Structural Damping Coefficients Research Articles

MAXIMUM SEISMIC RESPONSE PREDICTION BASED ON CAPACITY SPECTRUM METHOD FOR VIBRATION-CONTROLLED CEILING STRUCTURE EMPLOYED PULLEY MECHANISM

This paper proposes a new procedure for predicting the maximum seismic response based on the capacity spectrum method (CSM) for the passively controlled suspended ceiling structures named “Pulley Damper Ceiling System (PDCS)”. The structural system has a supplemental nonlinear viscous damper and a bilinear hysteretic damper in parallel with displacement amplification mechanisms of block and tackle pulley system. The single degree-of-freedom model of the PDCS is initially discussed. The accuracy of a simplified calculation method for obtaining the structural equivalent damping coefficient, determined by the sum of the inherent damping and the square root of sum of squares (SRSS) of each damping provided by the nonlinear viscous damper and the bilinear hysteretic damper, is verified by comparing with the full-scale shake table test results of the PDCS. Then, the pseudo capacity curve of the structure is generated by continuously plotting the transition of maximum force and displacement values under different amplitudes of sinusoidal waves. Finally, the availability of the response prediction based on proposed CSM procedure considering floor response spectrum (FRS) is examined by the comparison of time history analysis results, and the sufficient accuracy to evaluate the seismic response is confirmed.

Optimized Trapezoidal Acceleration Profiles for Minimum Settling Time of the Load Velocity

This paper deals with a method for generating symmetrical trapezoidal acceleration profiles for the motor of a vibrating system in rest-to-velocity motion. The aim was to significantly reduce the acceleration time and residual load vibration of lightly damped systems. Under undamped conditions, the analytical values of the jerk time are found to be in relation to the estimated natural frequency and the minimum value of the acceleration time is provided, also taking into account a limit value for motor acceleration. The analysis of the sensitive curves allows the designer to understand the magnitude of the residual vibration generated by an incorrect estimate of the natural frequency. Numerical simulations, with a closed-chain controlled motor and a zero or very small structural damping coefficient of the oscillating system, confirm the validity of the proposed method.

Wave propagation and vibration analysis of sandwich structure with a bio-based flexible core and composite face sheets subjected to visco-Pasternak foundation and magnetic field

In this study, the wave propagation and vibration analysis of sandwich structure with a bio-based flexible core and composite face sheets subjected to magnetic field are studied. In the present analysis, the material properties of composite face sheets are assumed viscoelastic based on Kelvin -Voigt model, and high-order sandwich panels theory is used for core modeling. The analysis of wave propagation and vibration of the sandwich structure is performed assuming complete adhesion between core and face sheets, and the governing equations of motion are derived by Hamilton's principle. Finally, the semi-analytical solution is applied to obtain the effects of the structural and foundation damping coefficients, different angles of the layers, the ratio of width to thickness, the ratio of the thickness of the core to the procedures, temperature variations, wave number, aspect ratios, elastic properties and number of layers on the wave propagation behavior of the sandwich plate for complete adhesion between layers. The results show that by increasing the ratio of the thickness of the core to the layers, the velocity of the wave propagation initially increases, and then decreases. Also, the application of the magnetic field has an increasing effect on the sandwich plate frequency. Finally, with the increase in the number of layers and the number of waves, the phase velocity increases, while the hardness of the system decreases when the temperature and damping coefficient rises.

Modified couple stress theory for wave propagation in viscoelastic sandwich microplates with FG-GPLRC core and piezoelectric face sheets as sensor and actuator

In the present investigation, wave propagation of the viscoelastic sandwich microplates with functionally graded graphene nanoplatelets’ reinforced composite (FG-GPLRC) core and piezoelectric face sheets as sensor and actuator has been analyzed by the refined zigzag theory (RZT). Electromagnetic field is exposed to core and piezoelectric layers. Young's modulus, mass density, and Poisson's ratio are calculated based on the modified Halpin–Tsai model and rule of mixtures because FG-GPLs are arranged as uniform, parabolic, and linear patterns along the thickness of core. In addition, viscoelastic properties of the structure are simulated by the Kelvin–Voigt model. The system is located on an orthotropic visco Pasternak medium. The modified couple stress theory (MCST) is applied to simulate the microscale effects of the structure. Hamilton's principle is utilized for deriving the motion equations. Phase velocity, cut-off, and escape frequencies are computed with an analytical solution. The influence of valuable parameters, such as geometrical dimensions of the system, magnetic field, external voltage, small scale parameter, viscoelastic structural damping coefficient, various foundation types, weight fraction, and different distributions of GPLs on phase velocity, will be studied. The results of this study have a significant effect on the design and fabrication of sandwich micro-structures used in various industrial equipment.

Identification of Mistuning Based on Forced Response Measurements and Assessment for a Real Compressor Blisk

Abstract We develop a novel method for the identification of mistuned blisks. The method relies on forced response measurements in a certain target frequency band. Modal stiffness deviations and an overall structural damping coefficient are obtained using a least-squares fit, fully consistent with a component-mode-based reduced-order model. To achieve a high frequency resolution in a very short test, we carry out rapid frequency sweeps and use a noise-robust, wavelet-based estimation of the steady-state response. The forcing is eliminated from the equations governing the mistuning parameters, and it is identified separately to reconstruct the forced response if requested. We first validate the method numerically and then apply it experimentally to a compressor blisk with an alternating (B-A) mistuning pattern. While most previous works on mistuning identification are limited to the lowest 1-2 mode families, we assess the method for the seventh (1C) and eighth (3T) mode family. Measured and reconstructed frequency responses are in good to very good agreement. We conclude that the developed method is useful to obtain high-quality estimates of mistuning parameters, which can then be used for vibration prediction.

Aeroservoelasticity of an Airfoil with Parametric Uncertainty and Subjected to Atmospheric Gusts

This paper presents the dynamics and adaptive control of an airfoil with structural stiffness and damping uncertainties, which is subjected to atmospheric gusts. The motion of the airfoil is modeled by three degrees of freedom (DOFs), namely, pitch, plunge, and flap. A flat spot or dead-zone-type stiffness is used for modeling the flap hinge free play. The nonlinear dynamics of the system without control and parametric uncertainty, where a cubic stiffness for pitch and a linear stiffness for plunge are considered, is examined. Numerical results show that the airfoil may become unstable via a Hopf bifurcation at a flow velocity well below the linear flutter speed; if the structural damping is not sufficiently high, it may also undergo chaotic motion. It was found that a proportional–derivative controller based on the partial feedback linearized system could effectively alleviate oscillations induced by gusts at flow velocities below and above the linear flutter speed. Next, an uncertain th-order polynomial stiffness for pitch and uncertain structural damping (modeled by viscous damping) coefficients for all DOFs are assumed. Considering such uncertainties, an adaptive controller with an estimation update law is designed to stabilize the airfoil subjected to gusts. A Lyapunov function is established to prove the stability of the closed-loop system. Simulation results demonstrate the effectiveness of the designed controller.

Nonlinear hygrothermal effects on the vibrations of a magnetostrictive viscoelastic laminated sandwich plate resting on an elastic medium

In engineering applications, composite structures supported by elastic foundations are being vastly utilized in various operating environmental conditions. The nonlinear hygrothermal effect on vibration analysis of a magnetostrictive viscoelastic laminated composite sandwich plate rested on two-parameter Pasternak’s foundations is studied in the present article. The material properties of the viscoelastic plate’s layers are considered based on the Kelvin–Voigt model. The governing equation system is derived according to Hamilton’s principle. The analytical solution is obtained to study influences of the hygrothermal change, half wave number, magnitude of the feedback control gain, aspect ratios, thickness ratio, and structural viscoelastic damping coefficients on vibration damping characteristics of the plate including the frequencies, the damping rate, and the deflection. The obtained results indicate that the natural frequency and deflection reduce with increasing the structural viscoelastic damping value. The plate takes a long time for suppressing its vibration due to increasing the hygrothermal factor.

Controlled motion of viscoelastic fiber-reinforced magnetostrictive sandwich plates resting on visco-Pasternak foundation

This article presents a controlled motion investigation of viscoelastic/fiber-reinforced/magnetostrictive/sandwich plates supported via visco-Pasternak foundations. The core of the plate is modeled as a Kelvin-Voigt viscoelastic model. The governing dynamic system is derived using Hamilton’s principle according to simple sinusoidal shear deformation plate theory. A simple feedback control system is utilized to control the structural vibration. Navier’s type solution of the system is obtained to study the influence of significant parameters, especially, the effect of the general thickness ratios, aspect ratio, the thickness ratio of the magnetostrictive layer to viscoelastic layer, sequence staking, foundations, viscoelastic structural damping coefficient, the magnitude of the feedback coefficient, and location of magnetostrictive layers on the vibrational behavior of studied sandwich plate. A comparison with previous studies is performed for validation of the corresponding numerical results and present formulation. Numerical outcomes indicate that increasing the thickness ratio of the viscoelastic layer to the magnetostrictive layer leads to improvement of the system vibration control, as well as the damping coefficient, grows and the damped natural frequency decreases with the increase of viscoelastic structural damping coefficient. The study maybe helps the designers and engineers in development of structural control systems in several applied fields.

Hygrothermal effect on vibration of magnetostrictive viscoelastic sandwich plates supported by Pasternak's foundations

In hygrothermal environment, vibration study of a simply supported smart sandwich plate embedded in an elastic substrate medium is presented in the present article. The sandwich plate contains layers of fiber-reinforced and magnetostrictive materials and core of viscoelastic material. The kinematic equations system is derived via employing Hamilton's principle with considering the transverse shear strains with and without the normal strains effect. Various numerical examples are carried out to study the effects of temperature rise, degree of moisture concentration, elastic foundations parameters, thickness ratio, aspect ratio, thickness ratio of magnetostrictive layer to viscoelastic layer, modes, lamination schemes, magnitude of the feedback coefficient, position of the magnetostrictive layers and viscoelastic structural damping coefficient on controlled motion and vibration characteristics of plate. Some observation about influences of the temperature and humidity concentrations on vibration characteristics of studied plate are presented in detail. The outcomes indicate that the hygrothermal environments have negative effects on vibration suppression of advanced composite structures especially the uniform hygrothermal distribution. The frequencies increase with increasing the viscoelastic structural damping coefficient and the foundation constants.

Vibration analysis of super-yachts: Validation of the Holden Method and estimation of the structural damping

The hull excitation generated by marine propellers constitutes one of the most significant vibration sources affecting comfort on passenger ships. Consequently, the evaluation of the propeller-generated excitation through reliable numerical tools during the preliminary stage of ship design is fundamental. The Holden Method (HM) is an empirical tool utilized to calculate the propeller-induced pressure distribution on a ship hull. The present paper validates the HM, which is applied to a twin-screw, 54-m super-yacht. Finite Element Analysis (FEA) is used to benchmark the HM numerical predictions against a set of full-scale vibration measures. The outcomes show that the magnitude of the propeller-induced dynamic excitation predicted by the HM is overestimated. Thereafter, the calibrated propeller-induced forces and the diesel engine excitation are applied to the FE model to perform a series of forced vibration analyses and estimate the global structural damping coefficient of the super-yacht. The study highlights the necessity of developing new empirical methodologies, analogous to the HM, to be applied to modern small luxury vessels.

A structural damping identification technique for coatings on blisks based on improved component mode mistuning model

Abstract Since the structural damping characteristics of damping coatings are much higher than that of the blisk substrate, the structural damping differences of coatings in each sector directly affect structural damping of the coated blisk. Therefore, for the coated blisk, it is very important to identify the structural damping differences caused by coating. A novel method for structural damping identification of coatings on the coated blisk is proposed. The component mode mistuning (CMM) model is improved for establishing reduced order model (ROM) of coated blisks. In the model, based on the consideration of blisk substrate, the coatings on each sector are decomposed into the mistuned substructures which are independent of each other. Based on this model, the identification formula for structural damping coefficients of coatings on each sector is deduced. A numerical case is given to illustrate the identification procedure. The vibration test methods for obtaining input parameters of damping identification are demonstrated by an actual case. The damping identifications of numerical case and actual case are carried out. The identification results shown that the identification method had high identification accuracy and can be well applied for the damping identification of the hard coating and viscoelastic coating.

Analysis of Viscoelastic Functionally Graded Sandwich Plates with CNT Reinforced Composite Face Sheets on Viscoelastic Foundation

In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown’s parameters and governing equations are reduced and also the using of shear correction factor is not necessary because the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. The governing equations obtained using Hamilton’s principle is solved for a rectangular viscoelastic sandwich plate. The effects of the main parameters on the vibration characteristics of the viscoelastic sandwich plates are also elucidated. The results show that the frequency significantly decreases with using foundation and increasing the viscoelastic structural damping coefficient as well as the damping coefficient of materials and foundation.

Size-Dependent Analysis of Orthotropic Mindlin Nanoplate on Orthotropic Visco-Pasternak Substrate with Consideration of Structural Damping

This paper discusses static and dynamic response of nanoplate resting on an orthotropic visco-Pasternak foundation based on Eringen’s nonlocal theory. Graphene sheet modeled as nanoplate which is assumed to be orthotropic and viscoelastic. By considering the Mindlin plate theory and viscoelastic Kelvin-Voigt model, equations of motion are derived using Hamilton’s principle which are then solved analytically by means of Fourier series -Laplace transform method. The parametric study is thoroughly accomplished, concentrating on the influences of size effect, elastic foundation type, structural damping, orthotropy directions and damping coefficient of the foundation, modulus ratio, length to thickness ratio and aspect ratio. Results depict that the structural and foundation damping coefficients are effective parameters on the dynamic response, particularly for large damping coefficients, where response of nanoplate is damped rapidly.

Wave propagation analysis in viscoelastic thick composite plates resting on Visco-Pasternak foundation by means of quasi-3D sinusoidal shear deformation theory

In this research, the wave propagation in a viscoelastic composite thick plate resting on a Visco-Pasternak foundation is analyzed by means of sinusoidal shear deformation theory (SSDT). The viscoelastic properties of the plate are considered by using Kelvin-Voigt model. The material properties of composite plate are assumed viscoelastic based on Kelvin-Voigt model. The governing equations of motion are derived by Hamilton's principle. The analytical solution is applied to obtain the effects of the structural and foundation damping coefficients, wave number, aspect ratios, elastic properties and number of layers on the wave propagation behavior of the viscoelastic composite plate including the dimensionless phase velocity, cut-off and escape frequencies. The obtained results indicate that the dimensionless phase velocity and natural frequency decrease with increasing the damping coefficient. Also, it is observed that the effect of layups on the phase velocity becomes more sensible for small wave numbers. However, the effect of the damping coefficient on the dimensionless phase velocity and natural frequency is only observed at large dimensionless wave numbers.

Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model

A higher-order nonlocal strain-gradient model is presented for the damped vibration analysis of single-layer graphene sheets (SLGSs) in hygrothermal environment. Based on Kirchhoff plate theory in conjunction with a higher-order (bi-Helmholtz) nonlocal strain gradient theory, the equations of motion are obtained using Hamilton's principle. The higher-order nonlocal strain gradient theory has lower- and higher-order nonlocal parameters and a material characteristic parameter. The presented model can reasonably interpret the softening effects of the SLGS, and indicates a reasonably good match with the experimental flexural frequencies. Finally, the roles of viscous and structural damping coefficients, small-scale parameters, hygrothermal environment and elastic foundation on the vibrational responses of SLGSs are studied in detail.

Nonlocal Thermal and Mechanical Buckling of Nonlinear Orthotropic Viscoelastic Nanoplates Embedded in a Visco-Pasternak Medium

This paper discusses the thermal and mechanical buckling of simply supported and clamped orthotropic viscoelastic graphene sheets (nanoplates) embedded in a visco-Pasternak elastic medium. For this purpose, the nonlocal continuum mechanical model is employed with two-variable plate theory. The material of the present nanoplate is assumed to be orthotropic and viscoelastic. The modified nonlinear Kelvin–Voigt viscoelastic model is utilized to formulate the constitutive relations depending on the viscoelastic structural damping coefficient. Moreover, the visco-Pasternak elastic medium is composed of both viscoelastic and shear layers. The viscoelastic layer includes a set of dashpots and elastic springs connected in parallel. In accordance with the two-variable theory, two governing equations are derived via Hamilton’s principle. These equations are analytically solved for various boundary conditions to obtain the explicit solution for critical buckling temperature and buckling load. The present buckling load and buckling temperature both are compared well with the published ones in the literature. In addition, various numerical studies are thoroughly carried out, concentrating on the influences of the plate geometric, nonlocal parameter, structural damping coefficient, elastic foundation parameters, foundation damping parameter and boundary conditions on the critical buckling load and temperature of the nanoplates. The results show that the involvement of the viscidity of the nanoplate and viscoelastic foundation enhances the strength of the nanoplates and therefore increases the resistance of them to external loads.

Non-linear vibration and resonance analysis of graphene sheet subjected to moving load on a visco-Pasternak foundation under thermo-magnetic-mechanical loads: An analytical and simulation study

Analytical solution for the steady-state response of a simply supported graphene sheet resting on a visco-Pasternak foundation under thermo-magnetic-mechanical loads based on the Eringen’s nonlocal theory and Kirchhoff-Love plate and Kelvin-Voigt models is studied in this research. The graphene sheet is subjected to the moving concentrated load with a constant velocity. At first, the partial differential equation is converted to the ordinary differential equation based on the Galerkin method. Then, the multiple scales method (a perturbation method) is applied to obtain the appropriate solutions. In order to verify of presented linear frequencies in this research, the molecular dynamics simulation (MD) is employed and the obtained results are compared with reported results in the other literatures. Results demonstrate that the jump phenomenon is postponed with the increase of the some parameters such as temperature changes, initial stress, magnetic field, linear stiffness, shear modulus of visco-Pasternak foundation and viscoelastic structural damping coefficients of Kelvin-Voigt model. But, the jump phenomenon occurs earlier with the increase in force amplitude and the nonlocal parameter. Moreover, it is found that the non-linear stiffness has an important role in studying of jump phenomenon for graphene sheet subjected to moving concentrated load. In the next section of the paper, frequency–response equations under super-harmonic and sub-harmonic excitations are investigated.

Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams

In this paper, free and forced vibration analysis of viscoelastic microcomposite beam reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) is studied using the modified couple stress theory (MCST). The material properties of micro composite beam by generalized rule of mixtures carbon nanotubes are estimated. In addition, these properties are stated as uniform, and functionally graded (FG) distributions in the thickness direction. Energy method and Hamilton’s principle are employed to establish the governing equations of motion for the vibration of viscoelastic damped micro composite beam reinforced by SWCNTs based on the Kelvin–Voigt model. The influences of material length scale parameter, structural damping coefficient and different distributions of SWCNTs on non-dimensional complex natural frequency and amplitude vibration of the viscoelastic micro composite beam are investigated. The results reveal that the lowest vibration amplitude of FG microcomposite beam by the FG-X and the highest occurs by FG-◊. Moreover, in the presence of external periodic load and the absence of structural damping coefficient, the vibration amplitude increases and FG microcomposite beam becomes unstable, even though the amplitude of vibration decreases with increasing structural damping coefficient. It is shown that the natural frequency of SWCNT reinforced composite is more than the frequency of multi-walled carbon nanotubes because SWCNT have more stiffness. In addition, the results illustrate that the experimental data by Lei et al. agree well with those predicted by the MCST in the present work.

Nonlocal piezo-hygrothermal analysis for vibration characteristics of a piezoelectric Kelvin–Voigt viscoelastic nanoplate embedded in a viscoelastic medium

This article presents vibration characteristics of a piezoelectric viscoelastic nanoplate under various boundary conditions embedded in a visco-Pasternak’s medium using nonlocal plate theory. The piezo-hygrothermal effects are all included. The hygrothermal piezoelectric nanoplate is made of orthotropic viscoelastic material. Also, the visco-Pasternak’s medium is modeled according to a Kelvin–Voigt foundation. A Two-variable sinusoidal shear deformation plate theory is presented. The imaginary and real parts of the eigenfrequency of piezoelectric viscoelastic nanoplates which are associated with viscoelastic foundation, nonlocal parameter, as well as the viscoelastic structural damping coefficient, are obtained. The effects of other parameters such as aspect ratio, side-to-thickness ratio, temperature change, and moisture concentration are all investigated. The predicted results are compared with the corresponding ones in the literature to check their validation. Additional results are presented and suitable discussions are made.

Size-Dependent Vibration of Axially Moving Viscoelastic Micro-Plates Based on Sinusoidal Shear Deformation Theory

In the present research, vibration and instability of axially moving viscoelastic micro-plate is investigated. Sinusoidal shear deformation theory (SSDT) is utilized due to its accuracy of polynomial functions than other plate theories. Based on Kelvin’s model, the viscoelastic structural properties of micro-plate are taken into consideration. The modified couple stress theory (MCST) is employed because of its capability to interpret the size effect. Using Hamilton’s principle, equations of motion are obtained and solved by hybrid analytical–numerical solution at different boundary conditions. Influences of various parameters such as size effect, axially moving speed, viscoelastic structural damping coefficient, thickness and aspect ratio on the vibration characteristics of moving viscoelastic micro-plate are discussed in detail. The results indicated that the critical speed of moving micro-plate is strongly dependent on the aspect ratio, therefore, the low aspect ratio should be considered for optimum design of this kind of moving micro-devices. The results of this investigation can be used in design and manufacturing of axially moving systems at the micro-scale such as micro-magnetic tapes.