Vibration Behavior Research Articles

Nonlinear dynamic behavior of single-layered black phosphorus with an attached mass

The investigation of black phosphorus-based (BP)-based mass sensors provides theoretical support for the development of mass-detection devices. This study examines the non-linear dynamic behavior of a rectangular single-layered BP (SLBP) with an attached mass through the utilization of molecular dynamics (MD) simulations and a nonlinear orthotropic plate model (NOPM) with a concentrated mass. The results indicate that significant deformation of an SLBP with an attached mass necessitates consideration of geometric nonlinearity, although the attached mass does not affect the deformation. Additionally, this paper discusses the impact of the attachment mass and the amplitude of harmonic force on the non-linear forced vibration of the SLBP. It is observed that as the attachment mass increases, the nonlinear vibration resonance frequency decreases, while the peak amplitude increases. Furthermore, the thermal nonlinear vibration of SLBP with an attached mass has been investigated, revealing that an increase in the attached mass leads to a decrease in the nonlinear vibration frequency but an increase in the amplitude of the nonlinear vibration of SLBP with an attached mass. Overall, comparison with MD simulation results, this investigation suggests that NOPM with a concentrated mass effectively describes the nonlinear vibration behavior of an SLBP with an attached mass, providing theoretical support for designing such devices to detect attached masses.

Multi-criteria decision making for timber constructions: analysis of ceiling types using utility analysis

Abstract Purpose: Timber constructions are gaining prominence in global decarbonization efforts for climate goals. While addressing greenhouse gas emissions is crucial, building planning must consider multiple factors. Methods: This study compares three timber construction methods for office ceilings—solid wood, linear-shaped, and composite timber-concrete—to conventional reinforced concrete. Fourteen timber alternatives are analyzed based on thirteen criteria, covering environmental and construction aspects of resource use, climate protection, building physics, and structural considerations. The utility analysis, a multi-criteria decision-making method, ranks the alternatives while considering all criteria simultaneously. Sensitivity analyses with different criteria weightings examine the robustness of the rankings. Results: A ribbed slab structure with a wet screed is recommended for office ceilings, prioritizing vibration behavior and environmental aspects. Solid wood and linear-shaped ceilings outperform composite timber-concrete or reinforced concrete in building physics and structural aspects. Dry-screed alternatives are not presently recommended due to vibration and economic reasons. Conclusions: This study shows that the utility analysis supports the decision-making in the wooden building parts’ design and planning process. Since the ranking of alternatives depends on the set criteria and their weighting, the seemingly objective decision is based on subjective evaluations. Thus, sensitivity analyses with different weightings are essential, and transparent decision-making documentation is crucial.

Ударное возбуждение магнитоупругой системы периодической последовательностью сверхкоротких импульсов поля

The nonlinear magnetization precession in normal magnetized ferrite film which has magnetic, elastic and magnetoelastic properties is investigated. The excitation field is presented as a vibration on resonance frequency which is modulated by short pulses which frequency is more lower than resonance frequency. It is proposed the formation procedure of periodic succession of ultra-short pulses by the involution to even degree of modulation signal sine. It is found two different cases of excitation: first when modulate pulse duration is larger than initial signal period and second when modulate pulse duration is smaller than initial signal period. In the first case the modulated signal has the form of main frequency vibrations tandem and in the second case the modulated signal has the form of unit sign-variation pulse. It is investigated the time development of magnetic and elastic vibrations whish are firmed by excitation field. It is shown that in the first case the magnetization vibrations at first hat sharp jump to upward and after this decreases by exponent. In this case the elastic vibrations after the same jump at first increases and then decreases by exponent. The elastic vibrations behaviour is interpret as energy pump from magnetic system to elastic system. In the second case the initial jump both vibrations is absent. It is investigated the degree modulation index influence to excited vibrations. It is shown that by increasing of this index the amplitude of magnetic and elastic vibrations decreases. It is investigated the magnetization excited vibrations character by different degree of magnetoelastic connection. It is introduced the coefficient multiple of magnetoelastic constant which is equal to ratio of considered constant to value of magnetoelastic constant of yttrium iron garnet. It is shown that by increasing of multiple coefficient the magnetization vibrations period is increased. It is found the sharp increasing the period by determined value of multiple coefficient which has a threshold character. It is investigated the excitation of magnetization in large time interval when the multiple coefficient is above the threshold value. It is found the principle difference between two cases when pulse duration is large or smaller as alternating field period. It is shown that in the first case the magnetization vibrations has the character of equilibrium position precession in conditions of orientational transition. In the second case the magnetization vibrations has the form of periodic re-orientational jumps from one equilibrium position to another. It is mentioned some properties of observed phenomena and proposed some recommendations for further investigations.

Vibrational Self-Consistent Field (VSCF) and Post-VSCF Method Calculations Combined with the Reference Interaction Site Model Self-Consistent Field Method Coupled with the Constrained Spatial Electron Density Distribution: Applications to NaHCOO in Aqueous Phase.

Investigating vibrational behavior in solution is crucial for understanding molecular dynamics within a solvent environment. Notably, the analysis of Raman spectra for molecules in solution is important owing to its ability to unveil intricate solute-solvent interactions. Previous studies have effectively employed frequency calculations utilizing the reference interaction site model self-consistent field method in conjunction with constrained spatial electron density distribution (RISM-SCF-cSED) to understand molecular vibrations in solution, primarily focusing on fundamental vibrational modes. However, the oversight of overtones and combination tones in these studies prompted us to combine the vibrational self-consistent field (VSCF) and vibrational second-order Mo̷ller-Plesset perturbation (VMP2) methods with RISM-SCF-cSED to address these aspects theoretically. Illustrating the efficacy of this integrated approach, we computed the Raman spectra of sodium formate (NaHCOO) in water, revealing the necessity of accounting for molecular anharmonicity in solution vibrational analysis. Our findings underscore the potency of VSCF and VMP2 in conjunction with RISM-SCF-cSED as a robust theoretical framework for such calculations.

Influence of 3D printed adherend design on structural performance and vibrational behaviour of adhesively bonded joints

Influence of 3D printed adherend design on structural performance and vibrational behaviour of adhesively bonded joints

Dynamic modeling and vibration suppression evaluation of composite honeycomb hemispherical shell with functional gradient protective coating

The vibration reduction performance of composite honeycomb hemispherical shells (CHHSs) coated with functional gradient protection coating (FGPC) are investigated in this work. Using the first-order shear deformation theory and the power-law distribution rule, the virtual spring technique, the regional decomposition method, and the Newmark-Beta approach, etc., a dynamic model of the FGPCCHHSs under base excitation is formulated to solve the inherent characteristics and displacement responses in time and frequency domains. After a set of convergence analyses are completed to ascertain an appropriate segment number and the stiffness values of virtual springs employed in the predictive model, the forecasted vibration parameters are verified using the literature and experimental results that are performed on uncoated and coated shells. The maximal natural frequency errors of the current model compared to the experimental results are 3.8% and 4.8%, and the displacement response errors under different excitation amplitudes are less than 10.3% and 12.7%, respectively, which demonstrate the correctness of such a model. Finally, the impact of key structural and material parameters on the vibration behaviors of the FPGCCHHSs is evaluated. To improve their vibration suppression capability, it is recommended to choose a high gradient index of coating material and a large thickness ratio of the FGPC to the overall shell with a reasonable moduli ratio of Material A to Material B of the FGPC to improve vibration reduction capability. This study offers a practical model tool and several important design recommendations for vibration prediction and dynamic attenuation of honeycomb sandwich hemispherical shell structures in aerospace engineering.

Nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells: Theoretical and experimental investigations

In this study, the nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells (FHSCSs) are investigated theoretically and experimentally. Initially, a time-domain minimum residual (TDMR) method is first adopted for the analysis of nonlinear free and forced vibrations of the FHSCSs, which is based on a dynamical model developed, with the effective material parameters of the foam-filled honeycomb core being obtained by employing the Gibson method and the Hamilton equivalence technique. Based on the high-order shear deformation shell principle and von Karman's theory, the nonlinear natural frequencies and resonant responses are solved using the Broyden iterative approach and TDMR method. Furthermore, several literature results are utilized for the rough verification of such a method. Meanwhile, the FHSCS specimens are made manually and comprehensive tests with various base excitation energies are undertaken to provide a thorough validation of the current method. It can be found that the largest calculation errors of natural frequencies and resonant responses are 4.9 and 12.3%, respectively. Finally, the influences of the core form and base excitation amplitudes on the nonlinear vibration behaviours of the FHSCSs are examined. It can be noticed that the foam-filled FHSCS structure exhibits a more excellent anti-vibration capability compared to the non-foam-filled structure. The solving method, fabrication technique, and valuable findings in the current study highlight the path for the design and implementation of such advanced shells.

Isogeometric 3D optimal designs of functionally graded triply periodic minimal surface plates

Recent research attention has been drawn to the interdisciplinary engineering applications of functionally graded triply periodic minimal surface (FG-TPMS) lattice structures due to their lightweight yet high mechanical properties. These features are especially important in the dynamic structural behaviors yet the TPMS gradation has not been studied in multi-dimensions. This paper presents the establishment of the optimization problem finding the 3D optimal designs of FG-TPMS plates under free vibration by assigning the relative density to each control point and applying the concept of NURBS-based interpolation for the continuous effective mechanical properties. The general 3D case of the constraint on total material volume is derived from the existing 1D case, which is required for the 3D optimization problem. Isogeometric analysis and generalized shear deformation theory are utilized to analyze the free vibration behavior of the FG-TPMS plates. Verification with the 1D case and a parametric study of the 3D FG-TPMS plate are conducted. Optimization examples include both basic and complex geometries. Unseen-before optimal 3D FG-TPMS designs with significantly elevated natural frequencies are obtained. The physical meaning of the optimal solutions can be explained by the similarity to porous structures in nature: less dense in the center or at free end, and more dense at the constrained boundaries and surfaces.

A preliminary study on generation of axle box vibration spectra for metro vehicles in China using the developed spectral synthesis method

ABSTRACT In-service metro vehicles in China exhibit diverse vibration behaviours. This study focuses on analysing the vibration characteristics of these vehicles, with a particular focus on the complex non-stationary axle box vibrations measured on-site, as they closely correlate with wheel-rail interaction dynamics. A developed PSD-based synthesis method is first proposed to quantify the axle box vibration. The axle box vibration spectra of the metro vehicles in China are then generated from the measurements for various vehicles. Furthermore, a multi-line segment flat spectrum, designed specifically for the shaker loading, has been produced. The results show that the proposed method can determine the parameters (segment number, quantile) by the energy conservation law, which avoids the empirical value selection in previous methods and can be effectively utilized to generate the vibration spectra of the axle box. In addition, a notable distinction exists between the IEC 61,373 standard spectrum and the axle box vibration spectra of Chinese metro vehicles. While the former represents a single-peak spectrum ranging from 20 ~ 100 Hz, the latter consists of a multi-peak spectrum with peak frequency bands exceeding 100 Hz. The wear condition of the wheel-rail surface has a pronounced contribution to the vibration spectral magnitude. In cases of wheel-rail surface severe wear, the vibration spectrum values in the Z direction surpass the standard spectrum values across most frequencies, with the highest spectral value notably observed within 50 ~ 200 Hz. Such observations should be thoroughly taken into account in the analysis of fatigue damage to mounted equipment.

Tailoring perovskite ceramics for improved structure, vibrational behaviors and radiation protection: The role of lanthanum in PbTiO3

This study investigates the characteristics of lanthanum (La)-doped lead titanate (PbLaxTi(1-3x/4)O3 where, x = 0.0, 0.02, 0.04, 0.06, 0.08, and 0.1), a type of perovskite ceramic. It specifically focuses on analyzing its structure, vibrational properties, and efficacy in shielding against radiation. The prepared samples are investigated by X-ray diffraction (XRD), which clarified that the small doping of La (x ≤ 0.06) produced the required phase, and increasing the La doping (x > 0.06) produced nonrequired phases (secondary phase). Also, increasing the La doping converted the crystal symmetry from tetragonal to cubic, which was confirmed by the tetragonality raio (c/a) calculations. Also, the samples are investigated by Fourier transform infrared (FTIR) spectroscopy to confirm the XRD results. Transmission electron microscopy (TEM) examination clarified that the prepared samples were in the nanoscale range with a maximum crystallite size value of around 70 nm. In addition, the shielding effectiveness of all the prepared samples was theoretically evaluated using the Phy-X/PDS program by considering characteristics such as the linear attenuation coefficient (GLAC), mean free path (GMFP), transmission factor (TF), and radiation protection efficiency (RPE). Increasing the La concentration increases the theoretical density to 4.98 gm/cm3 at x = 0.1, leading to low TF and GMFP values and high GLAC values. This produces samples with high attenuation to radiation and high shielding effectiveness.

Multiscale simulation and experimental studies on modal damping of ultra‐thick CFRP laminates

AbstractThe vibration characterization of ultra‐thick laminates widely used in aerospace and marine industries was different from that of thin laminates. However, modal testing and simulation methods were generally limited to relatively thin laminates. To explore the vibration behavior of ultra‐thick laminates, a novel multiscale simulation technology based on the representative volume modal strain energy (RVMSE) method is presented for predicting modal damping in this paper. The adaptive Greedy‐Based Generation (GBG) algorithm is used to create a 3D random distribution of fibers for composites. Modal shape information of the structure is obtained according to the Lanczos algorithm, which is used as an input parameter for the microscopic model. This is followed by homogenization based on the volumetric analysis performed on representative volume elements (RVEs) to determine the strain energy in six directions. The calculation of modal damping is performed by using the modal strain energy (MSE) method and the damping properties of the six directions. The fast rate of convergence and high accuracy of the method are demonstrated through different examples. The vibration response predictions produced by novel RVMSE methodology are shown to closely match experimental measurements, providing scope to expand the application of this approach to more complex, ultra‐thick laminate components.Highlights The RVMSE method uses a higher level of homogenization to overcome the limitations of the traditional MSE method for calculating the damping of ultra‐thick CFRP laminates. The modal parameter error is controlled to less than 10%, and the experimental results fill the gap of the damping data of ultra‐thick CFRP structure. The proposed RVMSE model improves the accuracy of dynamic response prediction for ultra‐thick laminates.

Influence of non-uniform elastic foundations on free vibration behavior of nanocomposite plates interacting with a fluid environment based on a novel shear deformation theory

Influence of non-uniform elastic foundations on free vibration behavior of nanocomposite plates interacting with a fluid environment based on a novel shear deformation theory

Optimization and comparative analysis of an AISD suspension system with inerter element for enhanced ride and handling

This paper presents a comprehensive study on the modeling and optimization of an advanced suspension system, known as the Air Springs Inerter-Spring-Damper (AISD) system, incorporating an inerter element. A linear quarter car model is utilized to analyze the vibrational behavior of the AISD system when subjected to harmonic road disturbances. The steady-state response of the system is investigated by deriving the root mean square (RMS) values of the absolute relative displacement and acceleration of the sprung mass. To optimize the quarter car model, a criterion based on minimizing the absolute acceleration RMS while considering the relative displacement RMS is employed to calculate the inerter coefficient. The performance of the AISD suspension system is compared to that of both conventional quarter car systems and traditional air quarter car systems, with a focus on ride comfort and handling. The results demonstrate that the proposed AISD system outperforms the other two suspension systems, exhibiting a significant improvement in ride quality. Specifically, the AISD system achieves a 45% enhancement over the air suspension and an 82% improvement over the classic suspension system.

Free vibration analysis of bio-inspired double- and cross-helicoidal laminated composite plates

Nature-built structures effectively sustain higher loads without failing, even though they are made of weak organic materials. The laminated construction mode in various fish scales provides them toughness and flexibility. The present manuscript aims to carry out the free vibration analysis of double- and cross-helicoidal laminated composite plates inspired by the scales of fish. The study has been carried out using the recently proposed finite element-based higher-order zigzag theory. The influence of aspect ratio, side-to-thickness ratio, skew angle, and end conditions on the free vibration behavior of double- and cross-helicoidal plates is depicted. The mode shapes of the plates are studied in detail. The free vibration behavior of skew plates is also studied for the first time. An improved performance of the helicoidal plate compared to the conventional lamination scheme has been obtained.

Mechanism of antimony ion doping to optimize microwave dielectric properties of zinc zirconate tantalate ceramic

Herein, first-principles calculations predicted the atomic-scale variation of Sb5+ substitution for ZnZrTa2O8, and combined with the solid-phase reaction method to prepare ZnZr(Ta1-xSbx)2O8 (0.0 ≤ x ≤ 0.10) ceramics. ZnZr(Ta0.94Sb0.06)2O8 ceramics demonstrated the optimum microwave dielectric properties after sintering at 1350 °C for 6 h: εr = 24.92, Q × f = 134053 GHz (@7.18 GHz), and τf = −46.21 ppm/°C. For the non-intrinsic factors, the relative density increased from 96.54 % to 97.74 % and the average grain size increased from 19.88 μm to 21.85 μm, both of which reduced the dielectric loss. Regarding intrinsic factors, the progressive elevation of the Raman characteristic peak wave number and the heightened ionicity of Ta/Sb–O bonds predominantly account for the observed enhancement in εr. In addition, the attenuation of lattice vibrational damping behavior, the augmentation in electron cloud density, and the escalation of lattice energy collectively contribute to a decrement in dielectric loss. This study refines the examination of ionic substitution in ZnZrTa2O8 ceramics, offering theoretical insights for optimizing their dielectric properties and promoting their application in microwave communications.

Free vibration analysis of a sandwich conical shell with a magnetorheological elastomer core, enriched with carbone nanotubes and functionally graded porous face layers

In this paper, the free vibration behaviors of a sandwich conical shell with a magnetorheological elastomer (MRE) core enriched with carbon nanotubes (CNTs) and two functionally graded (FG) porous face layers are investigated. The mathematical modeling of the shell is performed via the first-order shear deformation theory (FSDT) incorporating the continuity conditions between the face layers and the core. The porosity parameters are adjusted to provide the same mass for all porosity dispersion patterns. The governing equations and boundary conditions are derived via Hamilton’s principle and are solved through a semi-analytical solution to attain the natural frequencies and the loss factors for various boundary conditions. First, appropriate triangular functions are utilized to provide an exact solution in the circumferential direction. Then, a numerical solution is presented in the meridional direction utilizing the differential quadrature method (DQM). The influences of various factors on the natural frequencies and loss factors are investigated including intensity of the applied magnetic field, mass fraction of the CNTs subjoined to the core, thickness of the CNT-reinforced MRE core, thickness of the FG porous face layers, porosity parameter and dispersion pattern of the pores in the FG porous face layers, and the boundary conditions. Numerical results show that although subjoining CNTs to the MRE core and applying magnetic field have weak effects on the natural frequencies of the shell, increases in the mass fraction of the CNTs and intensity of the applied magnetic field result in remarkable increases in the loss factors, and provide stronger vibration suppression.

Non-linear primary resonance analysis of stiffened FGM conical panels resting on viscoelastic foundation

This article investigates the non-linear forced vibrations and primary resonance analysis of stiffened FGM conical panels (OCPs) resting on a viscoelastic foundation utilizing a semi-analytical method. The classical shells theory and von Kármán nonlinear strain–displacement relations are used to model of OCPs. The equations of motion are derived by applying Hamilton’s principle. Then, the dimensionless equations of motion are established and converted into dimensionless nonlinear ordinary differential equations by applying Galerkin’s method. The solution of the ordinary differential equations is carried out based on the multiple-scale method for analyzing the vibration behavior. In this regard, the necessary relations for the nonlinear primary resonance and internal resonance of stiffened FGM-OCPs are obtained. To validate the suggested methodology, first, the results are verified with various previous research. Second, a numerical method based on the fourth-order Runge-Kutta’s approach is used for verifying the nonlinear vibration analysis. Finally, changes in various parameters such as viscoelastic foundation coefficients, stiffeners, temperature, semi-vertex angle and subtended angle are examined by helping the frequency response plots.

Optimization of energy absorption and vibration behaviour of TPMS Schwarz P and Schoen Gyroid lattice structures using Taguchi L9 orthogonal array

In this study, the optimization of printing parameters in fused deposition modeling (FDM) is addressed, focusing on their impact on energy absorption and vibration behaviour of triply periodic minimal surface (TPMS) lattice structures, specifically Pseudo-periodic-based Schwarz P and Schoen Gyroid designs. The experimental design employs a Taguchi L9 orthogonal array involving layer height (0.15 mm, 0.30 mm, 0.45 mm), build orientation (0°, 45°, 90°), and extruder temperature (190°C, 200°C, 210°C) as inputs. These lattice structures are generated through Math Mod and simulated using Blender, with Autodesk Mesh mixer refining the STL file. The lattice fabrication employs PLA (polylactic acid). Comparative analysis is conducted against a high-density solid structure lacking lattice design. Optimal parameters for Schwarz P lattice are found to be 0.45 mm layer height, 0° build orientation, and 200°C extruder temperature, while for Schoen Gyroid lattice, 0.30 mm layer height, 0° build orientation, and 210°C extruder temperature. Solid structure optimization yields 0.30 mm layer height, 90° build orientation, and 190°C extruder temperature. Solid structures outperform Schwarz-P and Schoen-Gyroid in energy absorption and vibration behaviour, with Schwarz P showing superior properties over Schoen Gyroid.

Vibration of microphone membrane: Effects of thermal stress

The aim of this work is to improve theoretical and experimental tools for modelling and characterising the global behaviour of measurement microphones in a large range of environmental conditions. In most of measurement microphones, the sensitive part is a vibrating membrane stretched and clamped on the body of the microphone. If the sensor is operated at ambient temperatures that significantly differ from atmospheric one, thermal expansion of the microphone membrane and body causes strain and stress variations in the membrane, which lead to altered vibrational behaviour when it is submitted to an acoustic wave. An analytical approach is developed here to express the thermal stress related to the fact that thermal expansions of the microphone membrane and body are different. These effects are then taken into account in a classical modelling procedure for describing the vibration of a microphone membrane in vacuo. An experiment, that relies on the electrostatic actuator technique, has been performed in a fine vacuum to characterise the first resonance mode of a commercial microphone membrane in low temperatures range, from atmospheric to cryogenic. The experimental results highlight the significant effects of the thermal stress induced by the differences between thermal expansion properties of the materials constituting the microphone. These results are consistent with the membrane vibration predicted by the analytical modelling proposed. Thus, even small differences between the thermal expansion properties of the microphone membrane and body have to be taken into account in a modelling procedure to get reliable predictions of the membrane vibration at various ambient temperatures.

An enhanced quasi-3D HSDT for free vibration analysis of porous FG-CNT beams on a new concept of orthotropic VE-foundations

The original primary objective of this study is to conduct a comprehensive investigation into the free vibration behavior of beams with porosity, reinforced by carbon nanotubes (CNTs). These beams are supported by an arbitrary orthotropic variable elastic foundation (AOVEF). The focus lies on understanding how the presence of porosity and CNT reinforcement, coupled with the complex support provided by the AOVEF, influences the vibration characteristics of the beams. In addition, we intend to examine the impact of a number of micromechanical models on the vibration properties of these beams. Four carbon nanotube variables are introduced to symbolize several CNT variations. CNTs’ mechanical properties are examined through a variety of micromechanical models. Shear deformation effects are considered into account in the framework of higher-order shear deformation (HSDT) beam theory. The equations of motion are constructed using Hamilton’s concept and the equation system for the FG-CNT beam with supported ends is solved via the Navier methodology. A new approach in elastic foundation modeling is the Arbitrarily Orthotropic Variable Elastic (AOP-VE) foundation. It builds on the Winkler layer concept but introduces the idea of a variable response along the length of the beam foundation. Unlike the Winkler-Pasternak model, AOP-VE allows for control over the directional properties of the Pasternak foundation. The study looks into multiple aspects, involving various distribution kinds of CNTs, the impact of Winkler and Pasternak factors, mode values, side-to-length ratio, porosity, and angle variation. The results indicate that these parameters have a major effect on the inherent vibration features of FG-CNT beams. The study results in various novel findings that improve the understanding of the subject topic and set a standard for future studies.