the theoretical model.

Finite element analysis of the free-damped beam-stiffened plate

A finite element model is presented for free-damped beam-stiffened plates. The nodes of the plate elements are treated as master-nodes, and the corresponding nodes of the beam elements are considered as slave-nodes. The stiffness and mass matrices of the elements are developed. Based on the analysis of the dynamic properties of the structures, modal loss factors are predicted by the modal strain energy method. Finally, an example is given to compare the results obtained from the proposed method with the results of the ANSYS software. The results show that the method in this paper is computationally efficient, simple and feasible with high precision and engineering practicability.

Feasibility study of a large-scale tuned mass damper with eddy current damping mechanism

Tuned mass dampers （TMDs） have been widely used in recent years to mitigate structural vibration. However, the damping mechanisms employed in the TMDs are mostly based on viscous dampers, which have several well-known disadvantages, such as oil leakage and difficult adjustment of damping ratio for an operating TMD. Alternatively, eddy current damping （ECD） that does not require any contact with the main structure is a potential solution. This paper discusses the design, analysis, manufacture and testing of a large-scale horizontal TMD based on ECD. First, the theoretical model of ECD is formulated, then one large-scale horizontal TMD using ECD is constructed, and finally performance tests of the TMD are conducted. The test results show that the proposed TMD has a very low intrinsic damping ratio, while the damping ratio due to ECD is the dominant damping source, which can be as large as 15% in a proper configuration. In addition, the damping ratios estimated with the theoretical model are roughly consistent with those identified from the test results, and the source of this error is investigated. Moreover, it is demonstrated that the damping ratio in the proposed TMD can be easily adjusted by varying the air gap between permanent magnets and conductive plates. In view of practical applications, possible improvements and feasibility considerations for the proposed TMD are then discussed. It is confirmed that the proposed TMD with ECD is reliable and feasible for use in structural vibration control.

State-vector equation with damping and vibration analysis of laminates

Based on the modified mixed Hellinger-Reissner（H-R） variational principle for elastic bodies with damping, the state-vector equation with parameters is directionally derived from the principle. A new solution for the harmonic vibration of simply supported rectangular laminates with damping is proposed by using the precise integration method and Muller method. The general solutions for the free vibration of underdamping, critical damp and overdamping of composite laminates are given simply in terms of the linear damping vibration theory. The effect of viscous damping force on the vibration of composite laminates is investigated through numerical examples. The state-vector equation theory and its application areas are extended.

Effect of Deflected Disc's Thickness to the Damping Characteristic of Tube Shock Absorbers

Research is conducted on the relationship between thickness of deflected disc and damping force of tube shock absorbers. By analyzing performing characteristics of the throttling valve using throttling theory of small clearance space and thin place deformation theories, mathematical correlation between disc thickness and magnitude of damping force is formulated. Moreover, a rule concerning change of damping force in terms of disc thickness is concluded.

Forced Vibration Numerical Analysis of Rectangular Elastic Orthotropic Damped Inclined Mindlin Plate Using Finite Difference Algorithm

Plates vibrate when load moves on them. In this paper, the dynamic response of Mindlin plate analytical model was converted to its numerical form using finite difference algorithm. The numerical model was analysed to ascertain the critical parameters contributing to the deflection of Mindlin plate under a moving load. The examination was more reasonable as in the likelihood of the plate laying on a Pasternak foundation was put into thought. Likewise the impact of damping was not dismissed. The plate considered in this paper was an inclined Mindlin plate, where the impacts of shear deformation and rotatory inertia were considered. The numerical equations were solved with the help of a developed computer program and Matlab. The results were consistent with what we have in the literature. The effects of the Pasternak foundation, damping, angle of inclination, and the moving load to the dynamic response of the elastic plate were exceptionally self-evident.

Calculation of multi-layer plate damper under one-axial load

A multi-layer damper with waved plates under one-axial load is considered. A method of theoretical calculation of its energy dissipation coefficient is proposed. An experimental research of own frequencies and vibration transfer ratios for different parameters of damper structure, harmonic vibration load and random load is performed. Results of this research are approximated by functions; it is possible to use these functions for the calculation of the damper too.

基于多目标遗传算法的斜盘式轴向柱塞泵低脉动结构优化设计

由于轴向柱塞泵的非对称结构特性,其输出压力和输出流量存在脉动特性,对液压系统的输出稳定性和可靠性造成影响,因此提出了一种基于多目标遗传算法的斜盘式轴向柱塞泵低脉动结构优化设计方法。首先,通过CFD(computational fluid dynamics,计算流体动力学)仿真分析方法,对轴向柱塞泵上/下死点位的压力-流量脉动的产生机理进行了分析;其次,对阻尼槽结构参数对轴向柱塞泵输出压力-流量脉动的影响规律进行了分析,构建了阻尼槽结构的多目标优化模型;最后,求解了低脉动阻尼槽结构。优化后的结构参数:阻尼槽半径为2.21 mm,阻尼槽长度为10.32 mm,阻尼槽错配角为16.54°。优化后压力脉动率为0.59%,相比于优化前的0.75%降低了0.16%,脉动幅值为0.25 MPa;优化后流量脉动率为12.02%,相比于优化前的5.61%降低了43.59%。研究结果为轴向柱塞泵低脉动结构的优化设计提供了有效的理论支持和实践指导。

具有局部阻尼的二维Mindlin-Timoshenko板系统的镇定

该文研究了具有局部阻尼的二维Mindlin-Timoshenko板系统,首先将原系统转化成抽象柯西问题,运用算子半群理论得到了系统的适定性.借助系统频域稳定性结果,通过引入几何光学条件结合乘子技巧得到了系统的一致指数稳定性.

基于声阻抗匹配理论的弹性吸收体研究

基于时域耦合模型理论的吸收体研究,不适用于所有模型,且基于此理论的设计过程复杂,难以在工业工程得到广泛应用。因此提出一种基于声阻抗匹配理论的弹性吸收体的研究方法,并通过理论计算、数值仿真以及实验对吸收体的吸收曲线进行验证。结果表明:本文提出的方法能够快速、简便地实现弹性吸收体的结构设计,无需额外附加阻尼材料,更有利于满足航空工程中对于结构轻量化的要求,为振动波吸收领域,尤其是弯曲波的高效吸收和减振设计研究带来了新的可能性。

贴敷约束阻尼层的螺栓连接板半解析动力学建模及减振分析

在太空环境中太阳翼帆板的振动难以抑制,因此太阳翼帆板的减振研究至关重要。利用双搭接螺栓连接板结构模拟太阳翼帆板的展开状态,研究了通过贴敷约束阻尼层对其进行振动抑制的方法。创建了贴敷“H型”约束阻尼层双搭接螺栓连接板结构的半解析动力学模型,包含:利用层间剪切变形原理,推导了约束阻尼层结构的应力应变关系,用复模量表征黏弹性层的阻尼特性;考虑螺栓的影响区域,提出用复面弹簧单元和修正质量模拟双搭接螺栓结合部的刚度、阻尼和质量特性;引入正交多项式作为位移容许函数,利用拉格朗日方程和Hamilton原理建立了局部贴敷“H型”约束阻尼层的螺栓连接薄板的动力学方程。进行了实例研究,通过组建的试验系统证明了所创建的复合结构半解析模型在求解固有特性及振动响应参数方面的合理性,同时试验及半解析模型计算结果均证明约束阻尼层对双搭接螺栓连接板具有减振效果。最后,基于所创建的半解析模型分析了贴敷面积及约束阻尼层厚度对双搭接螺栓连接板减振效果的影响。

周期约束阻尼设计板结构减振降噪特性分析

为了探究更加高效的阻尼减振降噪结构设计,结合人工周期结构特性与约束阻尼减振降噪技术,通过对基体板和不同约束阻尼板结构的振动与声辐射进行有限元仿真计算和实验测试,分析周期约束阻尼设计板结构的减振降噪特性。研究结果表明,相比于传统约束阻尼设计,周期约束阻尼设计可以在附加阻尼质量相同的情况下,更加有效抑制基体板宽频振动与声辐射,尤其对350Hz以下的低频振动与噪声状况具有一定改善作用,并有助于实现阻尼结构的轻量化。同时,周期约束阻尼设计也可能会增大约束层的振动与噪声以及改变结构的声辐射效率。总体而言,周期性设计对于改善约束阻尼减振降噪性能具有积极意义。

具有强阻尼和白噪声的随机Plate方程解的渐近性(英文)

研究了具有强阻尼和白噪声的随机Plate方程解的渐近动力学行为,证明了解的渐近性并由此获得了方程随机紧吸引子的存在性.