Effect Of Structural Damping Research Articles

Seismic Control Strategy of a Multi-Story Subway Station Based on Probability Density Evolution Method

The method to protect the whole station structure by installing flexible devices at the column end has been proved to be effective in typical station structures. However, the damping effects and application of this method to multi-story subway station structures still need further study. In this paper, a stochastic analysis method, probability density evolution method (PDEM), is adopted to estimate the damping effect of a four-story subway station structure with lead rubber bearings (LRBs) installed in the central column. Stochastic analysis results show that the internal forces and plastic energy dissipation of columns installed LRBs are greatly reduced and the reliability is improved. Internal forces and plastic energy dissipation of columns without the installation of LRBs increase and the reliability decrease. There is little difference in structural deformation and plastic energy dissipation of structural components when LRB is installed in the middle of the column or at the column ends. When LRBs are installed only in some of the stories, the overall reliability of the structure is lower than that of the structure without LRB. When LRBs are installed in the columns of all stories, the structural reliability is higher than that of the structure without LRB. Based on the above results, to obtain better seismic control effect by installing LRBs, the multi-story subway station structure should be installed with LRBs in the columns of all stories, and LRBs can be installed at the upper, middle and lower end of the columns.

Numerical Experiments on Time Step Selection in Linear Dynamic Analysis of Structures

ABSTRACT The complex nature of the exciting force in earthquake engineering applications mandates employing numerical methods to obtain the response of structures to ground motions. Several numerical methods are in use in the field of earthquake engineering and structural dynamics to solve the ordinary differential equation of motion. Previous studies assumed that the appropriate time step for numerical schemes can be selected as a constant fraction of natural period of the system disregarding the period range. This study is concerned with assessing, through a comprehensive numerical experiment; the numerical error of the most commonly used schemes in structural dynamics applications and assessing the appropriateness of each method for different excitations and damping conditions using different natural period ranges. The current investigation involved testing the central difference method, Newmark, HHT, and HHT1 methods. The four methods were tested for linear single degree of freedom (SDOF) oscillator. Three different exciting forces were used to test the schemes; half-sine pulse wave, harmonic force, and actual ground motion record. Three natural periods were used to conduct the experiment, representing short, medium, and long period systems including the resonant condition. Three structural damping ratios, representing lightly, moderately, and heavily damped systems, were used to assess the structural damping effect on the accuracy associated with selected time steps. A new displacement error norm was introduced to define the accuracy of numerical schemes. The results of this investigation indicated that the commonly used assumption of time step as a constant fraction of natural period of the system, even for SDOF linear oscillator, disregarding the period range could result in significant numerical errors. The study also confirmed the significant effect of structural damping ratio on the accuracy of the numerical schemes. The paper also presents a recommendation matrix for the most appropriate time step for each scheme for different applications and structural conditions. The results of the current investigation are strictly limited to linear systems.

Nonlinear Dynamical Responses of Rotary Cylindrical Shells with Internal Resonance

The nonlinear forced vibration response of a thin, elastic, rotary cylindrical shell to a harmonic excitation is investigated in this study. Nonlinearities due to the large-amplitude shell motion are considered by using Donnell’s nonlinear shallow-shell theory, with consideration of the effect of viscous structural damping. Different from the conventional Donnell’s nonlinear shallow-shell equations, an improved nonlinear model without employing the Airy stress function is utilized to study the nonlinear dynamics of thin shells. The system is discretized using the Galerkin method, while a model involving two degrees of freedom and allowing for the traveling wave response of the shell is adopted. The method of harmonic balance is applied to study the nonlinear dynamic responses of the two-degree-of-freedom system. In addition, the stability of steady-state solutions is analyzed in detail. Finally, results are given for exploring the effects of different parameters on the nonlinear dynamic response with internal resonance.

Effect of distributed axial loading on dynamic stability and buckling analysis of a viscoelastic DWCNT conveying viscous fluid flow

In this article, dynamic stability and buckling analysis of a double-walled carbon nanotube (DWCNT) under distributed axial force are investigated. The visco-Pasternak model is used to simulate the elastic medium between nanotubes considering the effects of spring, shear and damping of the elastic medium. This system is conveying viscous fluid, and the relevant force is calculated by modified Navier–Stokes relation considering slip boundary condition and Knudsen number. The nanostructure is modeled as two orthotropic moderately thick cylindrical shells, and the effects of small-scale and structural damping are accounted based on modified couple stress and Kelvin–Voigt theories. The governing equations and boundary conditions are developed using Hamilton’s principle and solved with the aid of Navier and generalized differential quadrature methods. In this research, the dynamic instability occurs in the viscoelastic DWCNT conveying viscous fluid flow as the natural frequency becomes equal to zero. The results show that the velocity of viscous fluid flow, axial load, mode number, length-to-radius ratio, radius-to-thickness ratio, visco-Pasternak foundation and the boundary conditions play important roles on the critical pressure and natural frequency of the viscoelastic DWCNT conveying viscous fluid flow under axial force.

Combination resonance analysis of FG porous cylindrical shell under two-term excitation

This paper presents the combination resonances of FG porous (FGP) cylindrical shell under two-term excitation. The effect of structural damping on the system response is also considered. With regard to classical plate theory of shells, von-Karman equation and Hook law, the relations of stress-strain is derived for shell. According to the Galerkin method, the discretized motion equation is obtained. The combination resonances are obtained by using the method of multiple scales. Four types of FGP distributions consist of uniform porosity, non-symmetric porosity soft, non-symmetric porosity stiff and symmetric porosity distribution are considered. The influence of various porosity distributions, porosity coefficients of cylindrical shell and amplitude excitations on the combination resonances for FGP cylindrical shells is investigated.

Nonlinear primary resonance of imperfect spiral stiffened functionally graded cylindrical shells surrounded by damping and nonlinear elastic foundation

In this paper, an analytical method is used to study the nonlinear primary resonance of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal stiffeners. The SSFG cylindrical shell is surrounded by linear and nonlinear elastic foundation and the effect of structural damping on the system response is also considered. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. Three-parameter nonlinear elastic foundation model is consists of two-parameter linear elastic foundation (Winkler and Pasternak) and one hardening/softening cubic nonlinearity parameter. Based on the von Karman nonlinear equations and the classical plate theory of shells, the strain–displacement relations are derived. The smeared stiffener technique is used to the model of the internal stiffeners. Using the Galerkin method, the partial differential equations of motion are discretized. The nonlinear primary resonance is analyzed by means of the multiple scales method. The effects of various geometrical characteristics, material parameters and elastic foundation coefficients are investigated on the nonlinear primary resonance.

Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment

The current work suggests mathematical model for the seismic response of submerged cylindrical shells subjected to hygrothermal load. The structural damping effects are considered based on Kelvin-Voigt model. The cylindrical shell is reinforced by functionally graded (FG)-carbon nanotubes (CNTs) and carbon fibers where the Halpin-Tsai model is used for calculating the effective material properties of the structure. The acoustic wave equation is utilized for the effect of the fluid around the structure. The problem is framed combining shell motion equations with the acoustic wave equation where the fluid-loaded terms are considered with Hankel function of second kind. The equations of motion are derived based on Reddy shear deformation theory (RSDT) in conjunction with energy method and Hamilton's principle. The dynamic deflection of the structure is obtained using differential quadrature method (DQM) and Newmark approach. The effects of fluid, boundary condition, thermal load, moisture changes, structural damping parameter, length to thickness ratio of shell, CNTs volume percent and distribution type are shown on the dynamic deflection of the structure. The results show that with increasing the CNTs volume percent, the dynamic deflection decreases. In addition, the FG-X type (FGX) distribution of CNTs for the submerged cylindrical shell is the best choice among the FG-O type (FGO), FG-V type (FGV) and uniform distributions. Furthermore, the maximum dynamic deflection of the structure increases where the structure is in the hygrothermal environment.

Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory

Smart control and vibration analysis of laminated sandwich truncated conical shells with piezoelectric layers as sensor and actuator are presented in this paper. The core of the sandwich structure is reinforced by carbon fibers and carbon nanotubes (CNTs) where the effective material properties are obtained by Halpin–Tsai model. The actuator layer is subjected to external voltage and a Proportional-Derivative (PD) controller is used for sensor output control. Based on Kelvin–Voigt model, the structural damping effects are assumed. The formulation of the problem is based on the layerwise first order shear deformation theory (FSDT). Considering the continuity of the displacements and the internal stress fields at the interfaces of the layers, the motion equations are derived utilizing Hamilton's principle. The solution of the problem is carried out by differential quadrature method (DQM) for calculating the frequency of the smart sandwich structure. The effects of different parameters such as structural damping, weight percent of CNTs, boundary conditions, geometrical parameters of the structure, semi vertex angle of the cone, external voltage, temperature and moisture changes are examined on the vibration response of the smart sandwich structure. Numerical results indicate that using a PD controller can increase the frequency of the structure. In addition, the hygrothermal load decreases the vibration frequency of the system.

Effect of structural damping on the tuning between piezoelectric wafer active sensors and Lamb waves

Piezoelectric wafer active sensors have been widely used for Lamb-wave generation and acquisition. For selective preferential excitation of a certain Lamb-wave mode and rejection of other modes, the piezoelectric wafer active sensor size and the excitation frequency should be tuned. However, structural damping depends on the structure material and the excitation frequency and it will affect the amplitude response of piezoelectric wafer active sensor–excited Lamb waves in the structure, that is, tuning curves. Its influence on the piezoelectric wafer active sensor tuning reflects the effect of structural health monitoring configuration considered in the excitation. Therefore, it is important to have knowledge about the effect of structural damping on the tuning between piezoelectric wafer active sensor and Lamb waves. In this article, the analytical tuning solution of undamped media is extended to damped materials using the Kelvin–Voigt damping model, in which a complex Young’s modulus is utilized to include the effect of structural damping as an improvement over existing models. This extension is particularly relevant for the structural health monitoring applications on high-loss materials, such as metallic materials with viscoelastic coatings and fiber-reinforced polymer composites. The effects of structural damping on the piezoelectric wafer active sensor tuning are successfully captured by the improved model, with experimental validations on an aluminum plate with adhesive films on both sides and a quasi-isotropic woven composite plate using circular piezoelectric wafer active sensor transducers.

The semi-analytical method for damping of tubular transition layer damping structure

To solve the limited vibration consumption of the traditional tubular damping structure (TTDS), the tubular transition layer damping structure (TTLDS) is proposed; Based on viscoelastic materials and theories of thin cylindrical shells, the governing equation, the first order matrix differential equation describing vibration of TTLDS under harmonic excitation, is derived by considering the interaction between all layers and the dissipation caused by the shear deformation for transition layer and damping layer. By using the extended homogeneous capacity precision integration method to solve the control equation, a semi-analytical method for studying the vibration and damping characteristics of TTLDS is given. By way of comparison, the correctness of the method provided in paper is verified. At last, the influence of thickness, material and location of transition layer on damping effect is analyzed. The results show that the change for the thickness or material of the transition layer can make the structural damping effect change greatly, while the change for location of the transition layer plays only a few roles on the structural damping effect.

Experimental study on wake-induced vibrations of two circular cylinders with two degrees of freedom

Wind tunnel tests are conducted to investigate wake-induced vibrations of two circular cylinders with a center-to-center spacing of 4 diameters and attack angle varying from 0 to 20 for Reynolds numbers between 18,000 and 168,800. Effects of structural damping, Reynolds number, attack angle and reduced velocity on dynamic responses are examined. Results show that wake-induced vortex vibrations of the downstream cylinder occur in a wider range of the reduced velocity and have higher amplitudes in comparison to the vortex-induced vibration of a single circular cylinder. Two types of wake-induced instability phenomena with distinct dynamic characteristics are observed, which may be due to different generation mechanisms. For small attack angles like 5 and 10, the instability of the downstream cylinder characterizes a one-degree-of-freedom (1-DOF) oscillation moving in the across-wind direction. For a large attack angle like 20, the instability characterizes a two-degree-of-freedom (2-DOF) oscillation with elliptical trajectories. For an attack angle of 15, the instability can transform from the 1-DOF pattern to the 2-DOF one with the increase of the Reynolds number. Furthermore, the two instabilities show different sensitivity to the structural damping. The 1-DOF instability can be either completely suppressed or reduced to an unsteady oscillation, while the 2-DOF one is relatively less sensitive to the damping level. Reynolds number has important effects on the wake-induced instabilities.

Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: Dynamic buckling analysis

Dynamic buckling of viscoelastic sandwich truncated nanocomposite conical shell subjected to moisture, temperature and magnetic field is presented in this paper. This class of structures is of great interest due to its extensive use in aerospace applications. The layers of the structure are made from a multiphase nanocomposite consist of polymer-carbon nanotubes (CNT)-carbon fibers. The micromechanics and Halpin–Tsai equations in hierarchy are applied for calculating the effective material properties of the multiphase nanocomposite layers. The structural damping effects are considered based on Kelvin–Voigt theory. The surrounding medium is simulated using visco-Pasternak model. Utilizing the first order shear deformation theory (FSDT), energy method and Hamilton's principle, the motion equations are derived. Differential quadrature method (DQM) and Bolotin's method are applied for solution of the motion equations to obtain the dynamic instability region (DIR) of the structure. The effects of various parameters such as structural damping, viscoelastic medium, magnetic field, number of layers, volume fraction of CNTs, temperature and moisture changes as well as boundary conditions on the DIR of the structure are studied. The results reveal that by increasing the moisture and temperature changes, the DIR will be happened at lower excitation frequencies.

Dynamic instability response in nanocomposite pipes conveying pulsating ferrofluid flow considering structural damping effects

This paper deals with the dynamic stability of nanocomposite pipes conveying pulsating ferrofluid. The pipe is reinforced by carbon nanotubes (CNTs) where the agglomeration of CNTs are considered based on Mori-Tanaka model. Due to the existence of CNTs and ferrofluid flow, the structure and fluid are subjected to axial magnetic field. Based on Navier-Stokes equation and considering the body forced induced by magnetic field, the external force of fluid to the pipe is derived. For mathematical modeling of the pipe, the first order shear deformation theory (FSDT) is used where the energy method and Hamilton\'s principle are used for obtaining the motion equations. Using harmonic differential quadrature method (HDQM) and Bolotin\'s method, the motion equations are solved for calculating the excitation frequency and dynamic instability region (DIR) of the structure. The influences of different parameters such as volume fraction and agglomeration of CNTs, magnetic field, structural damping, viscoelastic medium, fluid velocity and boundary conditions are shown on the DIR of the structure. Results show that with considering agglomeration of CNTs, the DIR shifts to the lower excitation frequencies. In addition, the DIR of the structure will be happened at higher excitation frequencies with increasing the magnetic field.

Low velocity impact response and dynamic stresses of thick high order laminated composite truncated sandwich conical shell based on a new TDOF spring–mass–damper model considering structural damping

This paper deals with the low velocity impact response and dynamic stresses of composite sandwich truncated conical shells (STCS) with compressible or incompressible core. Impacts are assumed to occur normally over the top face-sheet and the interaction between the impactor and the structure is simulated using a new equivalent three-degree-of-freedom (TDOF) spring-mass-damper (SMD) model. The displacement fields of core and face sheets are considered by higher order and first order shear deformation theory (FSDT), respectively. Considering continuity boundary conditions between the layers, the motion equations are derived based on Hamilton's principal incorporating the curvature, in-plane stress of the core and the structural damping effects based on Kelvin-Voigt model. In order to obtain the contact force, the displacement histories and the dynamic stresses, the differential quadrature method (DQM) is used. The effects of different parameters such as number of the layers of the face sheets, boundary conditions, semi vertex angle of the cone, impact velocity of impactor, trapezoidal shape and in-plane stresses of the core are examined on the low velocity impact response of STCS. Comparison of the present results with those reported by other researchers, confirms the accuracy of the present method. Numerical results show that increasing the impact velocity of the impactor yields to increases in the maximum contact force and deflection, while the contact duration is decreased. In addition, the normal stresses induced in top layer are higher than bottom layer since the top layer is subjected to impact load. Furthermore, with considering structural damping, the contact force and dynamic deflection decrees.

Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects

This study gives a numerical work on dynamic response of cylindrical shells submerged in an incompressible fluid subjected to earthquake, thermal and moisture loads. The cylindrical shell is reinforced by carbon nanotubes (CNTs) where the Mori-Tanaka model is used for calculating the effective material properties of the structure considering agglomeration effects. The effect of the fluid is assumed using the acoustic wave equation. The structural damping effect is considered using Kelvin-Voigt model. Sinusoidal shear deformation shell theory (SSDT) is utilized in the shell dynamical equations based on energy method and Hamilton’s principle. The problem is framed combining shell motion equations with the acoustic wave equation where the fluid-loaded terms are considered with Hankel function of second kind. Differential quadrature method (DQM) and Newmark approach are employed to solve the shell problem. The influences of fluid, boundary condition, thermal load, moisture changes, boundary condition, structural damping parameter, length to thickness ratio of shell, CNTs volume percent and agglomeration are shown on the dynamic deflection of the structure. The results show that increasing the CNTs volume percent, the dynamic deflection decreases while considering the CNTs agglomeration leads to increase in the dynamic deflection of the structure.

Effects of structural damping on wind-induced responses of a 243-meter-high solar tower based on a novel elastic test model

The effects of structural damping to the responses of the vortex-induced vibration of solar tower should be investigated carefully to provide a reference for the structural designers. A new type of elastic test model for a 243-meter-high solar tower is particularly designed and manufactured. A core beam is designed in the test model to simulate the stiffness of the concrete structure, and a coat with baseplate (like a cup) is designed to simulate the steel structure. A structural damping ratio as low as 0.3% is realized, and four level of structural damping ratio, including 0.7%, 1.0%, 1.5% and 2.0%, can be conveniently achieved. A series wind tunnel tests are carried out to investigate the features of the wind-induced responses of the solar tower at the structural damping level of 0.3%, 0.7%, 1.0%, 1.5% and 2.0%. The results show that obvious vortex-induced vibration could be found within wind velocity range of U10 = 21.5–28.4 m/s for the structural damping ratio of 0.7%. At this time, the highest vortex-induced responses (at the wind velocity of U10 = 23.2 m/s), including acceleration at the top, base shear and base moment, are far larger than those at the design wind velocity (U10 = 41.0 m/s). Moreover, it appears that the wind-induced responses in cross-wind direction are far higher than those in the along-wind direction. The most important point is that the base shear and moment in the cross-wind direction measured from wind tunnel tests are far higher than the values obtained from the Code ACI 307–08. The wind-induced responses of the solar tower are extremely sensitive to the structural damping of the test model. For example, the highest acceleration, base shear and moment in cross-wind direction are respectively reduced by about 67%, 74%, 71% when structural damping ratio slightly increases from 0.7% to 1.0%. It seems that the vortex-induced vibration of the solar tower could be effectively mitigated if the structural damping ratio could be enhanced over 1.0%.

Rotordynamic Energy Expressions for General Anisotropic Finite Element Systems

It is often desirable to identify the critical components that are active in a particular mode shape or an operational deflected shape (ODS) in a complex rotordynamic system with multiple rotating groups and bearings. The energy distributions can help identify the critical components of a rotor bearing system that may be modified to match the design requirements. Although the energy expressions have been studied by researchers in the past under specific limited conditions, these expressions require computing the displacements and velocities of all degrees-of-freedom (DOFs) over one full cycle. They do not address the overall time dependency of the energies and energy distributions, and their effect on the interpretation of a mode shape or an ODS. Moreover, a detailed finite element formulation of these energy expressions including the effects of anisotropy, skew-symmetric stiffness, viscous and structural damping have not been identified by the authors in the open literature. In this article, a detailed account of orbit characteristics and planarity for isotropic and anisotropic systems is presented. The effect of orbit characteristics on the energy expressions is then discussed. An elegant approach to obtaining time-dependent kinetic and strain energies of a mode shape or an ODS directly from the structural matrices and complex eigenvectors/displacement vectors is presented. The expressions for energy contributed per cycle by various types of damping and the destabilizing skew-symmetric stiffness that can be obtained in a similar way are also shown. The conditions under which the energies and energy distributions are time-invariant are discussed. An alternative set of energy expressions for isotropic systems with the DOFs reduced by half is also presented.

Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm

Optimization of embedded piezoelectric sandwich nanocomposite plates for dynamic buckling analysis is presented in this work based on Grey Wolf algorithm. The Grey Wolf algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. In addition, the main steps of hunting, searching for prey, encircling prey, and attacking prey are employed. The structure is composed of a laminated functionally graded-carbon nanotubes reinforced layers as core integrated with sensor and actuator layers considering structural damping effects. Two-dimensional magnetic and 3D electric fields are applied to core and piezoelectric layers, respectively. Sinusoidal shear deformation theory is utilized for obtaining the motion equations and differential quadrature method is applied for solution. Also, a proportional–derivative controller is employed to control the dynamic behavior of the structure. Finally, the optimum designs for the structure are evaluated using proposed Grey Wolf algorithm based on the geometrical parameters of plate, applied voltage, controller parameters, volume fraction of carbon nanotubes, spring, and shear constants of foundation. Numerical results indicate that by applying the positive voltage and transverse magnetic field the optimum dimensionless frequency of the system decreases.

Low-velocity impact response of sandwich conical shell with agglomerated single-walled carbon nanotubes-reinforced face sheets considering structural damping

In the present article, dynamic response of a thick sandwich truncated conical shells with a transversely flexible/inflexible core and nanocomposite face sheets subjected to low-velocity impact was studied. The face sheets are reinforced with single-walled carbon nanotubes where the agglomeration effects are considered based on Mori–Tanaka model. A new equivalent three-degree-of-freedom spring-mass-damper model is utilized to describe the contact force between impactor and sandwich truncated conical shells. Based on an improved higher order sandwich panel theory, the equations of motion are derived by Hamilton’s principal incorporating the curvature, in-plane stress of the core and the structural damping effects. Differential quadrature method is applied for obtaining the contact force and displacement histories. After validity of the present study, the effects of the single-walled carbon nanotubes volume fraction, single-walled carbon nanotubes agglomeration, number of the layers of the face sheets, boundary conditions, semi-vertex angle of the cone, impact velocity, and mass of impactor on the low-velocity impact response of the nanocomposite structure are studied in details. Numerical results show that increasing the volume fraction of single-walled carbon nanotubes can reduce the amplitude of the dynamic response of the nanocomposite structure.

Analytical Prediction of Stability Lobes for Passively Damped Boring Bars

AbstractThe present article proposes the closed-form solution for analytical prediction of stability lobes in internal turning process. The passively damped boring bar is modeled as a cantilevered Euler-Bernoulli beam with constant cross sectional properties in which a Tuned Mass Damper (TMD) is embedded for the purpose of chatter suppression. The non-dimensional equations of motion are derived, assuming that the boring bar dynamics is well-represented by the fundamental mode of vibration. The stability of equivalent two-DOF dynamic model, i.e. boring bar with TMD, is analyzed in frequency domain. The closed- form expressions for critical depth of cut and spindle speed are presented in terms of boring bar and TMD characteristics. The proposed solution considers the effects of boring bar's structural damping and cutting geometry of insert on the stability behavior of passively damped cutting tool. An unconstrained optimization method is utilized to compute the most optimal set of tuning parameters for anti-chatter TMD. In order to improve the boundary of stability in a global sense, maximization of minimum critical depth of cut is selected as the objective of optimization. The superior performance of anti-chatter TMD is compared to H∞and H2TMDs for a wide range of applications. Moreover, the achieved results show a remarkable improvement of stability boundary compared to recent research works.