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An automated input–output experimental modal analysis technique has been developed and tested on a scaled laboratory model. An impulse force is generated by a heavy cogwheel (CW) at equidistant steps along a chosen driving path on a bridge. At least two accelerometers are required in order to evaluate the modal properties. Since the quality of the impact signal is not ideal, the moving mass along with corresponding frequency changes are applied to evaluate the mass-proportional mode shapes of the bridge with the CW mass eliminated. As an alternative, the mode shapes can be obtained from the relations between the fixed and moving accelerometers. The main advantage and novelty is that the process can be automated. Also new is the fact that a CW is applicable to experimental modal analysis as an exciter. The method provides modal parameters based on a dense network of measuring points.

This paper presents the dynamic analysis of a complex structure composed of two straight and curved beams connected through intermediate vertical beams, all made of functionally graded porous (FGP) materials. Unlike prior studies, which focused on simpler configurations, this work investigates the free and forced vibration behavior of such a structure for the first time. A novel finite element is developed, and its mass and stiffness matrices are derived to discretize the beams. Continuity conditions at the junctions of straight and curved beams are formulated, facilitating the assembly of the overall mass and stiffness matrices for the entire structure. The proposed method is validated through comparisons with simplified cases from the literature, demonstrating excellent accuracy. The study also explores the effects of various parameters on the dynamic response, offering practical insights for the design of advanced engineering structures such as bridges, roofs, and marine frameworks. By addressing the analysis of a complex structure, this work provides a foundational approach to improve the safety and performance of structural systems in diverse applications.

This research focuses on examining the vibrational properties of intelligent curved microbeams (CMBs) that incorporate metal foams and are enhanced with carbon nanotubes-reinforced piezoelectric (CNTRP) actuators. An advanced four-variable theory for shear and normal deformation is applied in the polar coordinate framework to investigate the microstructure, thereby negating the need for a shear correction factor. Additionally, the modified couple stress theory (MCST) is utilized to account for scale effects. The structural attributes exhibit thickness-dependent alterations following predefined functions. The governing equations of motion are deduced using Hamilton’s principle. In instances where the structure has simply supported ends, Fourier series functions are utilized to solve these equations. The outcomes are cross-validated in contradiction with previously documented works with more straightforward setups. The inquiry investigates the effects of critical parameters on the vibrational response of the structure. The results are corroborated in simpler scenarios using existing data in the literature to ensure accuracy.

This research investigates the free vibration of a rotating annular microplate under the flexoelectric effect. Initially, the Kirchhoff plate theory assumptions are used to express the displacement fields. After considering the displacement field, strains and their gradients are derived and substituted into the electric enthalpy and kinetic energy expressions. Subsequently, by applying Hamilton’s principle to the aforementioned equations, the electric and mechanical equations are computed. To derive the equations of motion, initially, the polarization vectors and their gradients are derived from the electric equations and associated boundary conditions. Subsequently, these are incorporated into the mechanical equations, which also encompass electric components. It is notable that by removing the time-dependent terms from the in-plane equations of motion, the static displacement due to rotation at each speed is obtained. After deriving the equations of motion and boundary conditions, these equations are non-dimensionalized using non-dimensionalizing relations. In the next step, Hamilton’s principle is used to discretize the equations and boundary conditions. Consequently, by applying the generalized differential quadrature method and extracting the stiffness and mass matrices resulting from the transverse equation of motion and boundary conditions, the natural transverse frequency of the rotating annular microplate under the flexoelectric effect is calculated. The results of this research are useful for promoting the use of rotating annular microplants under flexoelectric effect for microelectromechanical systems designers with high efficiency.

In this work, a rectangular cellular microplate is taken into consideration which is embedded between two functionally graded carbon nanotube-reinforced composite layers that have the piezoelectric ability. Different patterns for the carbon nanotube dispersion are considered. Moreover, an external electrical voltage is applied to them. The displacements are described based on a higher-order shear deformation theory which is called hyperbolic theory and the size influence is captured via the modified couple stress formulations. The governing motion equations are then derived using the variational technique and Hamilton’s principle. Then, for simply supported edge conditions, a closed-form solution is provided. Next, it turns to validate the results in simpler states, and after that, the effect of the most prominent parameters on the results is investigated. It is observed that by increasing the external applied voltage to the face sheets, the frequencies are reduced. Also, the natural frequencies have a tendency to decrease as the dimensionless material length scale parameter increases. This study’s outcomes may help design and manufacture micro-/nano-electro systems, sensors and actuators, small-scale devices, and other engineering structures.

In this paper, the bending, dynamic responses and multi-objective optimization of the pyramidal lattice sandwich plate are studied. Initially, the paper calculates the equivalent elasticity moduli and equivalent shearing moduli of pyramid lattice core. Then, the kinematic relations between the plate and the pyramid grid core are established by using the improved FSDT. The governing differential equations and the conditions for boundaries are deduced from the Hamilton principle, and solved by using Navier’s method. To validate that the theoretical model is accurate, the paper compares the center deflection and natural frequency derived from theoretical calculations with the experimental and finite element results. In detail, this paper studies the influence of the number of single cells, thickness ratio, and lattice rod radius on the bending and free vibration behavior. Then, the key elements are chosen as design parameters. Next, the space of design variables is explored using the hybrid PSO-GWO algorithm to find Pareto optimal solutions. The optimum number of single cells, thickness ratio and radius of the pyramid lattice sandwich plates are finally derived to satisfy the conflicting desired objectives of maximizing natural frequency and minimizing center displacement and mass. The results show that the proposed equivalent model can predict the static bending and dynamic responses of pyramidal lattice sandwich plate well. In order to satisfy maximizing natural frequency and minimizing center displacement and mass, different Pareto optimal solutions are given for different design options by using the hybrid PSO-GWO algorithm.

The purpose of this research is to study the free vibration response of composite plates made up of three-phase polymer–glass fiber (FG)–carbon nanotubes (CNTs). Polymer matrix has an important property, i.e. the elastic modulus and Poisson’s ratio decrease over time. In this study, the waviness of the CNTs is also taken into consideration. A three-step hierarchical approach is adopted to estimate the elastic properties of the composite media. The governing equations are derived by quasi-3D plate theory and Hamilton’s principle. The adopted quasi-3D model takes into account the nonuniform shear and normal strain distribution and also satisfies the condition of traction-free on top and bottom surfaces. The natural frequencies of this composite are found using the Navier solution method for simply supported boundary conditions. This work investigates how the dimensionless frequency is affected by time, plate geometry, fiber mass fraction, and CNT mass fraction, all of which have a substantial impact. For example, it is highlighted that for a specific plate, after 60s, the frequency drops by about 14% if one takes the time parameter into account. In addition, increasing the mass fraction of CNTs or FGs results in higher frequencies.

This study examined the free vibration of a three-layered annular microplate, whose core and face sheets are composed of functionally graded saturated porous (FGSP) materials and functionally graded-graphene platelet-reinforced composites (FG-GPLRC), respectively. The microplate is supported by an elastic base, with the mechanical characteristics of all layers varying along the thickness direction. Employing the extended dynamic formulation of Hamilton’s principle, the equations of motion and boundary conditions are derived from the modified version of couple stress and first-order shear deformation theories, subsequently solved using the generalized differential quadrature method as an effective numerical approach. The study examines the impact of many parameters, including pore distributions, porosity coefficient, pore compressibility, dispersion patterns of graphene platelets, elastic foundation, small-scale parameter, and microplate aspect ratio. The results of this study may be beneficial for the construction of lightweight and sophisticated buildings.

Elastic metamaterials (EMs) are a new kind of artificial composite medium composed of complex micro-structural elements, which have unique dynamic properties and elastic wave regulation ability that their constituent materials do not possess. The existing researches on EMs mainly focus on wave characteristics in two-dimensional and three-dimensional infinite domains. However, actual EM structures are always in the form of finite structures such as rods, beams and plates, so it is more important for engineering applications to understand and master their natural and forced vibration characteristics. Therefore, it is necessary to establish an effective simplified solution method and framework with certain accuracy for the vibration analysis of such structures. In the early stage, we have studied the natural and forced vibration characteristics of EM beams from this point of view, and presented a simplified solution process. In this paper, a kind of sandwich beam structure with EMs as the core is further constructed, the simplified solution process is extended to such more practical model analysis, and the free and steady forced vibration analysis processes of the finite-size sandwich beam are given. The vibration characteristics different from the traditional sandwich beam are investigated, and some interesting and useful phenomena are revealed, including the absence of natural frequencies within bandgap (BG), the gathering of natural frequencies in the vicinity of band edges, and the particular modal correspondence before and after BG. Then, the corresponding formation mechanisms are explained from the perspective of wave propagation.

During the last years, civil infrastructure has experienced an increasing development to satisfy the society’s demands such as communication, transportation, work and living spaces, among others. In this sense, the development and application of methods to guarantee the structure optimal operation, known as Structural Health Monitoring schemes, are necessary in order to avoid economic and human losses. Modern schemes employ the structure vibration response as any damage will modify the structure physical properties, which will be reflected in the vibration response. Thus, by measuring the waveform changes of the response, the structure condition can be determined. Considering this fact, this paper investigates the effectiveness of Katz fractal dimension, Higuchi fractal dimension, Box fractal dimension, Petrosian fractal dimension, and Sevcik fractal dimension which are nonlinear measurements to extract features of vibration signals in order to determine the health condition of a 3D 9-bay truss-type bridge. The obtained results show that the algorithms corresponding to Higuchi and Petrosian fractal dimension algorithms exceed the other nonlinear measurements in efficiency to discriminate between a healthy structure and a damage produced by corrosion.

Studies reveal that the most prominent cause of bearing failure is a crack on any of its mating surfaces. When the crack is initiated, the bearing can still be used for some duration, but this is majorly depending upon the loading conditions. This work primarily focuses on the effects of different levels of static loading on the crack propagation after crack initiation. To analyze the effect of static loading, an axial groove defect was seeded on the outer race of a taper roller bearing randomly and bearing run continuously under five different static loading conditions. Initially, the bearing was made to run under loading conditions to initiate the crack naturally but the crack was not initiated even after 800 h of running. Therefore, crack was initiated artificially for the purpose of studying crack propagation. It was observed from the experimentation that in the case of maximum static load of 20 kg, the crack propagates rapidly in terms of area after 109 h of continuous running, whereas in the case of no load, it started propagating quickly after 267.5 h of running. Statistical analysis was also carried out for the recorded signals at different intervals of times, and it was observed that the Shannon entropy value was showing a sudden rise with the edge breakage (visually verified) while the crack was propagating. However, in the statistical analysis, none of the parameters showed a correlation with crack propagation. To develop the correlation of crack propagation, Shannon entropy of high, medium and low frequency bands of continuous wavelet-based (CWT) was carried out using different wavelets. Shannon entropy for high frequency band of CWT using Daubechies 10 as mother wavelet has responded well to the crack propagation as the value showed a sudden rise and an overall increase for edge breakage and crack propagation, respectively. A high frequency band of CWT using Daubechies 10 was found suitable for detecting edge breakage and crack growth at the same time because of its capability to respond to transient characteristics for a large duration of time.

To implement a safe and reliable design for high-tech industrial buildings, the system response should be accurate enough to include the effect of soil–structure interaction (SSI). This study proposed a simplified building–soil system to analyze the dynamic responses, using parameters that are representative of the practical design values for typical semiconductor fab structures in Taiwan. The responses of the simplified building–soil system subjected to dynamic horizontal loadings are verified in the frequency domain and time domain. The dynamic responses of the simplified building–soil system are found to agree very well with those of the complete system obtained by the half-space theory and by the numerical analysis program. It is shown that the proposed simplified system can effectively analyze the coupled SSI effects in the translational and rotational directions. It is also found that the structural responses may deviate significantly by neglecting the coupling of horizontal and rocking motions as the building has a deeper embedded foundation and a stiffer upper structure. The proposed method can be applied to the vibration analysis of high-tech industrial buildings subjected to dynamic loadings.

This paper reports the results of an investigation on the use of Generalized Beam Theory (GBT) to assess the buckling and vibration behaviors of thin-walled members and frames built from cold-formed steel circular hollow section (CHS) profiles. Initially, the concepts and procedures involved in performing GBT buckling and vibration analyses are presented, paying particular attention to the derivation of the mass tensors that account for the influence of the inertia forces. Then, the formulation, numerical implementation and validation of a GBT-based beam finite element for isolated members are described. Next, the determination of the frame linear stiffness, geometric stiffness and mass matrices, which incorporate the influence of the frame joints, is addressed. Finally, in order to illustrate the application and capabilities of the proposed GBT finite element formulation, numerical results are presented and discussed — they concern the buckling and vibration behaviors of an "L-shaped" frame. For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the code ANSYS.

Beams and beam structures are structural components commonly used in mechanical, aerospace, nuclear, and civil engineering. To meet the different engineering design limitations such as operational conditions, weight, and vibrational characteristics, these components may be made of various materials such as functionally-graded materials (FGMs), composites, and homogeneous materials. Functionally-graded (FG) beams play a key role not only in classical structural applications, but also have vast applications in thermal, electric-structural and electric-thermal-structural systems, e.g. in the form of FG beam energy harvesters, sensors and actuators. In all these applications, using new materials like FGMs can greatly improve the efficiency of the structural components and systems. Since FG beams are mostly used as moving components in engineering structures, vibration analysis of these components has been studied by numerous researchers. In order to solve the governing equation and related boundary conditions of the FG beams, powerful numerical methods with a high level of accuracy and fast rate of convergence are often required. The differential quadrature method (DQM) is a powerful and reliable numerical method which has been extensively used by researchers to perform the vibration analyses of FG structures in the last decade. In this paper, firstly various mathematical models which have been used to express the material properties of FGMs are reviewed. Secondly different elasticity theories which have been applied in vibration analysis of FG beams are summarized. In addition, a review on the DQM and its applications is presented. At the next step, a comprehensive review on free vibration analyses of FG beams based on different elasticity theories and in particular those using the DQM is performed. In continue, a brief review on the application of other numerical methods in vibration analysis of FG beams is presented. Moreover, because of the importance of nonlinear vibration analysis of FG beams, a review on the application of various numerical methods and different elasticity theories on nonlinear vibration analysis of FG beams is performed. Finally, a brief review on linear and nonlinear vibration analysis of FG microbeams, as a special type of FG beams, is presented.

This paper investigates the behavior of a pre-stressed arch under a sliding load, where the initial configuration can be obtained from the buckling of a straight column. The shape of the pre-stressed arch can be varied by increasing the end shortening. Subsequently, a sliding load is applied at a certain height level. The orientation of the applied load maintains the right angle with respect to the tangential line of the arch. By moving the load horizontally, the behavior of the arch can be explored. The governing differential equations of the problem can be obtained by equilibrium equations, constitutive relation, and nonlinear geometric expressions. The exact closed-form solutions can be derived in terms of elliptic integrals of the first and second kinds. In this problem, the arch can be divided into two segments where each segment is a part of a buckled hinged-hinged column mounted on an inclined support. The shooting method is employed to solve the numerical solutions for comparing with the elliptic integral method. The stability of the pre-stressed arch is evaluated from vibration analysis, where the shooting method is again utilized for solving the natural frequencies in terms of a square function. A simple experiment is set up to explore the equilibrium shapes. Poly-carbonate sheet is utilized as the pre-stressed arch. From the results, it is found that the results obtained from elliptic integral method are in excellent agreement with those obtained from shooting method. The equilibrium shapes from the theoretical results can also compare with those from the experiment. The pre-stressed arch can lose its stability and snap into an upside-down (inverted) configuration depending on the ratio of rise to span-length and loading height. The instability of the arch is not only detected during the pushing of the sliding load but a pulling load can also cause unstable behavior of the arch.

The use of composite conical shell structures across the globe in various applications concentrates on nose cones and incredibly complex vehicle components in the aerospace and automotive industries. This work investigates the free vibration analysis of laminated conical shell (LCS) and sandwich conical shell (SCS) structures with various foam cores. The sandwich construction is fabricated using the hand layup technique. The vibration characteristics of the fabricated LCS and SCS specimens are validated with the Finite element software (ANSYS). Very minimal variation was observed between the experimental and numerical simulations. The various parametric analyses were also studied for the LCS and SCS with length, ply orientation, and boundary conditions. Further, for SCS, vibration behaviors across multiple core materials and core thickness were also investigated.

In recent years, with the development of urban rail transit, more and more attention has been paid to the vibration problems caused by its operation. As the main form of urban rail transit’s underground construction, the shield tunnel is the first to bear the brunt. However, the existing researches on the vibration of shield tunnel usually take it as a homogeneous barrel and do not consider the impact of its assembly joints on the vibration propagation. In this paper, to study the influence of the joints caused by the shield tunnel’s assembly forms on the propagation of vibration, two finite element models of shield tunnels with different assembly forms are established. The analysis and comparing results of these models show that the joints caused by segment assembly of shield tunnel have obvious hysteresis and reduction effect on the vibration waves and this ability is obviously related to its location. In addition, the ability to weaken the vibration wave is also related to the frequency of the vibration wave.

This study aims to examine the dynamic characteristics of a sandwich composite nanoplate when exposed to a nano damper–spring–mass stimulator. The composite structure consists of a core layer composed of magnetostrictive material, accompanied by upper and lower facesheets made of functionally graded material (FGM). Moreover, the proposed framework is designed to be based on a visco-Pasternak medium. The governing equations of nanoplates are derived using the higher-order shear deformation theory (HSDT) and Hamilton’s principle. In the end, Navier’s solution is utilized to solve partial differential equations, while the Laplace transform is employed for solving ordinary differential equations. Subsequently, a thorough investigation is conducted with a primary focus on examining the impact of different parameters on the dynamic response of the continuous system. The findings indicate that the incorporation of the damper–spring–mass system into the nanoplate has a notable impact on its natural frequency. The results can serve as reference points for the effective development of nanosensors, nanoresonators, drug delivery systems, and biosensors.

This study investigates free vibration analysis of a microplate featuring a honeycomb (HC) core and incorporates two nanocomposite piezoelectric (NP) layers. Carbon nanotubes (CNTs) are hired to enhance the electro-mechanical performance of the piezoelectric patches, which are subjected to an externally applied electric voltage. All layers are tightly bonded together and are supported by an elastic substrate according to the Pasternak model, capable of withstanding both normal and shear loads. To establish the kinematic relations, a trigonometric plate theory is employed. The governing equations of motion are deduced through the application of Hamilton’s principle and variational technique. The modified strain gradient theory, which includes three material length-scale parameters (MLSPs), is used to account for the scale effect. An analytical approach based on Fourier series functions is employed to solve the differential equations of motion. Subsequently, the impact of various factors, such as the geometrical characteristics of the HC core, distribution patterns of CNTs, and other significant parameters, on the normalized frequencies of the model is assessed after validating the accuracy of the results. The outcomes of this research have the potential to facilitate the advancement and production of lightweight and intelligent structures and devices, ultimately enhancing their efficiency.

Multiple variables have been shown to influence early marginal bone loss around dental implants. Among these factors, the location of the microgap related to the alveolar crest, occlusion, crest module and soft tissue thickness were reported to be important factors for deciding the final outcome of the implant treatment. The purpose of this study was to establish a damping model to simulate the mechanical function of dental implants in the oral cavity. The experimental implant model consisted of a screw-type implant (10mm). The implant was placed into epoxy resin which was used to simulate bone tissue. In this study, two kinds of epoxy resin were used: PL-1 (with elastic moduli of 2900MPa) and PL-2 (210MPa) were used to simulate cortical bone and cancellous bone, respectively. Above bone block, a soft lining material was used to simulate the soft tissue around implant. In addition, two-implant model with various distance between implants were established to discuss the effect of soft tissue effect on the damping factors (DF) of the implant system. A noninvasive impulse-forced vibration technique was used to detect the damping factors of the implant models as previous reported. Briefly, the signal excitation was detected through the micro-phone and sent to the spectrum analyzer. The frequency response was obtained from a vibration-time histogram using Fast Fourier Transform software. The DF value of the signal dental implant model was detected to be $0.044\pm 0.009$. This value is closed to the in vivo data that was reported previously. This result showed that the model established in this study is a validated model for damping analysis. Furthermore, the DF value of a dental implant surrounded with 3mm soft tissue ($0.127\pm 0.032$) is significantly higher than the implant with 2mm-surround soft tissue ($0.079\pm 0.013$). In addition, implant models with larger interval distance between implants showed higher DF values. According to the results of this study, it is reasonable to suggest that dental implant surrounded with higher amount soft tissue may reduce more vibration amplitude while an occlusal force was applied to a dental implant. This vibration reducing effect may be helpful to reduce alveolar bone resorption around implants.