A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain. The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response). Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy. This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy.

DYNAMIC BEHAVIOR ANALYSIS OF VISCOELASTICALLY DAMPED STRUCTURES

Analysis method for the dynamic behavior of viscoelastically damped structures isstudied.A finite element model of sandwich beams with eight degrees of freedom is set upand the finite element formulation of the equations of motion is given for theviscoelastically damped structures.An iteration method for solving nonlinear eigenvalueproblems is suggested to analyze the dynamic behavior of viscoelastically damped structures.The method has been applied to the complex model analysis of a sandwich cantileverbeam with viscoelastic damping material core.

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.

On the Dynamics of a Viscoelastic Fluid-Conveying Nanotube

The objective of the presented study is to perform a vibration analysis and investigate the stability of a viscoelastic-fluid conveying pipe with an intermediate support.The mathematical model is elaborated in the framework of the Euler-Bernoulli beam theory in combination with the Kelvin-Voight viscoelastic approach.The resulting differential equation of motion and the related boundary conditions and compatibility conditions in the mid-span support are solved analytically using a power series method.The results show that an intermediate support located atξ_(s)=0.1 andξ_(s)=0.5 increases the critical velocity up to 35%and 50.15%,respectively.Also,the non-dimensional critical velocity for an intermediate support atξ_(s)=0.1 is 4.83.

Axial mechanical experiments of unbonded flexible pipes

Axial structural damping behavior induced by internal friction and viscoelastic properties of polymeric layers may have an inevitable influence on the global analysis of flexible pipes.In order to characterize this phenomenon and axial mechanical responses,a full-scale axial tensile experiment on a complex flexible pipe is conducted at room temperature,in which oscillation forces at different frequencies are applied on the sample.The parameters to be identified are axial strains which are measured by three kinds of instrumentations:linear variable differential transformer,strain gauge and camera united particle-tracking technology.The corresponding plots of axial force versus axial elongation exhibit obvious nonlinear hysteretic relationship.Consequently,the loss factor related to the axial structural damping behavior is found,which increases as the oscillation loading frequency grows.The axial strains from the three measurement systems in the mechanical experiment indicate good agreement,as well as the values of the equivalent axial stiffness.The damping generated by polymeric layers is relatively smaller than that caused by friction forces.Therefore,it can be concluded that friction forces maybe dominate the axial structural damping,especially on the conditions of high frequency.

Mixed Finite Volume Element Method for Vibration Equations of Beam with Structural Damping

In this paper, for the initial and boundary value problem of beams with structural damping, by introducing intermediate variables, the original fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed. Numerical examples are provided to confirm the theoretical results. In the end, we test the value of δ to observe its influence on the model.

Development and optimization of a novel grain flow sensor based on PVDF piezoelectric film

A novel grain flow sensor consists of an impact plate and a PVDF(Polyvinylidene Fluoride)piezoelectric film was developed in this research.The kinetic model of the grain flow sensor was built to analyze the steady and transient vibration disturbances which had a significant influence on performance of the sensor,and the results showed that damping ratio of the sensor was the key factor to improve accuracy of the sensor.To maximize damping ratio of the sensor,the thickness of the impact plate and damping material were optimized according to a loss factor model of the free damping structure.The optimized results indicated the most appropriate thickness ratio of damping material and the impact plate was 6.A test rig equipped with the novel grain flow sensor and weight sensors which could simulate field situations was built to investigate the performance of the sensor,on which test experiments under different feed flows were conducted.The results showed that the maximum error of the sensor was 3.02%and the mean error was 2.15%,which revealed that the novel grain flow sensor could be used to measure grain flow.Comparing with conventional grain flow sensors,the novel grain flow sensor has the features of high accuracy,simple structure and flexible signal processing methods.

A novel structural modification to eliminate the early coupling between bending and torsional mode shapes in a cable stayed bridge

In this paper, a novel structural modification approach has been adopted to eliminate the early coupling between the bending and torsional mode shapes of vibrations for a cable stayed bridge model generated using ABAQUS software. Two lateral steel beams are added to the middle span of the structure. Frequency analysis is dedicated to obtain the natural frequencies of the first eight mode shapes of vibrations before and after the structural modification approach. Numerical simulations of wind excitations are conducted for the 3D model of the cable stayed bridge with duration of 30 s supporting on real data of a strong wind from the literature. Both vertical and torsional displacements are calculated at the mid span of the deck to analyze both the bending and the torsional stiffness of the system before and after the structural modification. The results of the frequency analysis after applying lateral steel beams declared a safer structure against vertical and torsional vibrations and rarely expected flutter wind speed. Furthermore, the coupling between the vertical and torsional mode shapes has been removed to larger natural frequencies magnitudes with a high factor of safety. The novel structural approach manifested great efficiency in increasing vertical and torsional stiffness of the structure.

Damping of Ni–Mn–Ga epoxy resin composites

By combining the advantages of effcient damping and high mechanical properties,Ni-Mn-Ga particle composites have a very good prospect for applications in damping structure design.In this paper,a ferromagnetic shape memory alloy Ni-Mn-Ga composite is prepared.Ni-Mn-Ga particle/bisphenol-A epoxy composite cantilever beam vibration tests under a magnetic feld and without the magnetic feld are conducted to analyze the structural damping ratios n.Meanwhile,the damping characteristics of the Ni-Mn-Ga composite are studied through the axial loading-unloading method and the acoustic emission signals method.The damping coeffcient of the composite for different Ni-Mn-Ga volume fractions is obtained.The interface properties of the composite are discussed by micro examination and axial loading.The relationships between the damping of the composite and that of the component materials are discussed.The specifc damping capacity（SDC）and acoustic emission counts diagram of different specimens with different Ni-Mn-Ga volume fractions are analyzed.

A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems

Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems.This paper presents a novel perturbative iteration(PI)algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems.Mathematical formulations of the proposed method are developed and based on these formulations,a computer algorithm is devised.Extensive numerical case examples are given to demonstrate the practicality of the proposed method.When all modes are included,the method is exact and when only a subset of modes are used,very accurate results are obtained.

BOUNDARY FEEDBACK CONTROL OF ELASTIC BEAM EQUATION WITH STRUCTURAL DAMPING AND STABILITY

In this paper, we consider the partial differential equation of an elastic beam with structuraldamping by boundary feedback control. First, we prove this closed system is well--posed; then weestablish tbe exponential stability for this elastic system by using a theorem whichbelongs to F. L.Huang; finally, we discuss the distribution and multiplicity of the spectrum of this system. Theseresults are very important and useful in practical applications.