Aseismic performances of constrained damping lining structures made of rubber-sand-concrete

Flexible damping technology considering aseismic materials and aseismic structures seems be a good solution for engineering structures.In this study,a constrained damping structure for underground tunnel lining,using a rubber-sand-concrete(RSC)as the aseismic material,is proposed.The aseismic performances of constrained damping structure were investigated by a series of hammer impact tests.The damping layer thickness and shape effects on the aseismic performance such as effective duration and acceleration amplitude of time-domain analysis,composite loss factor and damping ratio of the transfer function analysis,and total vibration level of octave spectrum analysis were discussed.The hammer impact tests revealed that the relationship between the aseismic performance and damping layer thickness was not linear,and that the hollow damping layer had a better aseismic performance than the flat damping layer one.The aseismic performances of constrained damping structure under different seismicity magnitudes and geological conditions were investigated.The effects of the peak ground acceleration(PGA)and tunnel overburden depth on the aseismic performances such as the maximum principal stress and equivalent plastic strain(PEEQ)were discussed.The numerical results show the constrained damping structure proposed in this paper has a good aseismic performance,with PGA in the range(0.2-1.2)g and tunnel overburden depth in the range of 0-300 m.

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping （PCLD）are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders＇ thin shell theory. Nu- merical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.

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.

DYNAMIC CHARACTERISTICS OF A CANTILEVER BEAM WITH PARTIAL SELF-SENSING ACTIVE CONSTRAINED LAYER DAMPING TREATMENT

The equations of motion governing the vibration of a cantilever beam with partially treated self-sensing active constrained layer damping treatment(SACLD) are derived by application of the extended Hamilton principle. The assumed-modes method and closed loop velocity feedback control law are used to analyze and control the flexural vibration of the beam nle influences of the bonding layer and piezoelectric layer thickness, material properties, placements of the Diezoelectric patch and feedback control parameters on the actuation ability of the vibration suppression are investigated. Some design considerations for pure passive, pure active control, and self-sensing active constrained layer damping are discussed.

VIBRATION CONTROL OF FLUID-FILLED PRISMATIC SHELL WITH ACTIVE CONSTRAINED LAYER DAMPING TREATMENTS

Active constrained layer damping （ACLD） combines the simplicity and reliability of passive damping with the light weight and high efficiency of active actuators to obtain high damping over a wide frequency band. A fluid-filled prismatic shell is set up to investigate the validity and efficiency of ACLD treatments in the case of fluid-structure interaction. By using state subspace identification method, modal parameters of the ACLD system are identified and a state space model is established subsequently for the design of active control laws. Experiments are conducted to the fluid-filled prismatic shell subjected to random and impulse excitation, respectively, For comparison, the shell model without fluid interaction is experimented as well. Experimental results have shown that the ACLD treatments can suppress vibration of the fluid-free and fluid-filled prismatic shell effectively. Under the same control gain, vibration attenuation is almost the same in both cases.

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping（i.e., ACLD）, combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.

Finite Element Modeling of a Fluid Filled Cylindrical Shell with Active Constrained Layer Damping

On the basis of the piezoelectric theory, Mindlin plate theory, viscoelastic theory and ideal fluid equation, the finite element modeling of a fluid-filled cylindrical shell with active constrained layer damping (ACLD) was discussed. Energy methods and Lagrange’s equation were used to obtain dynamic equations of the cylindrical shell with ACLD treatments, which was modeled as well with the finite element method. The GHM (Golla-Hughes-McTavish) method was applied to model the frequency dependent damping of viscoelastic material. Ideal and incompressible fluid was considered to establish the dynamic equations of the fluid-filled cylindrical shell with ACLD treatments, Numerical results obtained from the finite element analysis were compared with those from an experiment. The comparison shows that the proposed modeling method is accurate and reliable.

MULTI-LAYER PIEZOELECTRIC ACTUATOR AND ITS APPLICATION IN CONTROLLABLE CONSTRAINED DAMPING TREATMENT

A kind of novel multi-layer piezoelectric actuator is proposed and integrated with controllable constrained damping treatment to perform hybrid vibration control. The governing equation of the system is derived based on the constitutive equations of elastic, viscoelastic and piezoelectric materials, which shows that the magnitude of control force exerted by multi-layer piezoelectric actuator is the quadratic function of the number of piezoelectric laminates used but in direct proportion to control voltage. This means that the multi-layer actuator can produce greater actuating force than that by piezoelectric laminate actuator with the same area under the identical control voltage. The optimal location placement of the multi-layer piezoelectric actuator is also discussed. As an example, the hybrid vibration control of a cantilever rectangular thin-plate is numerically simulated and carried out experimentally. The simulated and experimental results validate the power of multi-layer piezoelectric actuator and indicate that the present hybrid damping technique can effectively suppress the low frequency modal vibration of the experimental thin-plate structure.

Finite element formulation of active constraining layer damping plate using laminate theory

A new finite element modeling method has been developed using laminate theory in a virtual work principle for active constraining layer damping plate. The frequency dependent modulus of viscoelastic material is described by introducing a few dissipation coordinates, known as GHM (Golla-Hughes-McTavish) method, a standard linear system with constant coefficient. The effectiveness of this method is validated by experimental model. Compared with conventional methods, this method can reduce a number of degrees of freedom and improve accuracy, provides a good model for analogous configurations.

Seismic isolation effect of lined circular tunnels with damping treatments

The Havriliak-Negami model for dynamic viscoelastic material behavior and Biot＇s theory of poroelasticity are employed to develop an exact solution for three-dimensional scattering effect of harmonic plane P-SV waves from a circular cavity lined with a multilayered fluid-filled shell of infinite length containing viscoelastic damping materials and embedded within a fluid-saturated permeable surrounding soil medium. The analytical results are illustrated with numerical examples where the effects of liner/coating structural arrangement, viscoelastic material properties, liner-soil interface bonding condition, seismic excitation frequency, and angle of incidence on the induced dynamic stress concentrations are evaluated and discussed to obtain representative values of the parameters that characterize the system. It is demonstrated that incorporating viscoelastic damping materials with a low shear modulus in the constrained layer configuration is an efficient means of enhancing the overall seismic isolation performance, especially for near-normally incident seismic shear waves where the amplitudes of induced dynamic stresses may be reduced by up to one-third of those without isolation in a relatively wide frequency range. Some additional cases are considered and good agreements with solutions available in the literature are obtained.

DEPENDENCE OF DAMPING CHARACTERISTICS OF A BEAM WITH DAMPING RUBBER MAGNETIC POWDER ON RUBBER PROPERTY

A cantilever beam with Damping Material Applying Rubber Magnetic Powder （DRM） has been investigated. Two methods are selected to hold DRM to a vibrating steel beam, one is to attach DRM by the magnetic attractive force （called DRM beam） and the other by adhesive bonding （called AB-DRM beam）. Different from the damping property of AB-DRM beam caused by shear deformation of damping material, the damping property of DRM beam is characterized by the sliding frictional loss together with the internal loss of damping material. The authors established a formulation to predict the damping characteristics of DRM beam, which was validated experimentally. It is found that rubber material loss factor β has a decisive influence on damping improvement of DRM beam versus AB-DRM beam. If β is smaller than the critical value around 0.8255, a valid range of vibratory amplitude always exists in which DRM beam can achieve better damping than AB-DRM beam; conversely, if β is bigger than the critical value, the valid range does not exist when slide occurs. Such results are used to determine the merits and limitations of DRM and develop design guidelines.

New matrix method for analyzing vibration and damping effect of sandwich circular cylindrical shell with viscoelastic core

Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented With an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.

TRANSFER MATRIX METHOD FOR ANALYZING VIBRATION AND DAMPING CHARACTERISTICS OF ROTATIONAL SHELL WITH PASSIVE CONSTRAINED LAYER DAMPING TREATMENT

The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.

MODELING AND DYNAMICS ANALYSIS OF SHELLS OF REVOLUTION BY PARTIALLY ACTIVE CONSTRAINED LAYER DAMPING TREATMENT

A new model for a smart shell of revolution treated with active constrained layer damping （ACLD） is developed, and the damping effects of the ACLD treatment are discussed. The motion and electric analytical formulation of the piezoelectric constrained layer are presented first. Based on the authors~ recent research on shells of revolution treated with passive constrained layer damping （PCLD）, the integrated first-order differential matrix equation of a shell of revolution partially treated with ring ACLD blocks is derived in the frequency domain. By virtue of the extended homogeneous capacity precision integration technology, a stable and simple numerical method is further proposed to solve the above equation. Then, the vibration responses of an ACLD shell of revolution are measured by using the present model and method. The results show that the control performance of the ACLD treatment is complicated and frequency-dependent. In a certain frequency range, the ACLD treatment can achieve better damping characteristics compared with the conventional PCLD treatment.

Constrained layer damping treatment of a model support sting

In transonic wind tunnel tests,the pulsating airflow is prone to induce the first order resonance of the sting support system.The resonance limits the wind tunnel test envelope,makes the test data inaccurate,and brings potential security risks.In this paper,a model support sting with constrained layer damping(CLD)treatment is proposed to reduce the first order resonance response.The CLD treatment mainly consists of material selection and geometric optimization processes.The damping performance of the optimized CLD sting is compared with an AISI 1045 steel sting with the identical diameter in laboratory.The frequency response curves of the CLD sting support system and the AISI 1045 steel sting support system are obtained by sine sweep tests.The test results show that the first order resonance response of the CLD sting support system is 37.3%of that of the AISI 1045 steel sting support system.The first order damping ratios are calculated from the frequency response curves by half power point method.It is found that the first order damping ratio of the CLD sting support system is approximately 2.6 times that of the AISI 1045 steel sting support system.

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。

基于传递函数方法的局部覆盖环状CLD圆柱壳动力学分析

采用传递函数方法对局部覆盖环状约束层阻尼(CLD)圆柱壳进行了动力学分析。基于Donnell薄壳简化,由Hamilton原理导出了局部覆盖CLD圆柱壳的运动方程和边界条件,通过Laplace变换并引入状态向量后,建立了系统的状态空间方程,利用传递函数方法求解方程得到了系统的固有频率、损耗因子和频响曲线。算例分析结果验证了该方法的有效性和精确性,且更适于处理黏弹性材料具有频变特性的问题。讨论了CLD覆盖率和黏弹层厚度对系统固有频率和损耗因子的影响,为局部覆盖CLD圆柱壳的优化设计奠定了基础。

部分覆盖PCLD圆柱壳振动分析的新矩阵方法

基于线弹性薄壳理论和线粘弹性理论,考虑被动约束层阻尼(PCLD)的剪切耗能以及层间的相互作用,首次导出了适用于最一般情况的环状覆盖PCLD圆柱层合壳在谐激励作用下的整合一阶常微分矩阵方程,它的12个状态变量具有明确的物理意义,而且由层合壳完整的位移量和内力量组成,应用范围很广。通过将该模型和齐次扩容精细积分法结合构建了一种高效率和高精度的半解析半数值方法,并与解析解结果进行了对比,验证了该方法的正确性和有效性,借此还分析了PCLD覆盖率和覆盖位置对频率响应函数的影响。

SCLD板模态控制模型及振动控制

为有效抑制薄板在外界激励下的低频振动,对机敏约束层阻尼(SCLD)结构进行了主动振动控制研究.首先,考虑了黏弹性材料随温度与频率变化的阻尼特性,结合GHM阻尼模型建立了耦合系统有限元动力学分析模型;其次,考虑到结构动力学模型自由度庞大,采用物理坐标下自由度动力缩聚和状态方程下复模态截断进行了两次降阶,并通过复模态空间向实模态空间转换,得到了低维实模态控制模型;最后,通过模态实验验证了理论模型,并基于低阶控制模型设计了振动控制器,证明了研究方法的正确性.研究结果表明,采用本文的组合降阶方法可以有效地对SCLD结构进行降阶,对模态控制模型主动控制取得了良好控制效果:在单位阶跃激励下,振动响应衰减时间从0.20 s缩短为0.08 s;在随机白噪声激励作用下,振动响应均方根值降低了39.65%.