Modal Frequency Response Research Articles

Analysis of the Human Middle Ear Dynamics Through Multibody Modeling.

The dynamics of the human middle ear (ME) has been studied in the past using several computational and experimental approaches in order to observe the effect on hearing of different conditions, such as conductive disease, corrective surgery, or implantation of a middle ear prosthesis. Multibody (MB) models combine the analysis of flexible structures with rigid body dynamics, involving fewer degrees-of-freedom (DOF) than finite element (FE) models, but a more detailed description than traditional 1D lumped parameter (LP) models. This study describes the reduction of a reference FE model of the human middle ear to a MB model and compares the results obtained considering different levels of model simplification. All models are compared by means of the frequency response of the stapes velocity versus sound pressure at the tympanic membrane (TM), as well as the system natural frequencies and mode shapes. It can be seen that the flexibility of the ossicles has a limited impact on the system frequency response function (FRF) and modes, and the stiffness of the tendons and ligaments only plays a role when above certain levels. On the other hand, the restriction of the stapes footplate movement to a piston-like behavior can considerably affect the vibrational modes, while constraints to the incudomalleolar joint (IMJ) and incudostapedial joint (ISJ) can have a strong impact on the system FRF.

Generation Mechanism and Development Characteristics of Rail Corrugation of Cologne Egg Fastener Track in Metro

By establishing vehicle-track space coupled model and rail corrugation evaluation model, the generation mechanism of rail corrugation was analyzed in frequency domain and time domain, and development characteristics of corrugation were studied by using corrugation growth rate. Analysis based on frequency domain: through modal analysis and frequency response analysis on the finite element model of track structure, it is found that there are natural frequencies of track structure close to measured corrugation passing frequencies. It shows that the vibration modes corresponding to these frequencies can be more easily excited, which can cause the resonance phenomenon of track structure and form the rail corrugation at corresponding frequencies. Analysis based on time domain: the time-history curves of rail vertical vibration acceleration and rail vertical displacement are calculated by using vehicle-track coupled model and the frequency domain transformation of the time-history data is carried out. It is found that there are characteristic frequencies close to the measured corrugation passing frequencies, which indicates that the vibration of track structure at corresponding frequencies is an important reason to promote the formation of corrugation. The change of vehicle speed has no effect on characteristic frequencies of corrugation growth rate curves, which reflects the fixed frequency characteristic of corrugation. With the increase of train operation times, the corrugation corresponding to characteristic frequencies will gradually form and develop, and the increase of vehicle speed will increase the wavelength range and development speed of rail corrugation.

Forced Vibrations of a Cylindrical Shell Immersed in Liquid

A numerical-analytical method is proposed for calculating the forced vibrations of a shell structure immersed in liquid. The structure is a set of finite elastic cylindrical shells and elastic rings to which concentrated discrete forces are applied. Examples of a comparative calculation of the frequency response and vibration modes of the shell structure in a vacuum and in liquid are given.

3DOF Ultrasonic Motor With Two Piezoelectric Rings.

A novel design of a multiple degrees of freedom (multi-DOF) piezoelectric ultrasonic motor (USM) is presented in the paper. The main idea of the motor design is to combine the magnetic sphere type rotor and two oppositely placed ring-shaped piezoelectric actuators into one mechanism. Such a structure increases impact force and allows rotation of the sphere with higher torque. The main purpose of USM development was to design a motor for attitude control systems used in small satellites. A permanent magnetic sphere with a magnetic dipole is used for orientation and positioning when the sphere is rotated to the desired position and the magnetic field synchronizes with the Earth’s magnetic dipole. Also, the proposed motor can be installed and used for robotic systems, laser beam manipulation, etc. The system has a minimal number of components, small weight, and high reliability. Numerical simulation and experimental studies were used to verify the operating principles of the USM. Numerical simulation of a piezoelectric actuator was used to perform modal frequency and harmonic response analysis. Experimental studies were performed to measure both mechanical and electrical characteristics of the piezoelectric motor.

Modal interactions for spindle, holders, and tools

This paper describes the interaction between vibration modes associated with the machine-spindle and those associated with the holder-tool when the holder-tool combination is inserted in the milling machine spindle. It is shown that when the bending natural frequency of the holder-tool is near a machine-spindle natural frequency, there is a combined two mode frequency response (similar to a dynamic absorber) for the assembly that exhibits increased dynamic stiffness over those situations when the interaction is absent. Experimental results are provided. The variation in tool point frequency response with tool extension length is then used to calculate the corresponding stability maps. These maps are evaluated to determine the effect of interactions between machine-spindle and holder-tool modes on milling stability. Conclusions are presented.

A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic parameters

A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic distribution parameters is proposed. The partial differential equation with spatial varying parameters for nonlinear vibration of beams with periodic parameters under harmonic excitations is derived. The procedure of the multimode perturbation method includes three main steps: first, the nonlinear partial differential equation is transformed into linear partial differential equations with varying parameters by applying perturbation method; second, the linear partial differential equations are transformed into ordinary differential equations with multimode coupling by applying Galerkin method, where multiple vibration modes of the beams are used and the equations are suitable to nonlinear vibration of periodic structures with high parameter-varying wave in wide frequency band; third, the ordinary differential equations are solved by applying harmonic balance method to obtain vibration response of the nonlinear periodic beam, which is used for characteristics analysis of frequency response and spatial mode. Furthermore, the stability problem of nonlinear harmonic vibration as multidegree-of-freedom system with periodic time-varying parameters is solved by applying direct eigenvalue analysis approach. The proposed method can incorporate multiple vibration modes into response analysis of nonlinear periodic structures and consider mode-coupling effects due to structural nonlinearity and parametric periodicity. Finally, a nonlinear beam with periodic supports under harmonic excitations is studied. Numerical results on frequency response of the beam are given to illustrate an application of the proposed method, new frequency response characteristics, and influences of periodic parameters on structural response. The results have potential application to nonlinear structural vibration control and support damage detection of nonlinear structures with periodic supports.

An exact approach to the dynamics of locally-resonant beams

This paper presents an exact analytical approach to calculate the dynamic response of elastic beams with periodically-attached resonators, generally referred to as locally-resonant beams. Showing that a typical resonator is equivalent to an external constraint, whose reaction force on the beam depends on the deflection of the application point through a pertinent frequency-dependent stiffness, the beam-resonators coupled system is handled using only the beam motion equation, with Dirac's deltas modelling the shear-force discontinuities associated with the reaction forces of the resonators. This is the basis to tackle the dynamics of infinite as well as finite beams, the first by a transfer matrix method to calculate frequency band gaps, the second by a generalized function approach. The dynamics of the finite beam is studied in frequency and time domains deriving the exact frequency response and the exact modal response, including modal frequency and impulse response functions. The proposed approach is formulated for arbitrary number of resonators and loads, and applies for both non-proportional and proportional damping.

Experimental and Numerical Assessment into Frequency Domain Dynamic Response of Deep water Rigid-Frame Bridge

ABSTRACT The dynamic responses of the deepwater rigid-frame bridge are assessed by underwater shaking table tests and numerical simulations. The frequency domain dynamic responses are estimated to illustrate the effect of water depth and superstructures on the bridge subjected to earthquake loading along the transverse direction. Major findings are summarized as follows: (a) the water depth changes the modal frequencies and vibration pattern of the bridge; (b) the superstructures affect the modal frequencies and frequency response peaks of pier; and (c) a practical method is proposed for seismic design of deepwater rigid-frame bridge by considering the influence of the superstructures.

Finite element model updating of jointed structure based on modal and strain frequency response function

To acquire a reasonable model for structural dynamic strength analysis, a bottom-up finite element modeling and updating methodology based on multi responses is proposed. The fundamental principles of structural dynamics analysis and model updating were introduced, and the proposed strategy was applied to the case study of an L-shaped jointed structure. Components of the jointed structure were modeled sequentially, and inaccurate model parameters were updated based on the corresponding experimental modal results in the first stage. In the second stage, components were connected together by bolts. The joint interfaces were represented by thin-layer elements, and local joint parameters were updated based on strain frequency response function (FRF). Finally, the precision of finite element model (FEM) was validated by acceleration frequency response function. The results indicated that the proposed methodology is able to reduce model simulation errors in both components and the overall jointed structure. Not only can the updated model of a jointed structure reproduce the experimental results used in updating, but also predict responses that are not used in the process of model updating.

Simulation of the frequency response of the ERC 1400 Bucket Wheel Excavator boom, during the excavation process

Abstract The paper deals with the modal analysis and frequency response analysis of a bucket wheel excavator (BWE) boom, obtained by simulation, based on a virtual model of an existing BWE boom. The boom, which generally is realized as a spatial truss, is the most vulnerable subsystem of the BWE, being submitted to severe operational loads characterized by very pronounced cyclical, dynamic and stochastic variability. This vulnerability is the consequence of its shape and constructive parameters and the nature, source and character of the external exciting loads to which it is exposed. The classical approach recommended by standards and norms cannot predict the occurrence of failures caused by vibration, which produces fatigue due to the load’s cyclical variability and the deformation produced by resonant vibration of some constitutive elements. As exciting load we considered the operational forces acting on the bucket wheel. In this manner we can take into account the constructive features – with modal analysis, and the vibration regime – with frequency response analysis. The proposed method is useful both in the design phase of new load-bearing structures of truss type subjected to high-variability forces, and also in refurbishment or improvement phases of the existing structures of this kind.

Piezo-actuated device for a bio-structural monitoring application through vibration-based condition and electromechanical impedance measurements

This study presents a numerical and experimental development of a piezo-actuated device used for monitoring the stiffness variations of its support through electromechanical impedance measurements. The piezo-device and its components define a clamped beam system activated dynamically by two piezo-transducers that transmit vibrations to the support (monitoring substrate). An harmonic finite element analysis was carried out to understand the effects of the substrate properties on the dynamics of the piezo-device. Experimental tests corroborated the simulations with the correspondence of modal shapes and frequency response functions (FRFs) when the substrate varies its stiffness. A biomedical application was conducted in a bone specimen with three embedded teeth to monitor the stiffness variations induced by drillings in the bone. Results showed that the bone stiffness monitoring could be possible through the teeth due to that the drillings effect were quantified by electrical impedance signals.

Efficient, wide-band coupled structural-acoustic computations combining time and frequency domain finite elements/equivalent sources

Time and frequency domain computations are complementary, and here, the overall goal is to combine them to generate wide-band solutions of coupled structural-acoustic problems. Modal frequency response computations are efficient for low frequencies but become inefficient as the number of basis functions required to represent the response grows large. Modal formulations are required for large problems because the coupled equation system becomes densely populated when acoustic pressure forces are included. In contrast, the equation system remains sparsely populated in time domain formulations when the time step size is chosen appropriately, allowing large problems to be solved efficiently in terms of nodal degrees-of-freedom. However, the analysis times depend linearly on the number of time steps and a large number are generally required to represent the ringing response of low frequency modes. Here, the number of time steps is limited by applying an exponential taper to the time domain solution and truncating the computations. This reduces leakage effects, but does not affect components of response that have damped out before it is applied. Examples are given to illustrate the computations and the tradeoff between number of basis functions in the modal frequency response computations and number of time steps in the transient analyses.Time and frequency domain computations are complementary, and here, the overall goal is to combine them to generate wide-band solutions of coupled structural-acoustic problems. Modal frequency response computations are efficient for low frequencies but become inefficient as the number of basis functions required to represent the response grows large. Modal formulations are required for large problems because the coupled equation system becomes densely populated when acoustic pressure forces are included. In contrast, the equation system remains sparsely populated in time domain formulations when the time step size is chosen appropriately, allowing large problems to be solved efficiently in terms of nodal degrees-of-freedom. However, the analysis times depend linearly on the number of time steps and a large number are generally required to represent the ringing response of low frequency modes. Here, the number of time steps is limited by applying an exponential taper to the time domain solution and truncat...

Multi-band power oscillation damping controller for power system supported by static VAR compensator

Low-frequency electromechanical oscillations damping is powerfully crucial in power system operation. In order to fulfill this requirement, power oscillation damping (POD) controllers are installed in synchronous generators and flexible alternating current transmission system devices. These controllers can have either a conventional fixed structure composed by stages of gain and phase compensation or a multi-band modern structure (PSS4B) composed by three bands that correspond to a specific frequency range (low, intermediate and high frequency). In the PSS4B structure, each band consists of two branches based on differential filters (with a gain, lead–lag blocks and a hybrid block). This paper investigates the application of PSS4B as a POD controller for the static VAR compensator (PSS4B-SVC-POD) to damp oscillations in multi-machine power systems. The proposed PSS4B-SVC-POD and power system stabilizers (fitted on generators) are simultaneously designed through an optimization approach aiming at maximizing the closed-loop damping ratio. Modal analysis, frequency responses and time simulations for the well-known two-area four-generator power system show the good performance of the proposed controller fitted on static VAR compensator.

Research on modeling method of honeycomb plate and its application on solar wing

Aerospace products need to simulate the complicated working conditions through dynamic simulation analysis to ensure the high reliability of product design. In this paper, the equivalent modeling method of honeycomb sandwich plate based on finite element analysis is studied, and the mechanical characteristic parameters of honeycomb core structure are obtained. At the same time, the composite components of satellite solar cell array are modeled and simulated. The modal analysis and frequency response analysis are carried out to provide an important basis for the design and improvement of the structure.

A general electromechanical model for plates with integrated piezo-patches using spectral-Tchebychev method

This paper presents a general electromechanical model for predicting the dynamics of thin or moderately thick plates with surface-integrated piezo-patches. Using spectral Tchebychev (ST) technique, the boundary value problem governing the electroelastic dynamics of the two dimensional (2D) plate and piezo-patch structure is developed with Mindlin plate theory assumptions. Mass and stiffness contributions of piezo-patch(es) as well as two-way electromechanical coupling behavior are incorporated in the model for both modal analysis and frequency response calculations. To validate the accuracy of the developed solution technique, the modal analysis results are compared against the existing Rayleigh-Ritz solution from the literature as well as the finite-element simulation results for various piezo-patch sizes on thin and moderately thick host plates; and it is shown that the maximum difference in the predicted natural frequencies between the ST and FE results are below 1%. The electromechanical frequency response functions (FRFs) including the vibration response and electrical output of the system under a transverse point force excitation are obtained using the ST model and the results are shown to match perfectly with the finite element (FE) simulations. Additionally, comparisons of the electromechanical FRFs calculated based on Rayleigh-Ritz method from the literature versus the developed framework is presented to highlight that the exclusion of shear deformation terms in the former model leads to an inaccurate estimation of electroelastic behavior for the case of thicker plates with integrated piezo-patches. Finally, the investigated case studies demonstrate that the computational efficiency of the developed method is significantly higher than that of FE simulations.

Mitigating the Dilution Effect in Auditors' Judgments Using a Frequency Response Mode

ABSTRACT This paper investigates the potential of using a frequency response mode to reduce the dilution effect of non-diagnostic evidence on auditors' fraud risk judgments. In two experiments, we test one hypothesis and examine a research question related to the dilution effect where response mode (frequency versus probability) and type of non-diagnostic or irrelevant information are manipulated between-participants. Results of the hypothesis tests show that auditors' fraud risk judgments demonstrate a significantly lower dilution effect when they evaluate diagnostic and non-diagnostic or irrelevant evidence using a frequency response mode, as compared to the probability response mode; this effect is most pronounced when auditors are provided with favorable non-diagnostic or irrelevant evidence. JEL Classifications: M4; M40; M420. Data Availability: Summary data are available from the authors upon request.

Forced vibration analysis of composite beams based on the variable separation method

This paper proposes a new strategy based on the proper generalized decomposition method to solve the forced vibration problem in two-dimensional (2D) layered beams. The approach redefines the problem by approximating the displacement field as a sum of separated functions of x, z, and ω and proposes an iterative algorithm that solves three 1D problems at each iteration. Several numerical tests with different slenderness ratios and boundary conditions are considered to validate the method. The results in terms of modal parameters and frequency response functions are analyzed and compared with exact elasticity solution and finite element simulations with very good agreements.

Structural design and simulation analysis of the carbon fiber-reinforced polymer main frame of a mapping camera system

The main frame is the primary load-bearing component of a mapping camera system. As the critical structure of the system, the main frame determines the mechanical properties of a camera system. The main frame design is hindered by its large size, complicated interface, as well as high-stability, high-frequency requirement, and lightweight requirements. During the launching process, the main frame should be able to withstand the mechanical action of the active section without affecting the performance of the camera system. This paper describes the design scheme of the main frame. The modal analysis, static analysis and frequency response analysis of the main frame are performed. The simulation analysis results prove that the natural frequency of the mapping camera system satisfies the design requirements and the main frame satisfies the required safety margin in the linear overload in X-, Y-, and Z-directions. Moreover, under condition of the frequency response in X-, Y-, and Z-directions, the main frame has excellent structural stiffness, which provides a proper mechanical environment for the camera system. The design scheme of the main frame is reasonable and feasible.

A Combined Numerical and Experimental Investigation on the Effect of Dynamics Characteristics of Metal Expansion Bellows

Metal expansion bellows is an important flexible element used to absorb extension or shrinkage and vibrations of the piping system used in various process applications. Failure of the bellows occurs due to the unpredictable behavior in its convolutions due to severe working conditions. Hence, determination of its dynamic characteristics is of prime importance. To find and analyse dynamic characteristics like axial natural frequencies, modal frequency responses and mode shapes of U-shaped convolution bellows as well as the effect of increase in number of convolutions on the dynamic characteristics. In this paper, analytical, numerical simulation and experimental investigations are performed to find the axial natural frequencies of bellows. Numerical simulation is performed using the mathematical model in MATLAB and modal analysis is performed using ANSYS 15. The deformation and axial natural frequency response of bellows with eight, nine and ten convolutions are obtained by FE analysis for various modes when bellows are subjected to different end conditions. As per the simulation and experimental modal analysis, it is seen that the range of axial natural frequencies with less number of convolutions shows maximum deformation and larger number of convolutions shows minimum deformation. To decrease the axial natural frequency for the given flow rate and to avoid resonance, the number of convolutions of the bellows should be increased for designing the new configuration.

An exact modal analysis approach to vibration analysis of structures with mass-spring subsystems and rotational joints

A novel exact modal analysis approach is presented for vibration analysis of plane continuous structures, which are coupled with discrete mass-spring subsystems and include elastic rotational joints modelling local flexibility. Using the theory of generalised functions to handle the discontinuities of the response variables, every continuous member with any number of mass-spring subsystems and joints is treated as a two-node element, for which a 6 × 6 exact dynamic stiffness matrix is obtained in closed form. As a result, the global dynamic stiffness matrix is built by a standard finite-element assembling procedure, with size depending only on the number of nonzero nodal degrees of freedom of member-to-member nodes. Upon deriving pertinent orthogonality conditions for the modes, the system response under arbitrary loads is obtained by modal impulse and modal frequency response functions, under the assumption of proportional damping. The solutions are exact and can be used as benchmark for classical finite-element solutions. The approach is formulated for various mass-spring subsystems, acting in transverse and axial directions relative to every member.