Structural Frequency Response Research Articles

A broadband second-order bandpass frequency selective surface for microwave and millimeter wave application.

This paper presents a frequency selective surface (FSS) with a wideband second-order bandpass response in the dual-band of microwave and millimeter wave. The overall structure consists of three layers of metal pattern and two layers of thin dielectric substrate. The top and bottom metal layers have capacitive patches with integrated curled Jerusalem cross slot resonators, while the intermediate metal layer has an inductive grid structure with cross-shaped slot resonators. The incorporated slot resonators play a pivotal role in achieving the desired transmission poles or zeros, which enable a wideband second-order filtering response in the dual-band and a quick roll-off at the passband edges, increasing the efficacy of electromagnetic shielding. To fully investigate the structure's frequency response, an equivalent circuit model of the structure is created, spanning the complete frequency range of 5-50 GHz. Physical samples are created and measured to confirm the suggested approach's efficacy. The passband center frequencies of the FSS are found at f1 = 19.42 GHz and f2 = 42.78 GHz, and the - 3dB bandwidth is 4.34 GHz (17.25-21.59 GHz) and 8.54 GHz (38.51-47.05 GHz), respectively. The simulation results align well with the experimental data. The transmission response rapidly transitions from the passband to the stopband at the passband boundaries.

Structural Damage Detection Based on Structural Macro-Strain Mode Shapes Extracted From Non-Stationary Output Responses

Abstract Long-gauge Fiber Bragg grating (FBG) strain sensors have been widely employed because of their broader measuring range and higher sensitivity. However, current structural damage detection methods using macro-strain modal parameters are based on structural frequency response function or stationary power spectrum density, which are not applicable to non-stationary responses. To overcome this limitation, an improved method is proposed in this paper for structural damage detection based on structural macro-strain responses under unknown multi-point non-stationary excitations. First, a new concept of macro-strain energy spectrum transmissibility (MEST) is proposed using structural non-stationary macro-strain responses, and it is derived that MEST at a certain system pole equals the ratio of macro-strain mode shape. Then, the singular value decomposition (SVD) technique is adopted for the MEST matrix to identify structural natural frequencies and macro-strain mode shapes. Finally, two damage detection indicators are constructed based on the identified normalized macro-strain mode shape (NMMS). The first indicator is the difference in structural NMMS before and after structural damage. The second one is based on the curvatures of structural NMMS, which can be used for structures without intact baseline. Numerical verifications are conducted to identify beam-type structural damage under multi-point nonstationary excitations or vehicle loads. Five damage scenarios with different measurement noise levels are investigated, and damage detection results validate the effectiveness of the proposed method.

Analyzing Temperature – Dependent Structural Changes and Frequency Response of a Ferroelectric Nanocomposite Based on Triglycine Sulfate with Oxidized Multiwalled Carbon Nanotubes

The present work is a continuing study on anomalous properties of the ferroelectric nanocomposite from triglycine sulfate (TGS) and oxidized multiwalled carbon nanotubes (OMWCNT). In this study, the nature of frequency response in a region of 102–107 Hz at low temperatures (63–273 K) will be clarified by analyzing structural changes when reducing temperature. It was found that the interaction between TGS and OMWCNT inhibited the switching of SO4 - groups, leading to a significant increase in relaxation time, activation energies and coercive fields. Consequently, the domain – wall freezing occurred at higher temperatures than those in pure TGS.

Temperature effects on noise radiated by concrete railway structures

In recent years, concerns have arisen regarding the periodic deformation of high-speed railway tracks owing to the temperature effects caused by the solar radiation. This phenomenon has prompted investigations into temperature-induced changes in the dynamic responses of vehicle–track–bridge systems. Previous studies have commonly taken the additional track irregularity caused by thermal deformation as the sole factor affecting dynamic responses while neglected changes in the structural frequency response characteristics. Structural radiation noise is also a prominent issue that affects the lives of people and the environment. However, studies on track–bridge-borne noise rarely consider the influence of temperature. To address the impact of temperature on structure-borne noise radiated by tracks and bridges, this study employed a sequentially coupled multi-physics analysis method. This approach allowed a comprehensive exploration of the temperature effects on track irregularities, structural frequency responses, and sound radiation efficiency. A full-scale temperature deformation field test of a CRTS III slab was also conducted to determine the necessary initial thermodynamic boundary conditions. The analysis results revealed that the thermally induced deterioration of track irregularity and changes in structural frequency response characteristics were the primary factors affecting structure-borne noise radiated by track–bridges under local climate conditions.

Frequency response of the construction of a large-span building with a cylindrical-and-slab roof†

Relevance of the research. Numerical studies of structural frequency response of a large-span building with cylindrical-and-slab roof as a large mechanical system were carried out. Finite element model No. 1 “Superstructure-Fixed-end” . The purpose of the study was to develop the methodology for modal analysis of a large-span building structure with a cylindrical-and-slab roof as a mechanical system with a large number of degrees of freedom . Methods. Numerical analysis of the building dynamics was carried out with the use of the САЕ (Computer-aided engineering) software package Femap NX NASTRAN, which implements the finite element method. Results. The “dangerous” resonant frequencies and forms of harmonic oscillations of the structure were revealed, and the sensitivity of the buildings’ reactions to various structural changes was analyzed. Frequency analysis of harmonic response of the building allowed to obtain dependences of amplitude values of nodal displacements (accelerations) and stresses in finite elements from the frequency of the inducing external force. In the next article, it is proposed to conduct a dynamic analysis of a large-span building with a cylindrical-and-slab roof for seismic effects.

Receptance coupling substructure analysis based FRF modeling for multi-segment shell with nonlinear joint interface

Multi-segment shell typical of underwater vehicles is currently important underwater equipment. Stealth performance is a key indicator to improve the working capacity of underwater vehicles. Low-noise design is an important means to improve stealthy performance. Accurate and effective identification of its structure Frequency Response Function (FRF) is the premise of low-noise design. However, the multi-section shell joint interface has many connection points, complex transmission path and typical nonlinear characteristics, which challenges the acquisition of its structural FRF. The Receptance Coupling Substructure Analysis (RCSA) is used to segment the multi-stage shell, which can realize the integration of finite element method and experimental method, and provide an effective way to obtain the FRF of multi-segment shell. At the same time, the multi-segment shell is a typical thin-wall structure, and its actual buckling process under impact is a nonlinear (large deformation) process. Therefore, the nonlinear joint interface is constructed based on linear connection, and the RCSA for nonlinear joint interface is studied. On the basis of accurately obtaining the FRF, it is of theoretical and application significance to study the low noise design of shell.

Numerical thermal frequency prediction of smart composite structure and experimental validation

Thermal eigenvalue characteristics of layered composite panels are obtained numerically utilizing the higher-order deformation kinematics, and the exactness of the solution has been verified with in-house experimentation. The laminated panel configuration bonded with and without shape memory alloy (SMA) fibres is modelled mathematical using the equivalent single-layer theory and third-order displacement kinematics. The functional composite structural properties under the elevated temperature are introduced in the current model for the necessary activation via the marching technique (to include the material nonlinearity due to SMA). The structural governing equation of motion is obtained by Hamilton’s principle and discretized using the isoperimetric finite element steps. Further, the computational modal responses are predicted using the in-house MATLAB computer code. The numerical solutions’ accuracy and stability have been compared with the earlier research data, including a few experimental verifications of thermal/ambient frequencies for laminated composite without SMA fibre. Further, a few numerical experiments have been carried out to show the significance of SMA fibre on the frequency responses of the parent structure, including temperature-dependent properties. The structural/material inputs, i.e., geometrical shapes, properties, geometrical parameters, and SMA-relevant data (volume fractions, VSMA; pre-strain, and recovery stress), are utilized for the computation of new results. The final insights have shown a significant improvement of frequency values, i.e., 4 %, 6 %, and 8 % of the laminated composite, while the volume fractions of SMA increase VSMA = 10 %, 15 % and 20 % for 3 % prestrain, respectively.

Interferometer-Based Distributed Optical Fiber Sensors in Long-Distance Vibration Detection: A Review

In unmanned monitoring such as perimeter security, pipeline detection, railway security, and so on, it is still a challenging task to accurately locate the irregular vibration events. Compared with traditional vibration detection technologies, distributed optical fiber vibration sensors (DOFVSs) have superior advantages such as high spatial resolution, large monitoring range, good concealment, excellent flexibility, and simple sensing structure. The DOFVS can be mainly classified into two types, i.e., the interferometer-based DOFVS (IDOFVS) and the backscattering-based DOFVS (BDOFVS). In particular, IDOFVS has unique sensing advantages, such as high stability, simple structure, high sensitivity, and wide frequency response. In this article, the development of long-distance IDOFVS in recent years has been summarized. The sensing principle of IDOFVS has been theoretically explained. The specific classification of the IDOFVS and the corresponding sensing structures are described in detail. In addition, the long-distance distributed vibration sensing structure and processing algorithms, such as denoising and locating algorithms, are analyzed. Finally, the performance of recent long-distance IDOFVS has been compared and the development direction has been discussed.

Mechanical Structure Design and Experimental Study of Gamma-ray Monitor for Small Satellite Payload

In this paper, a novel mechanical structure for a gamma-ray monitor (GRM) is designed for a small satellite payload. Its structural stiffness, strength and dynamic response are directly related to the performance of the novel GRM, which must meet the static and dynamic characteristic requirements of the structure in a harsh vibration environment. The static and dynamic simulation of the structure are carried out by finite element method (FEM), and the mechanical structure response laws of the novel GRM are analyzed and validated by vibration tests. Through comparing the frequency response simulation results with the vibration test results, the minimum safety factor of the key components of the structure is 4.07, the fundamental frequency error is within 5.04%, the acceleration response error is within 8.5%, the root mean square of total acceleration (Grms) error is within 14.2%, and the sinusoidal characteristic sweep frequency error before and after the vibration test is within 5.0%. The results show that the payload structure has large structural stiffness, high strength and reasonable frequency response characteristics, and meets the design requirements.

An efficient method for train–track–substructure dynamic interaction analysis by implicit-explicit integration and multi-time-step solution

In this work, a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train–track–substructure (TTS) system. It is called implicit-explicit integration and multi-time-step solution method (abbreviated as mI-nE-MTS method). The TTS system is divided into train–track subsystem and substructure subsystem. Considering that the root cause of low efficiency of obtaining TTS solution lies in solving the algebraic equation of the substructures, the high-efficient Zhai method, an explicit integration scheme, can be introduced to avoid matrix inversion process. The train–track system is solved by implicitly Park method. Moreover, it is known that the requirement of time step size differs for different sub-systems, integration methods and structural frequency response characteristics. A multi-time-step solution is proposed, in which time step size for the train–track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand, namely the time spent for m implicit integral steps is equal to n explicit integral steps, i.e., mI = nE as mentioned above. The numerical examples show the accuracy, efficiency, and engineering practicality of the proposed method.

On the electromechanical energy absorption of the reinforced composites piezoelectric MEMS via Adaptive neuro-fuzzy inference system and MCS theory

Capability of energy absorption in sandwich curved high-order beam structures is investigated in this study. The structure is composed of two surrounding piezoelectric layers with a composite core on a viscoelastic foundation. The composite core is made of carbon nanotube reinforced epoxy with 3 different patterns. Equivalent composite material properties are obtained utilizing Halpin-Tsai approach. Moreover, scale effects in this nano-composite is introduced using modified coupled stress theory (MCS) and the governing equations are derived employing Hamilton's principle. Generalized differential quadrature method (GDQM) along with Newmark-beta are used as a high performance and suitable method to numerically obtain time response of the system. In addition, artificial neural network is employed to overcome the complexity in formulation and solving differential equations with extremely lower computational costs. Utilization of ANN requires a valid dataset from experimental or numerical analyses. This dataset is collected from the numerical results in this study. The results are validated by comparing outcomes of the vibrational and damping responses of the present structure with results of a published study in this field. Afterwards, a detailed displacement–time analysis is presented for the current structure. In addition, the ANN shows capability of presenting high accuracy results to predict the amplitude, damping and frequency responses of the current structure in new loading and boundary conditions.

Using a rhythmic human shaker to identify modal properties of a stationary human body on a footbridge

Dynamic properties of the human body are basic parameters in biomechanics and many related areas. Experimental test is the most reliable manner to obtain dynamic parameters of the human body. Traditional method usually employs shaking table test or well-designed test rig driven by a mechanical shaker, which is always expensive and sometimes not available. This paper presents a simple but efficient transmissibility-based procedure for testing the dynamic properties of a human body. The excitation is generated by a human shaker with rhythmic movement acting on a flexible structure (either a footbridge or a long-span floor). Wide band excitation frequency can be generated even excite in a narrow-band owing to the multi-harmonics of the footfall force. The procedure consists of two main steps, namely, to identify the modal properties of the supporting structure and to establish the transmissibility of the human body. The human excitation force is found to be highly correlated with the body motion based on simultaneous footfall measurement and 3D motion tracking. To this end, the human excitation force is reconstructed and calibrated using the human body motion. The structural frequency response function is established using the footfall force and the bridge acceleration. Then the modal properties of the supporting structure, i.e. the vibration frequencies, mode shapes, and damping ratios and modal mass, are identified. The performance of human excitation method is checked by conventional ambient vibration testing and impact testing methods. Transmissibility of the human body is obtained by motion measurement at the supporting point and the stationary human body. The identified resonance frequency of the human body is further modified to obtain its natural frequency since the body is heavily damped. The feasibility of the procedure is demonstrated in identification of the dynamic properties of a footbridge with a stationary occupant having different postures.

Flutter Boundary Prediction Based on Structural Frequency Response Functions Acquired from Ground Test

Establishing an accurate, fast, and low-risk flutter boundary prediction method is of great significance for flight vehicle design. In this paper, a ground flutter boundary prediction method (GFBP) based on experimental structural frequency response functions (FRFs) is proposed. A low-order multi-input multi-output (MIMO) aeroelastic system is established by combining the structural FRFs acquired from a ground test and the calculated unsteady aerodynamic FRFs in physical coordinates. The multivariable Nyquist criterion is used to predict the flutter boundary. A fixed-root aluminum plate wing is selected as the research model. A GFBP experiment is carried out for the wing’s normal state, leading-edge clump weight state, and trailing-edge clump weight state. The feasibility and accuracy of the proposed method are verified by comparison with theoretical flutter results, in which the errors of flutter speed and frequency in the test statistics are no more than 1.7%. In a simulation model established by the proposed method, Monte Carlo simulation is used to study the influence of deviations in the mode frequency and damping of the structural FRFs and deviations in the positions of excitation and measurement points in the ground test. The experiment and simulation results show that the proposed method can predict the flutter boundary accurately with accurate positions of excitation and measurement points, and it has good robustness to deviations in the mode frequency and amplitude of the structural FRFs.

Vibration-Driven Triboelectric Nanogenerator for Vibration Attenuation and Condition Monitoring for Transmission Lines.

Vibration is an omnipresent energy source that is renewable and has the potential to cause damage to transmission lines. Harvesting harmful vibration energy can achieve vibration attenuation. Here, a vibration-driven triboelectric nanogenerator (V-TENG) with the potential for vibration attenuation is proposed as a power source for monitoring the operating condition of transmission lines. The V-TENG with structural optimization and frequency response range improvement is first discussed, indicating that it has a simple structural design with a good output performance. Then an energy management circuit is used to improve the charging efficiency of large capacitors. The vibration attenuation effect and wireless transmission system are verified in the simulation environment, benefiting from the well-designed structure and outstanding electric performance. This work demonstrates an efficient strategy for harvesting vibration energy through the TENG, which provides valuable guidance for further construction of online monitoring of transmission lines.

BEAM-TYPE ACOUSTIC METAMATERIAL DESIGN FOR VIBRATION SUPPRESSION WITH STRUCTURAL DAMPING

Vibration suppression of a beam-type acoustic metamaterial with periodic cavities filled by a viscoelastic membrane that supports a hollow mass still filled by a viscoelastic membrane that supports a local resonator is investigated. First, the proposed beam-type acoustic metamaterial is modeled as a one-dimensional mass-in-mass-in-mass (MMM) lumped parameter chain with structural damping, and then a mass-in-mass (MM) lumped parameter chain with structural damping is also given for comparison. For the two chains, the influence of structural damping on band structures are considered, and the loss factors associated with all propagating Bloch modes are compared. Finally, as an example, the beam-type metamaterials based on MM model with structural damping and MMM model with structural damping are designed to suppress vibration, respectively. The viscoelastic membranes act as structural damping. The finite element method based on Kirchhoff’s plate theory is developed to capture dynamic displacement fields of different metamaterials. Structural frequency response is calculated for different configurations of cantilevered structures when disturbance is considered. The results show that the proposed beam-type acoustic metamaterial based on MMM model with structural damping has higher dissipation and display high damping and does not sacrifice stiffness than MM model with structural damping.

Beam-type acoustic metamaterial design for vibration suppression with structural damping

Vibration suppression of a beam-type acoustic metamaterial with periodic cavities filled by a viscoelastic membrane that supports a hollow mass still filled by a viscoelastic membrane that supports a local resonator is investigated. First, the proposed beam-type acoustic metamaterial is modeled as a one-dimensional mass-in-mass-in-mass (MMM) lumped parameter chain with structural damping, and then a mass-in-mass (MM) lumped parameter chain with structural damping is also given for comparison. For the two chains, the influence of structural damping on band structures are considered, and the loss factors associated with all propagating Bloch modes are compared. Finally, as an example, the beam-type metamaterials based on MM model with structural damping and MMM model with structural damping are designed to suppress vibration, respectively. The viscoelastic membranes act as structural damping. The finite element method based on Kirchhoff's plate theory is developed to capture dynamic displacement fields of different metamaterials. Structural frequency response is calculated for different configurations of cantilevered structures when disturbance is considered. The results show that the proposed beam-type acoustic metamaterial based on MMM model with structural damping has higher dissipation and display high damping and does not sacrifice stiffness than MM model with structural damping.

A computational three-dimensional elasticity theory for bending and frequency analysis of the axisymmetric circular/annular plates via machine learning and discrete singular convolution integration methods

The present study deals with the frequency and bending behavior of annular/circular nanocomposite plates. The nanocomposite is made of three-phase materials of graphene oxide (nanoscale) and carbon fibers (microscale), and epoxy matrix (macro-scale) in multiple layers of different orientations. The governing equation extracted to investigate the multiscale hybrid laminated nanocomposite reinforced (MHLNR) is a three-dimensional elasticity theory. Furthermore, the whole structure is on the elastic substrate, which takes into account the horizontal forces in the calculations. The displacement compatibility and equilibrium condition are considered in the interlayers of the three, five, and seven layers of the composite structure. The bulk material properties at each layer are evaluated utilizing fiber micromechanics and Halpin–Tsai equations. The discrete singular convolution method is employed to transform the equations and solve equations. The obtained results are further verified using several references in this field. In addition, an adaptively tuned deep neural network model is designed based on the data of the current study to predict the results. Finally, a comprehensive parametric study is carried out to demonstrate the influences of different parameters on the internal stress field and frequency responses of the current sandwich structure.

A high performance hybrid passive base‐isolated system

This paper proposes a novel high performance hybrid passive base-isolated system integrating the base-isolated system (BIS) with the tuned tandem mass damper inerters (TTMDI), referred to as the BIS+TTMDI. To reveal the interaction between two components and their integrated control performance, the proposed configuration is modeled by a simplified four degree-of-freedom model together taking the dynamic characteristics of the isolation system, TTMDI, and superstructure into inclusion. Employing the optimization criterion defined as minimization of the dimensionless variance of superstructure displacement relative to the ground and by resorting to the particle swarm optimization, the system parameters of TTMDI are tuned to get their best integrated control performance. Evaluations are in turn unfolded on the performance taking into diverse TTMDI inertial properties and different isolation layer characteristics account and robustness, to fully explore the effectiveness of reducing both the displacement and acceleration for the isolation layer and superstructure, the TTMDI's energy dissipation mechanism and capacity, evolution of stiffness and damping, stroke, and structural frequency response. Subsequently, the findings of the BIS+TTMDI in the frequency domain is further tested via the time history analyses using the real records including both near-field with pulse and far-field earthquakes. In two analysis domains, the integrated performance of the proposed BIS+TTMDI is compared not only to the BIS but also to the BIS+TMDI, as well as to the BIS+TTMD and BIS+TMD. Results confirm that the BIS+TTMDI is a high performance system, namely, with high control effectiveness, high robustness, highly smaller stroke, and drastically reduced damping demand.

Modeling of Thin Plate Flexural Vibrations by Partition of Unity Finite Element Method

This paper presents a conforming thin plate bending element based on the Partition of Unity Finite Element Method (PUFEM) for the simulation of steady-state forced vibration. The issue of ensuring the continuity of displacement and slope between elements is addressed by the use of cubic Hermite-type Partition of Unity (PU) functions. With appropriate PU functions, the PUFEM allows the incorporation of the special enrichment functions into the finite elements to better cope with plate oscillations in a broad frequency band. The enrichment strategies consist of the sum of a power series up to a given order and a combination of progressive flexural wave solutions with polynomials. The applicability and the effectiveness of the PUFEM plate elements are first verified via the structural frequency response. Investigation is then carried out to analyze the role of polynomial enrichment orders and enriched plane wave distributions for achieving good computational performance in terms of accuracy and data reduction. Numerical results show that the PUFEM with high-order polynomials and hybrid wave-polynomial combinations can provide highly accurate prediction results by using reduced degrees of freedom and improved rate of convergence, as compared with the classical FEM.

A normalization strategy for BESO-based structural optimization and its application to frequency response suppression

The bi-directional evolutionary structural optimization (BESO) method has been widely studied and applied due to its efficient iteration and clear boundaries. However, due to the use of the discrete design variable, numerical difficulties are more likely to occur with this method, especially in cases with strong nonlinearity. This limits the application of the BESO method in certain cases, such as the suppression of structural dynamic frequency response under high-frequency excitation. In this work, a normalization strategy is proposed for the BESO-based topology optimization, by which the magnitude of the sensitivities can be efficiently unified to the same order to avoid the possible numerical instabilities caused by the nonlinearity. To validate its merit in applications, the normalization-based BESO (NBESO) method is proposed for minimizing the structural frequency response. By means of the weighted sum method, a normalized weighted sum method is also proposed for multi-frequency involved problems. A series of 2D and 3D numerical examples is presented to illustrate the advantages of the NBESO. The effectiveness of the NBESO for multi-frequency response suppression is also demonstrated, in which the frequency ranges below and above the eigenfrequency are involved, respectively.