Theoretical Frequency Response Functions Research Articles

Quantification of the human–structure interaction effect through full-scale dynamic testing: The Folke Bernadotte Bridge

An analytical expression for the frequency response function of a coupled pedestrian-bridge system is presented and evaluated using an experimental measurement campaign performed on the Folke Bernadotte Bridge in Stockholm, Sweden. A finite element model and the modal models that consider the human–structure interaction effect are calibrated with respect to the measurements. The properties of the spring–mass–damper model representing the pedestrians were identified, considering the different structural modes of the system. Good agreement was obtained between the experimental and theoretical frequency response functions. A sensitivity analysis of the obtained solution was performed, validating the determined analytical expression for the frequency response function of the coupled pedestrian-bridge system that takes into account the human–structure interaction effect.

Dynamic load mitigation using dissipative elastic metamaterials with multiple Maxwell-type oscillators

Dissipative elastic metamaterials have attracted increased attention in recent times. This paper presents the development of a dissipative elastic metamaterial with multiple Maxwell-type resonators for stress wave attenuation. The mechanism of the dissipation effect on the vibration characteristics is systematically investigated by mass-spring-damper models with single and dual resonators. Based on the parameter optimization, it is revealed that a broadband wave attenuation region (stopping band) can be obtained by properly utilizing interactions from resonant motions and viscoelastic effects of the Maxwell-type oscillators. The relevant numerical verifications are conducted for various cases, and excellent agreement between the numerical and theoretical frequency response functions is shown. The design of this dissipative metamaterial system is further applied for dynamic load mitigation and blast wave attenuation. Moreover, the transient response in the continuum model is designed and analyzed for more robust design. By virtue of the bandgap merging effect induced by the Maxwell-type damper, the transient blast wave can be almost completely suppressed in the low frequency range. A significantly improved performance of the proposed dissipative metamaterials for stress wave mitigation is verified in both time and frequency domains.

Nonlinear frequency response analysis of nonisothermal adsorption controlled by macropore diffusion

In this work, a nonlinear frequency response (NFR) approach is used for a theoretical study of nonisothermal adsorption controlled by macropore diffusion (NMD). Based on the nonlinear mathematical model on the particle scale for spherical geometry, the theoretical frequency response functions (FRFs) up to the second order have been derived, using the concept of higher-order FRFs. The FRFs for isothermal macropore diffusion model have also been derived for comparison. For the NMD model two series of FRFs define the process: one which relates the sorbate concentration in the particle to the pressure (F) and the other which relates the particle temperature to the pressure (Z). The obtained FRFs were simulated for seven different sets of parameters. The second-order F function exhibits specific bimodal pattern, which enables separation of the diffusional and heat-transfer time constant. The high-frequency asymptotic features of the second-order F function discriminates the NMD mechanism from micropore-macropore diffusion control. Based on the characteristic of the first- and second-order F and Z functions, the new procedure for direct estimation of the diffusional and heat-transfer time constants is proposed. Additionally, some equilibrium parameters, as well as the heat of adsorption, can also be estimated. The NFR approach shows significant advantages regarding analysis of NMD compared to the linear FR method.

Characterizing the low strain complex modulus of asphalt concrete specimens through optimization of frequency response functions

Measured and finite element simulated frequency response functions are used to characterize the low strain (~10(-7)) complex moduli of an asphalt concrete specimen. The frequency response functions of the specimen are measured at different temperatures by using an instrumented hammer to apply a load and an accelerometer to measure the dynamic response. Theoretical frequency response functions are determined by modeling the specimen as a three-dimensional (3D) linear isotropic viscoelastic material in a finite element program. The complex moduli are characterized by optimizing the theoretical frequency response functions against the measured ones. The method is shown to provide a good fit between the frequency response functions, giving an estimation of the complex modulus between minimum 500 Hz and maximum 18|000 Hz depending on the temperature. Furthermore, the optimization method is shown to give a good estimation of the complex modulus master curve.

Squeeze-film damping of flexible microcantilevers at low ambient pressures: theory and experiment

An improved theoretical approach is proposed to predict the dynamic behavior of long, slender and flexible microcantilevers affected by squeeze-film damping at low ambient pressures. Our approach extends recent continuum gas damping models (Veijola 2004 J. Micromech. Microeng. 14 1109–18, Gallis and Torczynski 2004 J. Microelectromech. Syst. 13 653–9), which were originally derived for a rigid oscillating plate near a wall, to flexible microcantilevers for calculating and predicting squeeze-film damping ratios of higher order bending modes at reduced ambient pressures. Theoretical frequency response functions are derived for a flexible microcantilever beam excited both inertially and via external forcing. Experiments performed carefully at controlled gas pressures are used to validate our theoretical approach over five orders of the Knudsen number. In addition, we investigate the relative importance of theoretical assumptions made in the Reynolds-equation-based approach for flexible microelectromechanical systems.

On the low frequency in-plane forced vibrations of pneumatic tyre/wheel/suspension assemblies

ABSTRACT The paper contains an interim report on a research project into the longitudinal vibrations of vehicles. The aim is to improve understanding of the process by which tyres come to vibrate by rolling along surfaces which may be smooth or profiled and the transmission of the vibration into the vehicle cabin. A description of a specially designed rig is given. This allows control of the boundary conditions of a tyre/wheel assembly which runs on a rotating drum, and allows forcing to be applied by an electromagnetic shaker to the hub in the vertical or longitudinal direction. A measurement scheme has been implemented to record forces and translational and spin accelerations of the hub. A mathematical model of the rig has been built using the multibody modelling software Autosim. The tyre is represented as a hub and rigid circular ring with translational and rotational freedoms between them. The hub is mounted in a suspension system allowing it translational and spin freedoms. The model and the measurements are used to generate frequency responses, and a parameter identification scheme is being followed to obtain a best fit of the theoretical results to the experimental results in the frequency range up to about 100 Hz. Vibration spectra and comparative experimental and theoretical frequency response functions are included.

Mechanical joint parameter estimation using frequency response functions and component mode synthesis

This paper treats the problem of finite element model updating of structures consisting of substructures connected through mechanical joints whose stiffness and damping properties are unknown. The model is updated by estimating the mechanical joint parameters via the curve fit of measured frequency response functions using a non-linear least-squares method. A damped component mode synthesis formulation is used to calculate the theoretical frequency response functions of the assembled structure given the joint stiffness and damping parameter values. It is shown that a good approximation of the sensitivity matrix may be obtained by finite differences at a smaller computational cost than the closed form expression. Identifiability criteria and estimation errors are addressed. A numerical example consisting of two free-free beams connected through axial springs and dampers illustrates the proposed method.