Calculated Frequency Response Research Articles

An analytical model of ultrasonic transducers considering acoustic losses of contact surfaces

In this paper, a continuum electromechanical model of a Langevin ultrasonic transducer is developed considering acoustic losses of contact surfaces. The calculated energy losses between components of a transducer are considered as loss modulus of backing and matching parts. Considering the losses, the calculated vibrations amplitude of the transducer is matched to measured values. In addition, the calculated frequency response of the electrical admittance of the transducer is in good agreement with experimental results. The errors of calculated resonant frequency, anti-resonance frequency and amplitude of vibrations compared to the experimental results are 0.02%, 0.03%, 4.5% respectively. The values of the electrical admittance in the resonant and anti-resonant frequency have errors of 2.7%, 9.5% compared to empirical results. The developed model, fixes the drawback of previous models to anticipate amplitude of vibrations and the frequency response of the electrical admittance of ultrasonic transducers.

A computational framework for uncertain locally resonant metamaterial structures

Locally resonant metamaterial structures, i.e., structures artificially engineered with periodic arrays of small resonators, are attracting a growing interest among scientists. The main reason lies in their remarkable attenuation properties of elastic waves over finite frequency ranges, named band gaps, resulting from periodicity and local resonance. Yet, very little attention has been paid to investigate whether and to which extent the behavior of these structures may be affected by uncertainties. This is indeed the purpose of our study, which proposes a comprehensive computational framework to calculate the frequency response of uncertain locally resonant structures, assuming an interval model for all the relevant parameters of the resonators: mass, stiffness and damping.The computational framework is conceived for finite-element models of the locally resonant structure and standard mass-spring-dashpot models of the resonators. The key steps are an exact dynamic condensation of the degrees of freedom within the resonators, the derivation of an exact and elegant expression for the transfer matrix of the locally resonant structure via the Sherman-Morrison-Woodbury formula, the calculation of the interval frequency response via either a sensitivity-based method or a global optimization method, the choice being driven by a preliminary monotonicity test. Considering two typical locally resonant structures, a beam and a plate, the computational framework proves easy to implement, accurate and robust as compared with the standard Monte Carlo method.

High-Power and High-Speed Ge/Si Traveling-Wave Photodetector Optimized by Genetic Algorithm

We experimentally demonstrate a 4-stage and an 8-stage Ge/Si distributed traveling-wave photodetectors (TWPDs) with high RF output powers and large bandwidths. The genetic algorithm is utilized to synergistically optimize multiple relevant design parameters, including the dimension of the coplanar waveguide electrode and the aperiodic arrangement of the PD array. After the genetic algorithm optimization, the 3dB bandwidth of the 4-stage TWPD is improved from 46 GHz to 54 GHz under the constraint that the bandwidth of the unterminated single PD element is 50 GHz. Meanwhile, the 3dB bandwidth of the 8-stage TWPD is improved from 33 GHz to 40 GHz. A good agreement between measured and calculated frequency responses is obtained. The measured maximum RF output powers of the aperiodic 4-stage and 8-stage TWPDs at 30 GHz are 2.5 dBm and 6.3 dBm, respectively. Furthermore, the effectiveness of our design methodology is verified by measurement results of devices fabricated at different silicon photonics foundries.

Broadband Spatial Spectrum Estimation Based on Space-Time Minimum Variance Distortionless Response and Frequency Derivative Constraints

The two-dimensional optimization capability of the space-time minimum variance distortionless response (STMVDR) can improve the spatial spectrum estimation performance of the broadband beamformer with limited samples, but its high sensitivity to frequency errors may lead to the suppression of some narrowband signals not at the grid point of the frequency response calculation. In order to reduce the sensitivity of STMVDR to frequency errors, a broadband spatial spectrum estimation method based on STMVDR and frequency derivative constraints is proposed in this paper. First, based on the beam response of the STMVDR beamformer, an arbitrary order frequency derivative constraint is derived. Second, combining the gain constraint and frequency derivative constraint, the linear constrained minimum variance problem is established to solve the optimal weight of the beamformer. Finally, the calculation method of the broadband spatial spectrum is derived. Numerical simulations show that the proposed method not only solves the problem of frequency mismatch caused by the insufficient number of points for calculating frequency response, but also does not cause the spatial response related peaks to deviate from the true direction due to the broadening of the main lobe of frequency response. In addition, the proposed method can reduce the computational complexity of the algorithm by more than half by increasing the interval of the frequency calculation grid points, and does not significantly loss in the angular resolution capability and estimation accuracy of the algorithm.

Finite element computation of nonlinear modes and frequency response of geometrically exact beam structures

An original method for the simulation of the dynamics of highly flexible slender structures is presented. The flexible structures are modeled via a finite element (FE) discretization of a geometrically exact two-dimensional beam model, which entirely preserves the geometrical nonlinearities inherent in such systems where the rotation of the cross-section can be extreme. The FE equation is solved by a combination of harmonic balance (HBM) and asymptotic numerical (ANM) methods. The novel solving scheme is rooted entirely in the frequency domain and is capable of computing both the structure’s frequency response under periodic external forces as well as its nonlinear modes. An overview of the proposed numerical strategy is outlined and simulations are shown and discussed in detail for several test cases.

Numerical Calculation of Pick-Up Coils Frequency Response as a Useful Tool for Local Magnetic Field Sensors Design

The aim of this article is to present a useful numerical procedure suitable to accurately model pick-up probes for design-oriented purposes, reducing the required prototyping activity and allowing more accurate results with respect to analytic estimations, taking into account both inductive and capacitive effects in complex geometries. The proposed methodology is characterized by the following steps: 1) a partial element equivalent circuit (PEEC) formulation, speeded up by a parametric model order reduction (pMOR) technique, is used to efficiently model the probe in the frequency domain taking into account both inductive and capacitive effects; 2) a nonlinear least-squares solver is used to identify an equivalent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RLC$ </tex-math></inline-formula> network describing the full behavior of the probe up to the first resonance frequency; and 3) a circuital model, considering the probe, the transmission line (TL), and the terminating impedance, is used to estimate the bandwidth of the complete system from the probe to the acquisition system. The experimental validation of the proposed method against the RFX-mod2 three-axis pick-up probe prototype is also presented, together with the application to the design of the magnetic sensors for the new Divertor tokamak test (DTT) facility.

Nonlinear vibration analysis of FGM sandwich structure under thermal loadings

The geometrically nonlinear thermal frequencies of the functionally graded (FG) sandwich structures are predicted numerically in the current work considering the variable temperature distributions (linear and nonlinear). For numerical analysis of the FG sandwich structure, an in-house finite element code has been developed in MATLAB using the higher-order shear deformation theory (HSDT) and Green–Lagrange nonlinear strain kinematics. The governing equation of motion for the graded sandwich structure is obtained using Hamilton’s principles, and the direct iterative method is used to predict the nonlinear vibration response of the sandwich structure. The temperature distributions along the thickness of the sandwich structure are considered. Temperature dependent material properties are considered in the present work for computation of frequency responses under thermal environment. The material properties are described in accordance with the power-law distribution. The current models are initially validated with the published results. The influence of various input parameters, i.e. the curvature ratio (CRO), thickness ratio (TRO), aspect ratio (ARO), boundary conditions, and power-law indices on the nonlinear vibration behaviours of FG sandwich structure have been studied.

Efficient computation of frequency response for non-proportional damped systems

Frequency response analysis is required in many structural dynamic applications. For large-scale problems, the cost of performing a frequency response analysis within a frequency interval of interest can be computationally very expensive and prohibitive, because the evaluation of the structural response for each excitation frequency requires solving a system with complex coefficients. For such purposes, a new method for the frequency response analysis of a non-proportional damped system in the frequency interval 0,ωmax is established. We first determine the lower-order modes in the interval 0,ωmax/ψ and retain the quantity, where ψ is an optional parameter which is greater than zero and less than 1. The default value of ψ is set to 0.5. We then approximate the unknown higher-order mode contributions by using partial sums of the constructed convergent power series of excitation frequency. The number of items in the partial sum is determined adaptively by an iterative algorithm performed at ωmax. The resulting analytical expression for the frequency response is applied to the frequency interval 0,ωmax. Consequently, the frequency response analysis can be fulfilled simply by changing the excitation frequency in the analytical expression. Although the proposed method is derived based on the state space approach, its implementation is transformed to the original space to reduce the computational effort and storage space. The accuracy and effectiveness of the proposed method are illustrated and validated by two numerical examples.

Extrinsic crosstalk suppression based on a calibration convolutional neural network for glasses-free 3D display

Extrinsic crosstalk degrades the 3D imaging quality and it occurs due to fabrication errors of the light control optical component and assembling errors of the display system. Here, an extrinsic crosstalk suppression method based on a calibration convolutional neural network (C-CNN) is demonstrated for glasses-free 3D display. The C-CNN is established to calibrate the 3D imaging with extrinsic crosstalk, which can obtain the high-order nonlinear decoding function of the light control optical component with fabrication errors and assembling errors. Furthermore, model for 3D imaging with both extrinsic and intrinsic crosstalk can be mathematically established using the C-CNN integrated with the frequency response calculation. Additionally, according to the calibration for real-life 3D imaging with extrinsic crosstalk, pixels of elemental image array (EIA) contributing to viewpoint crosstalk are extinguished to suppress extrinsic crosstalk. The experiment verifies the feasibility and superior of the proposed method. A 5-degree viewing angle and 5 viewpoints glasses-free 3D display with improved 3D imaging quality is demonstrated.

Topology optimization of proportionally damped structures under harmonic excitations: Analysis of velocity and acceleration responses

Topology optimization of proportionally damped structures subjected to harmonic excitations within a frequency interval is a challenging task. In this work, we consider the structural velocity and acceleration responses in a frequency interval as the optimization objectives. The optimized structures will be significantly different from those with the displacement response only due to the influence of excitation frequencies. In particular, if the acceleration amplitude of structural frequency responses in a frequency interval is considered, the optimization process usually converges to a configuration that is unable to ensure engineering feasibility. An optimization model that takes the structural static response of the structure as a weighted part of the objective function is proposed, it can make the optimized configuration more applicable for engineering design. An efficient method for calculating frequency responses over a frequency interval is also introduced. The derivatives of the objective function are derived by the adjoint method and can be calculated in a manner similar to the frequency response. Two illustrative examples are given to examine the accuracy and validity of the proposed method.

Lossless longitudinal bars as Fabry-Perot resonators (FPRs)

Fabry-Perot resonator (FPR) is an important concept for the study of optical and microwave systems. But it is a relatively alien concept for mechanical engineers. This paper reveals that a lossless bar (i.e. a bar whose Young’s modulus is a real number) undergoing longitudinal vibrations is essentially a Fabry-Perot resonator. First, the harmonic response of a longitudinal bar with generic mass-damper-spring (MDS) boundaries is derived to show that it is identical to the Airy function of an optical FPR. The derivation confirms that the resonance of a longitudinal bar is due to the superposition (i.e. interference) of the longitudinal waves travelling back and forth between the two boundaries. Next, the transmission and phase shifts at the MDS boundaries are derived. Based on which, the resonant frequencies of the longitudinal bar with different boundary conditions are determined directly from the phase matching condition. A perfect agreement with those obtained from conventional approaches was achieved. Finally, the concepts of whitelight interference (WLI) and fringe analysis are applied to determine the bar length from the calculated frequency response function (FRF). The results presented demonstrate that the data processing algorithms developed for optical and microwave FPRs are directly transferable to the study of longitudinal bars. This work lays the theoretical foundation for future developments of mechanical FPR sensors.

An Improved Finite Element Model Updating Method Based on the Singular Values of Frequency Response Functions

Aiming at the problems that Markov chain Monte Carlo algorithm is not easy to converge, has high rejection rate, and is easy to be disturbed by the noise when the parameter dimension is high, an improved model updating method combining the singular values of frequency response functions and the beetle antennae search algorithm is proposed. Firstly, the Latin hypercube sampling is used to extract the training samples. The Hankel matrix is reconstructed using the calculated frequency response functions and is decomposed by singular value decomposition. The effective singular values are retained to represent the frequency response functions. Secondly, according to the training samples and the corresponding singular values, the support vector machine surrogate model is fitted and its accuracy is tested. Then, the posterior probability distribution of parameters is estimated by introducing the beetle antennae search algorithm on the basis of standard Metropolis–Hastings algorithm to improve the performance of Markov chains and the ergodicity of samples. The results of examples show that the Markov chains have better overall performance and the acceptance rate of candidate samples is increased after updating. Even if the Gaussian white noise is introduced into the test frequency response functions under the single and multiple working damage conditions, satisfactory updating results can also be obtained.

Modal loss factor approximation for u-p formulation FEM using Modal Strain and Kinetic Energy method

An approximation method for estimating the modal loss factors of a coupled structural-acoustical problem is proposed using the finite element method. This method provides a practical approach in terms of computational time and memory consumption. To validate our approach, we consider a coupled system in which the acoustical region is enclosed by a structural region, and both structural and acoustical regions are composed of various materials with individual damping characteristics. To obtain the modal loss factors, the modal strain and kinetic energy (MSKE) method is extended to the coupled problem by utilizing the sound pressure as a nodal unknown variable in the acoustical region. An air-filled PVC box was used as the test specimen. The measured and calculated frequency responses of the normalized sound pressure showed good agreement, verifying the reliability of the proposed method. Various damping parameters were tested for the sound-absorbing material inside the box to investigate the scope of the application of the proposed method. The discrepancy between the reference value and the proposed method is small considering fiberglass as a standard sound-absorbing material used in buildings. The proposed method also showed better management characteristics in terms of memory consumption and computational time.

Mechanics and dynamics of two-dimensional quasicrystalline composites

Periodic configurations have dominated the design of phononic and elastic-acoustic metamaterial structures for the past decades. Unlike periodic crystals, quasicrystals lack translational symmetry but are unrestricted in rotational symmetries, which leads to largely unexplored mechanical and dynamic properties. We investigate a family of continuous elastic quasicrystals with different rotational symmetry orders that are directly enforced through a design procedure in reciprocal space. Their mechanical properties are investigated as a function of symmetry order and filling fraction. Results indicate that higher order symmetries, such as 8-, 10- and 14-fold, allow for high equivalent stiffness characteristics that interpolate those of the constituent material while maintaining high levels of isotropy for all filling fractions. Thus, quasicrystals exhibit more uniform strain energy distributions when compared to periodic hexagonal configurations. Similarly, nearly-isotropic wave propagation is observed over a broader range of frequencies. Spectral contents are also investigated by enforcing rotational symmetry constraints in a wedge-type unit cell, which allows for the estimation of band gaps that are confirmed in frequency response computations. The investigations presented herein open avenues for the general exploration of the properties of quasiperiodic media, with potentials for novel architectured material designs that expand the opportunities provided by periodic media.

Subspace Identification of Linear Time-Periodic Systems With Periodic Inputs

This paper proposes a new methodology for subspace identification of linear time-periodic (LTP) systems with periodic inputs. This method overcomes the issues related to the computation of frequency response of LTP systems by utilizing the frequency response of the time-lifted system with linear time-invariant structure instead. The response is estimated with an ensemble of input-output data with periodic inputs. This allows the frequency-domain subspace identification technique to be extended to LTP systems. The time-aliased periodic impulse response can then be estimated and the order-revealing decomposition of the block-Hankel matrix is formulated. The consistency of the proposed method is proved under mild noise assumptions. Numerical simulation shows that the proposed method performs better than multiple widely-used time-domain subspace identification methods when an ensemble of periodic data is available.

Efficiency analysis using complex ultrasonic vibrations in electroacoustic spraying of axial cutting tools

The article considers the electric spark intensification doping methods by using ultrasonic vibrations to obtain the method of electroacoustic deposition. The ultrasonic vibrations use in the deposition process is possible due to the use of an acoustic system at the end of which a naturally swirled waveguide is used. To analyze the waveguide oscillation amplitude dependence on the frequency, the article presents analytically obtained dependences of the longitudinal and torsional components of vibrations. The obtained results reliability of theoretical studies is confirmed by the good convergence of the theoretical and calculated frequency response resonant peaks. The electroacoustic deposition effectiveness method is confirmed by experimental studies of maintaining the hardened drills performance. The experimental data analysis showed a 2-4 fold increase in the total durability period of hardened drills.

Frequency Response Model and Its Closed-Form Solution of Two-Machine Equivalent Power System

For the purpose of considering the spatial-temporal characteristics (STC) of large-scale interconnected power system in the modeling, calculation, and analysis of dynamic frequency response (FR), this paper establishes a two-machine equivalent frequency response (TEFR) model and gets its closed-form solution (CFS), which can be used to analytically analysis and fast calculation. In the modeling, the network structure is idealized through simplified matrix of DC power flow and the system is reduced to a typical two-degree-of-freedom vibration system with viscous damping and excitation forces through breaking closed-loop and variable approximation. After that, modal analysis method is managed to obtain TEFR-CFS which represent the dynamic FR of TEFR model as the superposition of system FR and frequency oscillation. And the influence of parameters on frequency oscillation, such as electrical distance, inertial distribution, initial disturbance power distribution coefficient, etc., are analyzed. Furthermore, the analytical expressions of the key characteristics of dynamic FR, such as the initial decline slope, the nadir and the arrival time of nadir, etc., are derived. Numerical simulation proves that STC has significant influence on FR and can be described by TEFR model, TEFR-CFS and the expressions of its key characteristics with accuracy and efficiency.

Frequency response calculations of carbon nanotube based nanothermophones

Due to the extraordinary high thermal conductivity and low heat capacity, carbon nanotube (CNT) has shown a great potential as a thermo-acoustic (TA) material recently. It can be used to fabricate novel TA loudspeaker free of magnets and moving parts, a promising device that directly converts thermal energy into acoustic energy. In this paper, we have systemically analysed the frequency responses of the dot/wire/film TA emission from CNTs by using the equations we derived for acoustic field of TA emission from point source and arbitrary source. Formulas used for TA calculation from near-field to far-field can be the same. The dependence of sound pressure level (SPL)-frequcecy response of all kinds of CNT based nanothermophones on distance and angle are investigated in detail. It is found that TA sound pressure fluctuates in near-field, while increases linearly with logarithmic frequency in far-field. The amplitude of near-field fluctuation increases with increasing distance, but the frequency cycle of the fluctuation decreases and tends to be a constant depending on angle. These studies lay the foundation for further development of CNT based nanothermophones.

Dynamic wheel-rail interaction at high speed based on time-domain moving Green's functions

Many issues of concern in the railway industry are fundamentally caused by dynamic wheel-rail interaction. To deal with these issues, the characteristics of the interaction must be accurately predicted and fully understood; this becomes even more challenging when the train speed is high. Although much research has dealt with wheel-rail interaction, some aspects related to high speed trains still need to be further addressed. In this paper, an approach based on time-domain moving Green's functions developed previously is extended and employed to calculate wheel-rail forces. The extension includes consideration of the flexibility and rotation of the wheelset by incorporating the associated time-domain moving Green's functions in the method. These are derived from the corresponding receptances by applying an experimental modal analysis technique to the calculated frequency response functions. Cases are considered for a single, or multiple, wheelsets rolling over a track represented as an infinitely long periodic structure. Wheel-rail forces are calculated for a set of parameters typical of the Chinese high-speed railway and for a number of typical excitation cases, including purely parametric excitation on a smooth rail, an indentation on the rail, wheel polygonisation and rail corrugation, for the purpose of revealing the frequency content of high-speed wheel-rail interaction. Effects of the wheel rotation on the wheel-rail forces are studied and comparisons are made between a single wheelset and multiple wheelsets.

Improvement of the band-gap characteristics of active composite laminate metamaterial plates

The characteristics of vibration frequency band-gaps for the composite laminate metamaterial plates are improved by equidistantly placing macro-fiber composite (MFC) piezoelectric patches along one direction of the plates. An acceleration feedback control strategy is proposed to actively regulate the band-gap characteristics of the metamaterial plates. The spectral element method (SEM) and transfer matrix method are used to calculate frequency response curves and attenuation constants of the metamaterial plates, and the calculated results by the SEM are compared with that of the finite element method (FEM) to validate the correctness and accuracy of the present numerical method. The obtained results demonstrate that when lattice constant of the structure is properly designed, superior band-gap properties in the low and medium frequency ranges can be achieved by adjusting the dimensions of the MFC piezoelectric patches. Improved characteristics of the Bragg scattering band-gaps in the medium and high frequency regions can also be obtained using the acceleration feedback control strategy. Moreover, band-gap widths can be significantly enlarged by actively tuning the acceleration feedback gain. In addition, the starting frequencies and band-gap widths of the composite laminate metamaterial plates can be adjusted using different cross-ply angles of the MFC piezoelectric patches and composite laminate metamaterial plates.