Natural Frequencies Of Structure Research Articles

Mechanical Properties and Dynamic Characterization of Gradient IWP Structures Fabricated by Additive Manufacturing

This paper focuses on the study of the unique performance of gradient lattice structures in terms of mechanical properties and dynamic characterization to fill the current research gap in this area. A series of IWP (I-graph-wrapped package) structures with various density gradients were designed and then manufactured by using Laser Powder Bed Fusion (LPBF) technology. Mechanical properties were evaluated via quasi-static compression tests, and frequency sweeping tests and simulations analyzed the dynamic characteristics. The results indicate that the density gradient rate, as a key design parameter, significantly affects the structure's compressive elastic modulus, yield strength, and energy absorption capability. Increased gradient rates reduce stiffness and strength but enhance energy dissipation. Additionally, both experimental and simulation results consistently show that the gradient type has a decisive impact on the structure's natural frequency. Positive gradient structures exhibit lower natural frequencies compared to negative gradient structures, accompanied by shifts in the vibration isolation frequency bands, resulting in varying vibration isolation effects across different frequency ranges. This study not only enhances the understanding of the performance characteristics of gradient lattice structures but also establishes a solid foundation for the optimized design and application of such structures in future engineering practice.

On the mechanism of frequency lock-in vibration of airfoils during pre-stall conditions

Potential frequency lock-in vibration can frequently occur in aircraft flying at separated flow conditions during take-off and landing stages, severely threatening the safety of the aircraft. A deeper understanding of the lock-in phenomenon in pre-stall (steady separated flow) conditions is necessary to improve aircraft reliability and safety. In this paper, a reduced-order model (ROM) for the pitching NACA0012 airfoil in steady separated flow is established. A linear aeroelastic model is then obtained by coupling the ROM with the structural dynamical equation with the pitching degree of freedom, and it is verified by the computational fluid dynamics/computational structural dynamics (CFD/CSD) simulation. Next, the mechanism of frequency lock-in vibration is revealed by the ROM-based aeroelastic model of different structural natural frequencies. Results from the complex eigenvalue analysis indicate that the instability can be divided into two patterns. At high frequencies, the flutter frequency locked onto the natural frequency of the structure, and it is dominated by the instability of structural mode. At low frequencies, the flutter frequency follows the fluid characteristic frequency, which is dominated by the instability of the fluid mode. Finally, the effects of the angle of attack and mass ratio are investigated. The damping of dominant fluid mode decreases with the increase of angle of attack, which affects the structural mode through coupling effects. Therefore, the angle of attack influences the upper boundary of the coupling system’s instability (high frequency boundary). On the contrary, the mass ratio mainly influences the lower boundary of instability (low frequency boundary), because fluid mode becomes unstable at low frequencies merely when the mass ratio is relatively low.

Vertical vibration characteristics of wheelset-gearbox-bogie frame system in different track irregularity conditions: simulation and full-scale test

ABSTRACT The vibration characteristics of a wheelset-gearbox-bogie frame system are studied under wheel-roller roughness and varying track irregularities utilizing a full-scale rolling test rig. A corresponding dynamic model is developed based on the discrete time transfer matrix method, which integrates a modular flexible wheelset model. The results reveal that, (1) low-frequency vibrations (0–50 Hz): dominated by track irregularities below 200 km/h but by wheel-roller rotation above 350 km/h; (2) mid-frequency vibrations (50–500 Hz): prominent shock effects appear at discrete frequencies above 350 km/h, related to wheel-roller roughness; (3) high-frequency vibrations (500–1000 Hz): great differences under various irregularities and distinguishing structural natural frequencies becomes difficult. Amplitude contributions at speeds below 200 km/h are mid (57–62%), low (26–32%), and high (11–14%). Above 350 km/h, mid-frequency increases while low-frequency decreases by 15%, respectively. To improve vibration performance at superspeed (e.g., 500 km/h), stricter wheel-rail roughness control becomes imperative.

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.

Dynamic characteristic of transonic aeroelasticity affected by fluid mode in pre-buffet flow

Transonic aeroelasticity remains a significant challenge in aerospace. The coupling mechanism of aeroelastic problems involving the coexistence of fluid modes and multiple structural modes still needs further investigation. For this purpose, we analysed the dynamic characteristic of a two-degree-of-freedom (2DOF) NACA0012 airfoil in pre-buffet flow. First, we constructed an aeroelastic reduced-order model, which can represent near-unstable transonic flow using the dominant fluid mode. Then, the flutter mechanism was investigated by studying the main eigenvalues of the model that vary with the natural pitching frequency. The results revealed that the existence of the fluid mode transitions the transonic flutter type from coupled-mode flutter to single-DOF (SDOF) flutter, which leads to a reduction in the flutter boundary. Under the effect of the fluid mode, the system produces six aeroelastic phenomena at different structural natural frequencies, including SDOF heaving/pitching flutter, heaving/pitching instability within coupled-mode flutter, forced vibration and stable state. Moreover, we identified two types of SDOF flutter in the 2DOF system. The first type corresponds to the traditional SDOF flutter, where the coupling of other modes has a small impact on the system's stability in most cases. However, within specific ranges of natural frequencies, this type of SDOF flutter may disappear due to coupling with other modes. The second type of SDOF flutter is characterized by strong coupling dominated by the unstable mode. It arises from the interaction among the flow, heaving and pitching modes, and does not manifest in the absence of any of these modes.

Novel rod-sprung-mass model to investigate characteristics of building structural vibration induced by railways

Railway-induced vibrations in building structures require predictions to assess the serviceability. Fundamental properties such as the predominant modes of railway-induced vibrations are critical in structural design and mitigation approaches. However, the existing numerical models are customised to specific buildings. This renders these models unsuitable for broader mechanistic investigations. To address this, this study proposes a rod-sprung-mass (RSM) model to investigate the dynamic behaviour of structures under vertical ground excitations induced by railways. The columns were modelled as axial vibration rods, with each floor suspended on the rod as a sprung mass. The model was validated using a three-story steel frame structure and a five-story concrete structure. Subsequently, the dynamic characteristics of the structures and railway-induced responses were discussed. The structural vertical modes are attributed to the interaction between the columns and slabs, and the structural natural frequencies are outside the frequency range of the individual components. Parametric studies revealed that lower-order structural modes are generally predominant. Under such circumstances, the floor response tends to first decrease and subsequently increase with the floor height. As a result, low-rise buildings exhibit the maximum amplitude on the top floor, whereas the maximum amplitude is on the ground floor for high-rise buildings. Meanwhile, when structural high-order modes become predominant owing to a high-frequency input, the responses of the middle floors intensify, and the peak responses can be altered to the middle floors. This study emphasises the necessity of considering vertical global modes, whereas existing studies have focused mainly on mode shapes on particular floors. The RSM model is an efficient tool for structural design and vibration control.

Nonlinear interactions of an n-layer X-shape low-frequency vibration isolator equipped with a nonlinear vibration absorber at 1:1 internal resonance: analytical and numerical investigations

This work addresses, for the first time, the nonlinear dynamics of an n− layers bioinspired X− shape low-frequency vibration isolation system equipped with a nonlinear vibration absorber. The comprehensive mathematical model governing the two-degree-of-freedom system has been derived using Lagrangian mechanics. The method of averaging was applied to obtain an accurate analytical solution for the derived mathematical model. Utilizing the established analytical solution, the dynamical characteristics of the X− shape vibration isolator have been explored both as a single-degree-of-freedom system and after coupling with the proposed vibration absorber, as a two-degree-of-freedom system. The influence of different system parameters, including the number of structure layers, the initial inclination angle, the X− shape rod length, and the absorber stiffness and damping coefficients, on the vibration isolation performance has been investigated. The main findings indicate that while the single-degree-of-freedom X− shape low-frequency vibration isolator performs well in eliminating low-frequency vibration excitations, it exhibits strong vibration levels when the base excitation frequency exceeds the structure's natural frequency. Additionally, it was found that coupling a highly damped linear vibration absorber to the X− shape isolator not only eliminates the strong oscillations of the structure when subjected to high-frequency base excitations but also enhances the structure's low-frequency vibration isolation performance. Moreover, it was reported that integrating a nonlinear vibration absorber with either soft or hard spring characteristics instead of a linear one may degrade the vibration isolation performance of the structure rather than enhance it. Finally, numerical validation of all the analytical results was performed, which showed excellent correspondence with the analytical findings.

Morphological analysis of a novel scissor-type deployable cable dome structure

A novel deployable scissor-type strut cable dome structure was proposed, which can improve the lateral stiffness of the traditional cable structure and achieve the characteristics of fast unfolding and closing during construction. However, the geometric stability and optimal initial prestressing theory of traditional cable dome structures cannot be applied to the new structure. Based on the equilibrium matrix theory, the geometric stability analysis was conducted and the number of self-stress modes, mechanism displacement modes, and feasible prestress modes was calculated. Then, the formula for the initial prestress distribution of the structure was derived based on the node equilibrium equation. Furthermore, the geometric stability and initial prestress distribution of the structure with different rise-to-span ratios, number of circumferential struts, and hoop cables were studied. Finally, the dynamic properties of the structure are explored by finite element simulation. The analysis results show that the structure has excellent structural stability. The rise-to-span ratios, the number of circumferential struts, and hoop cables are the important factors affecting the geometric stability and the initial prestress distribution. The rise-to-span ratios have no effect on the number of structural modes, while the number of circumferential struts and cables will cause significant changes in the number of self-stress modes. The internal force of the structural members decreases with the rise-to-span ratio and the number of circumferential struts increases, and the number of circumferential struts has the greatest influence on its internal force. The structural natural frequency exhibits a dense distribution, which indicates that the structure has good stiffness. In summary, the research has provided an idea for the application of the deployable scissor-type strut cable dome structure as a new structural system in the field of structural engineering.

A simplified approach for judging and evaluating the contribution of higher-order modes to the wind-induced acceleration of high-rise buildings

Acceleration is the control parameter for the occupant comfort, often solved in the frequency domain with modal decomposition. In general, the first-order mode response is adopted to represent the total acceleration in practice. However, considering only the first-order mode has been demonstrated to yield underestimated results up to 20 %, while no exact criterion exists to determine whether higher-order modes require to be considered or not. Hence, underlying factors, like the structural natural frequencies, the excitation dominant frequencies, and the distributions of building masses/stiffness, which may significantly affect the contribution of higher-order modes to the acceleration, are analyzed first. Notably, the ratio of the natural frequency of the higher-order mode to that of the first-order mode plays a decisive role in the contribution of the higher-order mode's acceleration. Moreover, the third-order and beyond modes can be largely disregarded. Subsequently, an empirical approach is introduced to determine the need for considering high-order modes. Finally, a simplified formula for estimating acceleration response in the frequency domain is derived to consider second-order modal response. This study provides a method for determining the contribution of higher-order vibration modes to acceleration and a simplified formula to consider the higher-order modal response.

Operational Dynamic Load Testing for Repair Recommendations Case Study of Access Road to Vehicle Weight in Motion

The indication of inaccuracies in vehicle weight measurement using Weight in Motion (WIM) technology on mining roads has been identified due to the non-fulfillment of the design criteria required by the WIM manufacturer. This study aims to identify the gap between the actual pavement conditions and the design criteria and to design improvements to eliminate this gap. The method employed involves dynamic load testing, followed by processing the test data with operational modal analysis (OMA) to obtain dynamic parameters that will serve as a reference for calculating the pavement capacity. From OMA, a natural structural frequency of 26.342 Hz was obtained, while the theoretical calculation based on the design criteria was 29.481 Hz. This frequency decrease indicates structural damage of 10.65% and a capacity reduction of 26.8% from the design criteria. This finding is reinforced by a critical damping ratio of 5.25%, which is higher than the damping for intact concrete, ranging between 2%-5%. This indicates energy dissipation through concrete cracks. It is recommended to inject the cracks in the existing pavement with a cement base and perform a 130 mm overlay with mortar grout (fc’= 50 MPa) with one layer of M12 wire mesh. The connection with the old pavement will use concrete bonding and D13-600/600 chemical anchors. With this improvement, the structural capacity will become 104% of the design criteria.

Stochastic force identification for uncertain structures based on matrix equilibration and improved Tikhonov regularization method

Accurate identification and estimation of stochastic forces applied to in-service engineering structures play a vital role in structural safety assessments. This study devised an effective force power spectral density (PSD) identification method to address the challenge of identifying multipoint stationary stochastic forces in uncertain structures. Initially, a probability model was employed to characterize structural uncertainties. Subsequently, an integral relationship was established between the probability density function (PDF) of the random structural parameters and that of the stochastic force PSD. By employing a point-selection technique based on the generalized F-discrepancy and a smoothing method, the uncertainty problem was transformed into a finite number of stochastic force PSD identification problems for deterministic structures. Simultaneously, based on the inverse pseudo-excitation method, a matrix equilibration approach and an improved Tikhonov regularization method were used to address the problem of large identification errors near structural natural frequencies. In comparison to the traditional weighting matrix method, the proposed method further reduces the condition number of frequency response function matrices, thereby enhancing the accuracy of force PSD identification. Finally, numerical examples were presented to validate the effectiveness of the proposed method in solving the stochastic force identification problem.

Research on Quantification of Structural Natural Frequency Uncertainty and Finite Element Model Updating Based on Gaussian Processes

During bridge service, material degradation and aging occur, affecting bridge functionality. Bridge health monitoring, crucial for detecting structural damage, includes finite element model modification as a key aspect. Current finite element-based model updating techniques are computationally intensive and lack practicality. Additionally, changes in loading and material property deterioration lead to parameter uncertainty in engineering structures. To enhance computational efficiency and accommodate parameter uncertainty, this study proposes a Gaussian process model-based approach for predicting structural natural frequencies and correcting finite element models. Taking a simply supported beam structure as an example, the elastic modulus and mass density of the structure are sampled by the Sobol sequence. Then, we map the collected samples to the corresponding physical space, substitute them into the finite element model, and calculate the first three natural frequencies of the model. A Gaussian surrogate model was established for the natural frequency of the structure. By analyzing the first three natural frequencies of the simply supported beam, the elastic modulus and mass density of the structure are corrected. The error between the corrected values of elastic modulus and mass density and the calculated values of the finite element model is very small. This study demonstrates that Gaussian process models can improve calculation efficiency, fulfilling the dual objectives of predicting structural natural frequencies and adjusting model parameters.

Refinement and Validation of the Minimal Information Data-Modelling (MID) Method for Bridge Management.

Various approaches have been proposed for bridge structural health monitoring. One of the earliest approaches proposed was tracking a bridge's natural frequency over time to look for abnormal shifts in frequency that might indicate a change in stiffness. However, bridge frequencies change naturally as the structure's temperature changes. Data models can be used to overcome this problem by predicting normal changes to a structure's natural frequency and comparing it to the historical normal behaviour of the bridge and, therefore, identifying abnormal behaviour. Most of the proposed data modelling work has been from long-span bridges where you generally have large datasets to work with. A more limited body of research has been conducted where there is a sparse amount of data, but even this has only been demonstrated on single bridges. Therefore, the novelty of this work is that it expands on previous work using sparse instrumentation across a network of bridges. The data collected from four in-operation bridges were used to validate data models and test the capabilities of the data models across a range of bridge types/sizes. The MID approach was found to be able to detect an average frequency shift of 0.021 Hz across all of the data models. The significance of this demonstration across different bridge types is the practical utility of these data models to be used across entire bridge networks, enabling accurate and informed decision making in bridge maintenance and management.

Structural damage detection based on structural macro-strain mode shapes extracted from non-stationary output responses

Abstract Long-gauge fiber Bragg grating 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 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 non-stationary 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.

Structural acceleration response reconstruction based on BiLSTM network and multi-head attention mechanism

The effectiveness of structural health monitoring often relies on the precise analysis of structural response data, with data completeness directly impacting the performance of monitoring systems. Addressing the common issue of data loss in structural health monitoring systems, this study proposes a Bidirectional Long Short-Term Memory (BiLSTM) network based on a multi-head attention mechanism for the reconstruction of missing structural acceleration responses. Firstly, employing a two-layer BiLSTM network to establish an encoder-decoder framework for extracting spatio-temporal correlation features among sensor data. Subsequently, innovatively embedding a multi-head attention mechanism into the network framework enhances the modeling capability of long-distance input elements and establishes dependencies among different sensors, thereby enabling the network to better capture the global features of input information. The proposed method undergoes validation through a numerical example of a simply supported beam, practical monitoring data on the Hardanger Bridge from the Norwegian University of Science and Technology, and an experimental study of steel frame structure from our laboratory. These validations are compared with alternative response reconstruction models. The experimental results make obvious that the proposed method demonstrates superior accuracy in response reconstruction. Additionally, the suitability of this method for modal identification is validated. Through the utilization of reconstructed responses, the method effectively discerns the structural natural frequencies with accuracy.

Research on abnormal vibration of high-speed train based on wheel-rail coupling modal analysis

During dynamic line testing of a high-speed train, it was observed that the vehicle exhibited significant abnormal vertical vibrations under specific track conditions. The frequency of this vibration varies with the train speed and exhibits harmonics through analysis. As the speed approaches 400 km/h, the peak frequency is close to 44 Hz, corresponding to the system structure's natural frequency. A finite element model of the wheel-rail coupling was established for modal analysis, which revealed that the coupling between the bogie and the track will form a bogie P2 force resonance mode, which closely matches the frequency range of the abnormal vibrations. A dynamic model of vehicle-track rigid-flexible coupling was established, to simulate vibration reproduction and the bogie P2 force resonance mode variation law. Additionally, irregularities of specific wavelengths on the track can excite this mode, leading to a significant increase in amplitude. Some sections of the track line have slab warping, with a wavelength of approximately 2.45m. The frequency range of excitation formed when the vehicle speed approaches 400 km/h is close to that of the bogie P2 resonance mode. As a result, coupling resonance occurs between the vehicle and track systems, ultimately causing abnormal vibrations.

Feasibility Study of Earthquake-Induced Damage Assessment for Structures by Utilizing Images from Surveillance Cameras

Rapid and accurate structural damage assessment after an earthquake is important for efficient emergency management. The widespread application of surveillance cameras provides a new possibility for improving the efficiency of assessment. However, it is still challenging to directly assess the structural seismic damage based on videos captured by indoor surveillance cameras during earthquakes. In this study, we elaborate on the concept of estimating the structural natural frequency based on the relative pixel displacement of inter-stories. Furthermore, we propose a strategy for post-earthquake structural damage assessment that integrates the computer vision and time-frequency analysis. This approach aims to navigate the difficulties inherent in earthquake damage assessment and improve emergency responses. The relative pixel displacement between the camera and the fixed features on the floor is extracted from videos by using the Harris corner detection and Kanade–Lucas–Tomasi algorithms. The structural natural frequency is estimated using the synchroextracting transform-enhanced empirical wavelet transform. The natural frequency shift-related seismic damage index is defined and calculated for damage assessment. A shake table experiment of a small-scale steel model is conducted to verify the accuracy and feasibility of the approach, and the practicality of the proposed approach is further verified by utilizing the data from a full-scale reinforced concrete benchmark model experiment. The results demonstrate that the approach can accurately and efficiently evaluate the structural damage after an earthquake based on the video captured by surveillance cameras during the earthquake. The error of the acquired damage index is less than 0.1. We will apply more advanced algorithms in the future to alleviate this problem.

Analytical solution to a coupled system including tuned liquid damper and single degree of freedom under free vibration with modal decomposition method

This research focuses on employing a linear analytical approach to transform free surface waves and velocities into mode coordinates, with the aim of investigating the free vibration behavior of a coupled system consisting of a Single Degree of Freedom and a sloshing tank. Through a series of manipulations and simplifications of the coupled equations, a fourth-order ordinary differential equation is derived to showcase the overall response of the system, highlighting the contribution of each odd mode. Key concepts explored include system stability, mode-specific natural periods, establishment of initial boundary conditions, and formulation of the complete system response. The analytical method applied to study Tuned Liquid Dampers, a type of elevated sloshing tank, reveals that in higher modes, the lower frequency aligns with the structural natural frequency, while the higher frequency is approximately n times the structural natural frequency (where n is the odd mode number). This approach also elucidates why the system's response does not exhibit a higher-frequency component in higher modes. The study further investigates concepts such as employing an initial perturbation to excite higher frequencies and the potential for approximating the system through the first mode. Additionally, a numerical model was developed using variable separation and modal decomposition methods to complement and validate the analytical approach. Finally, further verification of the model was performed using the Preismann scheme applied to the relevant equations and the central upwind applied to nonlinear equations.

Utilizing data-driven algorithms for blind modal parameter identification of structures from output-only video measurements

In structural dynamics and vibration analysis, modal identification plays a pivotal role in understanding and characterizing the dynamic behavior of complex systems. Traditional modal analysis techniques heavily rely on accurate sensor placement and knowledge of the excitation forces, which may not always be feasible or practical in real-world scenarios. Recently, non-contact video-based modal analysis methods for structures with arbitrary complexity using computer vision techniques have gained much importance. But these methods need to know ahead of time where the structure's natural frequency ranges are, and they use steerable pyramids, which are complicated multi-scale image decomposition filters. To address these issues, a blind modal identification technique is suggested to extract the modal parameters (modal frequency and mode shapes) from the recorded structural vibration video signal. The proposed algorithm for unsupervised machine learning is the Non-Negative Matrix Factorization (NNMF) method, which is combined with the Generalized Complexity Pursuit (GCP) method for blind source separation. The NNMF algorithm is directly applied to the raw pixel-time series made from the video data to get the temporal components, which are then separated using GCP to find the individual modal frequencies and mode shapes. The above algorithm is first validated on a numerical model and then implemented on laboratory scale models (cantilever, single-degree, and multi-degree frame models). Finally, the proposed methodology is implemented on real-world recorded structural vibration videos to determine its noise sensitivity, such as the Tacoma Narrows bridge and the London Millennium footbridge. The modal parameters extracted are compared with those from the available literature for validation. The estimation errors obtained from all the validations are well below 1%, which makes the technique quite suitable and reliable for structural vibration monitoring by identifying and reproducing complex vibration modes.

A symmetric substructuring method for analyzing the natural frequencies of conical origami structures

Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorption capacity. Previous investigations have commonly focused on the static characteristics of these lightweight structures. However, the efficient analysis of the natural vibrations of these structures is pivotal for designing conical origami structures with programmable stiffness and mass. In this paper, we propose a novel method to analyze the natural vibrations of such structures by combining a symmetric substructuring method (SSM) and a generalized eigenvalue analysis. SSM exploits the inherent symmetry of the structure to decompose it into a finite set of repetitive substructures. In doing so, we reduce the dimensions of matrices and improve computational efficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis. Finite element simulations of pin-jointed models are used to validate the computational results of the proposed approach. Moreover, the parametric analysis of the structures demonstrates the influences of the number of segments along the circumference and the radius of the cone on the structural mass and natural frequencies of the structures. Furthermore, we present a comparison between six-fold and four-fold conical origami structures and discuss the influence of various geometric parameters on their natural frequencies. This study provides a strategy for efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contribute to the efficient design and customization of origami metastructures with programmable stiffness.