Mode Natural Frequencies Research Articles

Accelerating composite sandwich plate analysis: A hybrid higher-order XFEM and ANN approach for natural frequency prediction

Free vibration analysis of laminated composites plays a critical role in design optimization, material selection, structural integrity assessment, vibration suppression, and fatigue life prediction. A novel coupled higher-order extended finite element method (HO-XFEM) and artificial neural network (ANN) approach is implemented for predicting the natural frequency of sandwich plates with a composite layout of 0°/θ°/0°/core/0°/θ°/0°, where θ varies from 15 to 90 degrees. A total of 557 data points are generated through HO-XFEM, which is then utilized to construct an optimized ANN model for predicting nondimensionalized natural frequency. The ANN model, designed specifically to predict the first mode of natural frequency, is optimized with a structure of 4-90-90-1 and softmax transfer functions in intermediate layers. It predicts the nondimensional natural frequency with the average, minimum, and maximum mean-squared error values of 0.0984 %, 0.00339 %, and 0.49 %, respectively. The optimized ANN model computes the natural frequency for different sandwich plate configurations a few million times faster compared to HO-XFEM and thus establishes a transformative framework for real-time structural integrity assessment.

Application of Homogenization Method in Free Vibration of Multi-Material Auxetic Metamaterials

Different additive manufacturing modalities enable the production of multi-material components which can be used in a wide range of industrial applications. The prediction of the mechanical properties of these components via finite element modelling rather than through testing is critical in terms of cost and time. However, due to the higher computational time spent on the modelling of lattice structures, different methods have been investigated to accurately predict mechanical properties. For this purpose, this study proposes the use of a homogenization method in the two most common types of multi-material lattices: honeycomb and re-entrant auxetics. Modal analyses were performed, and the first six mode shapes were extracted from explicit and implicit models. The results were compared in terms of mode shapes and natural frequencies. The results showed that homogenization can be successfully applied to multi-material honeycomb and re-entrant auxetic lattices without compromising the accuracy. It was shown that the implicit models predict the natural frequencies with an error range of less than 6.5% when compared with the explicit models in all of the mode shapes for both honeycomb and re-entrant auxetic lattices. The Modal Assurance Criteria, which is an indication of the degree of similarity between the mode shapes of explicit and implicit models, was found to be higher than 0.996, indicating very high similarity.

Vibration-Based Damage Prediction in Composite Concrete–Steel Structures Using Finite Elements

The prediction of structural damage through vibrational analysis is a critical task in the field of composite structures. Structural defects and damage can negatively influence the load-carrying capacity of the beam. Therefore, detecting structural damage early is essential to preventing catastrophic failures. This study addresses the challenge of predicting damage in composite concrete–steel beams using a vibration-based finite element approach. To tackle this complex task, a finite element model to a quasi-static analysis emulating a four-point pure bending experimental test was performed. Notably, the numerical model equations were carefully modified using the Newton–Raphson method to account for the stiffness degradation resulting from material strains. These modified equations were subsequently employed in a modal analysis to compute modal shapes and natural frequencies corresponding to the stressed state. The difference between initial and damaged modal shape curvatures served as the foundation for predicting a damage index. The approach effectively captured stiffness degradation in the model, leading to observable changes in modal responses, including a reduction in natural frequencies and variations in modal shapes. This enabled the accurate prediction of damage instances during construction, service, or accidental load scenarios, thereby enhancing the structural and operational safety of composite system designs. This research contributes to the advancement of vibration-based methods for damage detection, emphasizing the complexities in characterizing damage in composite structural geometries. Further exploration and refinement of this approach are essential for the precise classification of damage types.

Benchmark exact free vibration solutions of two-dimensional decagonal piezoelectric quasicrystal cylindrical shells

Abstract Quasicrystalline materials with piezoelectric effects show significant potential for advancing actuators, sensors and energy harvesters. In this paper, the free vibration characteristics of two-dimensional decagonal piezoelectric quasicrystal cylindrical shells (PQCSs) are investigated in the framework of symplectic mechanics system. By introducing an original vector and its dual variable vector as the fundamental unknowns, the governing equations are reduced into a set of low-order ordinary differential equations system, thus the free vibration analysis is transformed into an eigenvalue problem within the symplectic space. By using the symplectic mathematics, the exact solutions for free vibration of PQCSs are finally obtained and expanded as a series of symplectic eigensolutions. Finally, accurate natural frequency and analytical vibration mode shapes for arbitrary classical boundary conditions are obtained simultaneously. The accuracy of the obtained solutions is verified by comparing with existing results in open literature. In addition, the effects of geometrical parameters, temperature rise, external voltage and coupling fields on the natural frequency and vibration mode shapes are investigated in numerical examples. Results indicate that the phason field exhibits significant influences on the natural frequencies and cannot be neglected in free vibration analysis of PQCSs. Furthermore, all the results can be served as benchmarks for the development of new analytical and numerical approaches.

Mechanistic insights into mosquito antennal architecture for auditory adaptations.

Unlike organisms equipped with tympanal ears, mosquitoes hear using their antennae, which are lightweight sensory structures capable of detecting sound. Here, we study the antennae of two species - Aedes aegypti and Uranotaenia lowii - known to use hearing for different functions. Through the use of geometrically comprehensive computational models, we find that architectural features in the mosquito antenna provide mechanisms that promote the detection of species and sex specific acoustic targets amidst the non-target signals produced by their own wingbeats. Structurally, we find that the increased surface area of sensory hairs provides enhanced sensitivity while the tapering effect of intersegmental variation affects the tuning response. These features result in the highest antennal sensitivity through vibration at specific natural frequency modes that correspond to frequencies associated with their acoustic targets. STATEMENT OF SIGNIFICANCE: Our study provides valuable insights into the remarkable architectural design of mosquito antennae and its role in auditory adaptations. By dissecting the intricate geometry of antennal architecture in Aedes aegypti and Uranotaenia lowii, we uncover mechanisms that enhance sensitivity to specific acoustic cues while mitigating interference from wingbeat noise. This research builds upon and extends the existing understanding, providing a deeper comprehension of how mosquitoes navigate their acoustic environment. Our findings have significant implications for understanding sensory adaptations in insects and may inspire the development of bioinspired sensing technologies. We believe our work will interest a broad audience by offering new perspectives on the intersection of biomechanics and sensory biology, which can also find applications in the design of bioinspired architected materials.

Analysis of modal characteristics and strengthening effect of truss roof

The modal characteristics are an important basis for measuring the stability and safety of the truss roof structure. Based on the finite element method, the modal calculation of the overall structure of the truss roof was carried out, and the first six-order modal shapes and natural frequencies were obtained. The modal test method was adopted to test and analyze the vibration response of the truss roof through the hammering method, verifying the accuracy and effectiveness of the modal simulation. According to the analysis results of the modal shapes, the structure was reinforced at the weak positions. The thickness of the end face was reduced by 1 mm, and five ribs at the connection between the panel and the lateral beam were add. Through the modal calculation, the dynamic response of the optimized structure was obtained. The results show that the optimized structure can significantly increase the natural frequency, reduce the vibration amplitude, avoid the low-frequency resonance problem, and meet the lightweight design requirements at the same time, which is of obvious help for the improvement of the truss performance.

Nonlinear vibration and transient stress analysis of disc brake based on computer simulation technology

The nonlinear vibration and dynamic stress characteristics of disc brakes are key factors affecting braking noise and safety. Based on the working principle of disc brake, a six-degree-of-freedom dynamic model was constructed, and the amplitude-frequency response of vibration under diverse braking pressures and initial velocities was acquired. The modal characteristics of the brake disc were computed using the finite element simulation approach, and the natural frequency and vibration mode were obtained. The accuracy of the modal calculation was verified by means of the laser detection method. In order to study the dynamic stress variation law more accurately, a coupled model of temperature and displacement was established, and transient stresses on different paths were obtained. The results indicate that the finite element model has high accuracy, with a maximum calculation error of only 5.1 % for the natural frequency. Besides, temperature variations will lead to thermal deformation of the brake disc, which intensifies the random vibration characteristics associated with the friction process.

Modal and dynamic stress analysis of crane support frame based on CAE technology

The support frame is the main load-bearing component of crane equipment, of which modal and dynamic stress response characteristics have a critical impact on the safety and service life of the entire mechanical structure. Based on the finite element method, the support frame model was reasonably simplified and established. By arranging REB2 elements on the contact surface of the components to be connected, the rigid connection effect of the weld was realized. Through simulation calculation and modal testing, the natural frequency and vibration mode were obtained. Through modal analysis, the dynamic response analysis model was established to determine the maximum dynamic stress variation under instantaneous loading and emergency braking conditions. The results indicate that the reliability and accuracy of the finite element analysis model are high, and the maximum deviation of natural frequencies between experimental and simulation results is less than 10 %. Besides, the performance of the support frame shows good dynamic response efficiency, which proves that the mechanical structure has high stability.

The optimization of the actuator and sensor layout for piezoelectric smart blades

To reduce vibration-induced fatigue fractures of aero-engine blades, an active vibration control scheme for aero-engine blade has been developed proposed. In this paper, the Macro Fiber Composite (MFC) are used as actuators and sensors to suppress the vibration of the blade, but the position of the actuators and sensors has a great influence on the effectiveness of the blade vibration suppression. To achieve optimize suppress effect, the objective criterion for position optimization was proposed to be the absolute value normalized superposition of the strain of the first few natural frequency modes of the blade. First, a finite element analysis was conducted on the blade model. Then, the positions of the actuators and sensors were determined by using the differential evolution algorithm for optimization. The blade model with three layout strategies was constructed in ADAMS, and the ADAMS-Simulink joint simulation platform was constructed. Finally, the comparison of actuator and sensor effects with three position layout strategies is completed, the layout optimization strategy proposed in this paper achieves more significant vibration suppression with less control force was verified though the feedforward control experiments, and the effective of the proposed strategies are verified on the experimental platform for blade active vibration control.

"Torsional vibration control in diesel engine-driven centrifugal pump: Validation through experimental results"

This study addresses the critical issue of torsional vibration in turbomachinery, which can lead to significant damage if not properly managed. The primary objective is to develop a practical design approach to enhance system resilience against torsional vibration problems. The research focuses on post-natural frequency analysis steps, including methods like Holzer's method for natural frequency determination and mode shape analysis. The study suggests that while identifying natural frequencies is manageable, accurately predicting torsional vibration problems remains challenging. The analysis recommends analyzing all interference points before considering design modifications, advocating for techniques like examining mode shapes or torque vs. speed curves to eliminate non-critical interference points. For remaining points, a damped forced vibration analysis is recommended, with guidelines provided for different machinery classes. Overall, this study provides a comprehensive, step-by-step analysis procedure applicable to most turbomachinery systems. By addressing the complexities of torsional vibration, this research aims to contribute to the development of safer and more reliable turbomachinery systems Specifically, conducting a torsional analysis on a pump package driven by a diesel engine to achieve similar behavior when it is driven by an electric motor. Replacing the electric motor with a diesel engine as a driver for the pump could cause a maximum to increase the vibration with 25 % while using the optimal damping for the diesel engine could lead to vibration deduction with 70 % when operate the pump without diesel engine damping.

A new concept reduced scale aeroelastic model of the four-cable suspension bridge with truss girder and its validation

The accuracy of the aeroelastic model or truss girders has consistently been a decisive factor influencing the results of full-bridge aeroelastic wind tunnel tests. A novel design approach, termed the Multi-Spine Frame System, is introduced for the reduced-scale model of the stiffening girder. This system incorporates multiple spines, thinner beams and columns to minimize aerodynamic interference while accurately simulating overall stiffness, mass, and constraints. The design procedure is formulated as an optimization problem with the objective of optimizing the low-order natural frequencies (lateral bending, vertical bending, and torsion) of the aeroelastic model. Pattern search method and penalty functions are employed to identify a locally optimal solution that satisfies engineering applications for this optimization problem. This design method is applied to an actual project involving a four-cable suspension bridge with a truss girder, and the test results demonstrate the accuracy of this approach in simulating the dynamic characteristics of the aeroelastic model. Corresponding wind tunnel tests on flutter instability, as well as numerical multi-modal flutter analysis, are conducted to analyze the critical flutter speed, vibration shapes, and frequencies of this bridge. Furthermore, the impact of deviation in structural mode shapes and natural frequencies on flutter instability is investigated using ten design schemes achieved by altering boundary conditions, mass distributions, and stiffness distributions, were examined. Significant differences in critical flutter speed (up to 9%) are observed due to deviations in mode shapes, emphasizing the necessity of considering modal frequencies and other modal information, such as mode shapes, in aeroelastic model design. This approach contributes to the advancement of aeroelastic model design for bridges with truss girders by introducing an effective system and an optimization method, providing a basis for future studies on wind instability and structural dynamics and also underscores the importance of accurate mode shape representation in flutter analysis.

Study on the Influence of Wind Load on the Safety of Magnetic Adsorption Wall-Climbing Inspection Robot for Gantry Crane

The maintenance of the surface of steel structures is crucial for ensuring the quality of shipbuilding cranes. Various types of wall-climbing robots have been proposed for inspecting diverse structures, including ships and offshore installations. Given that these robots often operate in outdoor environments, their performance is significantly influenced by wind conditions. Consequently, understanding the impact of wind loads on these robots is essential for developing structurally sound designs. In this study, SolidWorks software was utilized to model both the wall-climbing robot and crane, while numerical simulations were conducted to investigate the aerodynamic performance of the magnetic wall-climbing inspection robot under wind load. Subsequently, a MATLAB program was developed to simulate both the time history and spectrum of wind speed affecting the wall-climbing inspection robot. The resulting wind speed time-history curve was analyzed using a time-history analysis method to simulate wind pressure effects. Finally, modal analysis was performed to determine the natural frequency and vibration modes of the frame in order to ensure dynamic stability for the robot. The analysis revealed that wind pressure predominantly concentrates on the front section of the vehicle body, with significant eddy currents observed on its windward side, leeward side, and top surface. Following optimization efforts on the robot’s structure resulted in a reduction in vortex formation; consequently, compared to pre-optimization conditions during pulsating wind simulations, there was a 99.19% decrease in induced vibration displacement within the optimized inspection robot body. Modal analysis indicated substantial differences between the first six non-rigid natural frequencies of this vehicle body and those associated with its servo motor frequencies—indicating no risk of resonance occurring. This study employs finite element analysis techniques to assess stability under varying wind loads while verifying structural safety for this wall-climbing inspection robot.

Multi-directional and multi-modal vortex-induced vibrations for wind energy harvesting

A conventional vortex-induced vibration (VIV)-based energy harvester is typically restricted to capturing wind energy from a very limited range of wind directions, making it inefficient in varying wind conditions. This Letter proposes a tri-section beam configuration for VIV-based piezoelectric energy harvester to enable harnessing wind energy from varying incident angle with different vibration modes being triggered. The finite element analysis investigates the tri-section beam harvester's mode shapes and natural frequencies. A wind tunnel experiment is conducted for a comparative study of the energy output performance of the harvesters with straight and tri-section beams. The findings show that the proposed harvester with the tri-section beam can efficiently capture wind energy from a much wider range of incident angles, as opposed to the specific limited directions of its counterpart with the straight beam. The proposed harvester can also widen the lock-in speed range with a higher bending mode being triggered and achieve the optimal output power of 1.388 mW when the proposed harvester works in the second mode at a higher natural frequency, superior to that of its counterpart (0.386 mW) that can only work in the first mode. The proposed configuration sheds light on developing multi-directional and multi-modal VIV-based energy harvesters adapted to wind conditions in natural environments.

Fatigue Damage and Reliability Assessment of Wind Turbine Structure During Service Utilizing Real-Time Monitoring Data

Under the action of wind load, a wind turbine tower will produce alternating stress, which leads to fatigue failure. According to the mean wind speed at the wind turbine impeller collected from the SCADA system, the mean wind speed of the simulation point is calculated by using the wind speed exponential model formula. Davenport spectra are used to simulate the pulsating wind speed time series. The wind spectrum is obtained using the harmonic superposition method. Subsequently, the wind speed time series and wind load time series at the simulation point are calculated. Structural modeling of a 5 MW wind turbine tower is performed in ABAQUS 2021. The modal shape and natural frequency are obtained by modal analysis to verify the rationality of the model. Subsequently, wind loads are applied to the model, and structural stress time history is obtained by transient modal dynamics analysis. The stress time history of the maximum stress area of the tower structure is extracted, and the rain flow counting method is applied to it to obtain the stress spectrum. The Weibull distribution of the stress spectrum is fitted, the mean and variance of the total damage in one day are calculated, and the fatigue reliability analysis of the maximum stress area of the tower structure is carried out. And the nonlinear fatigue cumulative damage analysis of the region is carried out. This work has implications for fatigue reliability studies for approximate operating conditions.

Free vibration of flexible two links manipulator with variable cross-sectional areas

This paper demonstrated the free vibration of a planar two-link flexible manipulator with harmonic drivers and non-uniformity in the cross-section of links. A dynamic model has been developed that incorporates flexibilities in both link and joint experiencing harmonic vibration, with joint flexibility modeled as torsional spring-inertia components combination. Two links were modeled based on Von Karman’s nonlinear strain relations and theory of the Euler-Bernoulli beam. The nonlinear governing equations were derived using the extended Hamilton’s principle for planar two-link flexible manipulators with variable cross-sections for each link. The coefficients of the obtained partial differential equations were as a function of spatial coordinates and were reduced to the ordinary differential equations for a family of cross-section geometries with exponentially varying widths of rectangular sections of each link. The frequency equation was obtained and analytical solutions of the vibration were achieved for different exponential shapes of each link (widening and narrowing beam for each link). Natural frequencies and mode shapes were presented for varying cross-section areas of the links. The effects of the end masses, payload, beam mass density, flexural rigidity ratio, and joint frequency were investigated on the mode shapes and natural frequencies when the power of the exponential function of the cross-sectional areas of two links was varied. The numerical results were verified with experimental results.

Evaluation of Static Displacement Based on Ambient Vibration for Bridge Safety Management.

The evaluation of bridge safety is closely related to structural stiffness, with dynamic characteristics and displacement being key indicators. Displacement is a significant factor as it is a physical phenomenon that bridge users can directly perceive. However, accurately measuring displacement generally necessitates the installation of displacement meters within the bridge substructure and conducting load tests that require traffic closure, which can be cumbersome. This paper proposes a novel method that uses wireless accelerometers to measure ambient vibration data from bridges, extracts mode shapes and natural frequencies through the time domain decomposition (TDD) technique, and estimates static displacement under specific loads using the flexibility matrix. A field test on a 442.0 m cable-stayed bridge was conducted to verify the proposed method. The estimated displacement was compared with the actual displacement measured by a laser displacement sensor, resulting in an error rate of 3.58%. Additionally, an analysis of the accuracy of displacement estimation based on the number of measurement points indicated that securing at least seven measurement points keeps the error rate within 5%. This study could be effective for evaluating the safety of bridges in environments where load testing is difficult or for bridges that require periodic dynamic characteristics and displacement analysis due to repetitive vibrations, and it is expected to be applicable to various types of bridge structures.

Development of planar 9-DOF dynamic model with small damping and natural characteristics sensitivity analysis for a double-deck vibrating flip-flow screen

The current double-deck vibrating flip-flow screen (DDVFFS) exhibits swing motion due to an unreasonable structural design, which compromises vibration stability and impacts screen frame displacement response. Therefore, it is essential to investigate the dynamic characteristics of the DDVFFS. For this reason, a 9-degree-of-freedom (DOF) dynamic model of the DDVFFS is established, and a corresponding testbed for the DDVFFS is designed. A sensitivity analysis is conducted to examine the impact of design parameters on the natural frequency and vibration mode, thereby serving as valuable guidance for the design of DDVFFS. The damping matrix in the dynamic model is determined through modal testing, while the displacement response of the testbed is obtained by solving the dynamic model. The test results from the vibration testbed demonstrate that the actual amplitude of each sieve frame closely matches the theoretical amplitude.

Investigating the robustness of interface topological modes in rods

Topological phononic crystals and metamaterials are structures that can present waveguiding and energy concentration phenomena, which can be of interest in structural dynamics for energy harvesting and passive vibration and noise control. The periodicity of the typical phononic crystals and metamaterials is broken for these structures, which need to present at least two crystal lattices with different topological characteristics. Thus, the topological invariant, such as the Zak phase, which defines the topological characteristic, must be computed. A rod metastructure exhibiting two low-frequency band gaps, each with a topological interface mode, was designed. It has bolt sets whose weights generate variability, which was modeled and inferred. In order to increase variability along the rod metastructure, washers were included or removed. Experiments were performed to validate the simulations. It was observed that the variability of the topological mode in the first band gap is more robust considering its mode shape, natural frequency, and energy concentration at the interface than the second interface mode, at higher frequency. As variability increases, the robustness of the energy concentration at the interface and of the mode shape of both topological modes decreases. The same behavior was observed for the natural frequencies of the topological modes.

Thermomechanical and Viscoelastic Characterization of Continuous GF/PETG Tape for Extreme Environment Applications

The thermomechanical and viscoelastic properties of a glass fiber polyethylene terephthalate glycol (GF/PETG) continuous unidirectional (UD) tape were investigated using differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and dynamic mechanical analysis (DMA). This study identified five operational conditions based on the Army Regulation 70-38 Standard. The DSC results revealed a glass transition temperature of 78.0 ± 0.3 °C, guiding the selection of temperatures for TMA and DMA tests. TMA provided the coefficient of thermal expansion in three principal directions, consistent with known values for PETG and GF materials. DMA tests, including strain sweep, temperature ramp, frequency sweep, creep, and stress relaxation, defined the material’s linear viscoelastic region and temperature-dependent properties. The frequency sweep indicated an increased modulus with rising frequency, identifying several natural frequency modes. Creep and stress relaxation tests showed time-dependent behavior, with strain increasing under higher loads and stress decreasing over time for all tested input values. Viscoelastic models fitted to the data yielded R2 values of 0.99, demonstrating good agreement. The study successfully measured thermomechanical and viscoelastic properties across various conditions, providing insights into how temperature influences the material’s mechanical response under extreme conditions.

Nonlinear dynamic analysis and vibration reduction of two sandwich beams connected by a joint with clearance

The dynamics and vibration reduction characteristics of the clamped–clamped two sandwich beams jointed with clearance is studied theoretically and experimentally. A transverse and torsional spring system with clearance is used to equivalent the joint model. The homogenization method is used to equivalent the core layer and Rayleigh-Ritz method is utilized to derive the mode function of the interconnected sandwich beam by using a sequence of orthogonal polynomials. The nonlinear motion equation of the two jointed sandwich beam structure with clearance is derived by the application of the Hamilton principle and then solved using an improved Newmark integration approach. In order to validate the accuracy of the natural frequency and vibration mode, the finite element model is established. This paper examines the impact of clearance on the amplitude frequency response and vibration transmission of the two jointed sandwich beam structure, it is found the jointed sandwich beams show obvious nonlinear characteristics and intermittent vibration transmission phenomenon due to the clearance. Moreover, the vibration transmission analysis reveals that the existed clearance demonstrates significant vibration reduction effect, for which an experiment is conducted to validate the results. In general, this work proposes a novel approach for modeling sandwich structures with clearance with improved vibration reduction performance.