Fundamental Natural Frequency Research Articles

Effect of Frequency Content of Earthquake Ground Motions on Structures with Varying Dimension

An earthquake is a catastrophe which is always a topic of concern for structural designers and civil technocrats. Not only it causes physical damage to the structures but also successful to impart psychological disorder in human minds for long-run. In order to mitigate the devastating effects of earthquake on society, it is eminent to study the dynamic characteristics in detailed manner i.e. to examine how the structure responds owing to the seismic characteristics. The various ground motion characteristic includes time-duration and velocity, frequency content and amplitude, displacement, incremental velocity and incremental displacement, peak ground accelerations (PGAs), etc. Out of these, effect of frequency content and maximum amplitude value of earthquake ground motions on the seismic response of structures is often underestimated. This paper investigates the effect of frequency content and maximum amplitude value on the seismic response of structures which is dominant of all characteristics. The study proceeds with recording time-history of acceleration obtained from conventional unidirectional harmonic shake table. Further, FFT (Fast Fourier Transform) analysis of applied time-history is done and the effect of frequency content and the maximum amplitude value of applied time-history on the seismic responses of structures is investigated and studied. For this, structures with varying dimensions (height, length, and width) are modelled and time-history analysis of structural models has been carried out in SAP2000v19. Seismic responses of analysed structures are represented in the form of fundamental natural frequency, storey displacement, and base shear. It is reported that out of many earthquake indices, frequency content and amplitude of earthquake ground motions are the most dominating. It is reported that the resonance phenomena occurs for the less height structure and thus it shows maximum displacement and base shear responses. Also, as height, length, and width of structure increases; displacement, base shear, and fundamental time-period of structure increases.

A nonlinear Chebyshev-based collocation technique to frequency analysis of thermally pre/post-buckled third-order circular sandwich plates

In the current research, a comprehensive frequency analysis is performed for the circular sandwich plates in the pre-and post-buckling ranges occurred because of an in-plane thermal field. A sandwich system is fabricated with an open-cell foam (OCF) core and laminated composite face sheets reinforced with graphene platelets based on the functionally graded models (FG-GPLRC). The displacement field is counted using Reddy’s third-order shear deformation theory because the thick layers form the desired circular structure. Due to large deformations in the post-buckling situation, the geometrically nonlinear strain–displacement relations based on the von Kármán model are employed. The Chebyshev collocation solution is implemented to attain the discrete form of equilibrium and dynamic equations. A displacement control iterative procedure is also adopted to address the nonlinear equilibrium state of the system. Moreover, the adjacent-equilibrium criterion is considered to recognize the static paths from small-amplitude vibrations. After performing validation studies with available articles, novel results are displayed to verify the influence of geometrical and physical characteristics on the post-buckling path and fundamental natural frequency of circular sandwich plates.

Experimental study on the vibration of poplar LVL orthogonal ribbed box floor

In this paper, a new type of Popular Laminated Veneer Lumber (LVL) orthogonal ribbed box floor is proposed. Six full-scale specimens of box-shaped floors were tested using the natural excitation method and the human induced excitation method in order to examine the dynamic characteristics and vibration response. The results indicate that the box-type floor specimens with the thickness of the cladding plate, the height of the rib beam, and the distance between the short rib beams of 18.3, 285, and 600 mm exhibit the largest fundamental natural vibration frequency and damping ratio, as well as the best dynamic characteristics. With increasing cladding panels and higher rib beams, peak acceleration decreases, whereas it increases with increasing thickness and shorter rib spacing. The peak acceleration of the floor gradually increases as stride frequency and walking number increase. With the same stride frequency, the peak acceleration of the floor when a single person jumps is greater than when stepping or walking continuously. Combined with related specifications, the root mean square acceleration, peak acceleration, and acceleration vibration level were used to evaluate the vibration comfort of the floors. The methods are presented to predict the fundamental natural frequency and the peak acceleration of the Popular LVL orthogonal ribbed box floor under single walking or jumping conditions, and the predicted results agree well with the experimental results. The research results provide designers with theoretical support for solving the vibration comfort problem on wooden floors.

A topology optimization methodology for the offshore wind turbine jacket structure in the concept phase

This paper proposes a topology optimization methodology for offshore wind turbine (OWT) jacket structure design in the concept phase. First of all, modal analysis and load calculation of a 5 MW reference OWT are performed. On the basis of finite element analysis, the displacement and von Mises stress of multi-jacket support structures in various ultimate loading conditions are explored. Furthermore, structural topology optimization formulation aims to minimize a weighted normalized objective for the OWT jacket structure. Therefore, several optimum structures are obtained by adjusting weighting coefficients. For the coupling effect between the structure and applied load, load recalculation, displacement, and stress reanalysis are performed on the jacket structure based on the topological configuration under a specific weighting factor. Comparisons are made between the reference structure and optimized structure. Without the addition mass, the fundamental natural frequency of the optimized structure is marginally increased, but the maximum displacement and von Mises stress are drastically lowered, indicating that the optimized structure outperforms its reference counterpart. These findings conclusively demonstrate that the proposed TO technique for the design of OWT jacket structures is feasible and preferable.

Damage Detection in Cantilever Piping System-Transporting Fluid Using Finite Element Method

Fracture existence in a pipe is considered disruptive as well as detrimental to the pipe systems and equipments. Cracks are the most common mechanism of failure for pipelines of any kind. Therefore, early crack identification may help save the pipe system from catastrophic breakdown. This study focuses on fluid-transporting cantilevered tapered pipes. By using the Bernoulli beam theory, ANSYS is used to simulate the pipe's performance by the finite element method for an incompressible fluid flow through a tapered cantilevered pipe. The effect of a non-propagating open crack on the dynamic and modal behavior of a cantilevered pipe used to convey fluid is investigated. Flow velocity and crack relative location, as well as the crack's depth, will be explored as they relate to the fundamental natural frequency, second, and third natural frequency. Results have showed clearly that crack depth and relative position play a significant role in natural frequency variation. However, fluid inlet velocity is found to have less impact on the natural frequencies considered at a certain relative crack position.

The role of graphene oxide in the strength and vibration characteristics of standard and high-grade cement concrete

This study presents the results of an experimental study of the influence of graphene oxide (GO) on the static and dynamic mechanical characteristics of cement concrete. Four different dosages of GO, 0.05%, 0.10%, 0.15% and 0.20% by weight of cement and two different grades of concrete, standard concrete (M30) and high strength concrete (M60) were studied. The static properties such as compressive strength and chord modulus of elasticity were determined. The impact hammer technique was used to obtain dynamic characteristics such as fundamental natural frequency, damping ratios, and mode shapes of concrete beams under free-free condition. In addition, fundamental resonant frequencies under different modes of vibration were determined. The dynamic elasticity modulus, dynamic shear modulus and dynamic poisons ratio of all concrete mixes were also determined. Experimental results revealed that the compressive strength of the concrete with the incorporation of GO was remarkably enhanced. The highest increase in compressive strength was found at GO dosage of 0.15%, and the improvement at 7 and 28 days was 58.2% and 47.7% for standard concrete and 51.2% and 24.3% for high strength concrete respectively compared to control concrete. The impact hammer test revealed that the maximum increase in fundamental natural frequency was 8.0% and 6.6%, and the maximum decreased damping ratio was 29.1% and 26.3% for standard concrete and high strength concrete respectively when compared to the control concrete. Ultrasonic pulse velocity results indicated that the homogeneity of the concrete with GO addition was significantly improved. SEM and EDX microstructure investigations found that the addition of GO to concrete promoted the development of improved hydration phases leads to the dense microstructure. The findings of this study demonstrated that GO nanomaterial had a potential future as a reinforcing material in cement concrete for improved microstructure, strength, and free vibration characteristics.

Detection of the instantaneous frequency degradation due to damages of a fixed offshore jacket platform using the iEEMD‐based Hilbert Huang transform under a wave excitation

In online structural health monitoring of the fixed offshore jacket platform, the determination of the time-dependent degradation of structures due to damages is the most important step in a maintenance strategy. This paper presents the application of the Hilbert Huang transform method based on the iEEMD (improved ensemble empirical mode decomposition) algorithm to identify the instantaneous natural frequency degradation due to damages of the fixed offshore structure under the random wave excitation. The iEEMD algorithm is proposed to restrain the mode mixing and used to adaptively process the big response data of the offshore structure during the wave loading with a wide frequency range. The vibration response measurement experiment for the offshore structure was conducted in a wave tank in this study. The identified fundamental natural frequencies by the iEEMD-based Hilbert Huang method were evaluated and compared with results of the numerical model of the eigenvalue analysis. The main result demonstrates that the instantaneous frequency degradation and nonlinear time-varying behavior due to the brace damage of the fixed offshore jacket platform can be successfully identified by the iEEMD-based Hilbert Huang transform technique under a wave load.

Energy harvesting of inverted piezoelectric flags in an oscillating flow

The energy harvesting potential of flexible structures (e.g. flags) made of piezoelectric materials has drawn rapidly increasing attention in recent years. In this work, we numerically study the energy harvesting performance of an inverted piezoelectric flag in an oscillating flow using an immersed boundary-lattice Boltzmann method for Reynolds number of 100, mass ratio of 2.9 and non-dimensional bending stiffness of 0.26 which correspond to the maximum flapping amplitude for a single inverted flag in a uniform flow. 2D simulations are conducted by varying the ellipticity (e), the ratio R of the frequency of the oscillating flow to the fundamental natural frequency of the flag and the horizontal velocity amplitude (Au) of the flow. Three coupling regimes at Au=0.5 are identified: chaotic oscillations regime I (0.1≤R≤1 ), large periodic and symmetric oscillation regime IIa1.1≤R≤1.5and IIb(2.1≤R≤3.0), and small periodic and asymmetric oscillation regime III(1.6≤R≤2). The maximum mean electrical power coefficient C¯P occurs in regime IIa at R=1.5 with Au=0.5, α (piezo-mechanical coupling parameter) = 0.5, and β (piezo-electric tuning parameter) = 1.5. C¯P is 0.10 for a single inverted flag, and is 148%, higher than that of the corresponding flag in the uniform flow. This improvement is attributed to the higher flapping angular amplitude (180°), higher ratio of the flapping frequency to the oscillating frequency (virtually constant at 0.5) of the flags, and constructive vortex interaction in regime IIa.

Design and nonlinear dynamics of FG curved sandwich beams with self-adapted auxetic 3D double-V meta-lattice core

The functionally graded (FG) curved sandwich beams with the self-adapted auxetic 3D double-V meta-lattice core and GRC (graphene reinforced composite) facesheets are designed, modeled, and analyzed to reveal their linear vibration and nonlinear dynamic behaviors. The 3D double-V meta-lattices with negative Poisson’s ratio (NPR), developed from the 2D double arrowed honeycombs, are designed that can be self-adapted to meet the spatial requirements of curved sandwich beams. Through micromechanical modeling according to the extended Halpin-Tsai model, the material properties are determined for GRC facesheets, which are further designed to have different distributions of graphene sheets along the structural radial direction, to make the whole sandwich beams possess FG configurations. By linear vibration analysis, the distinct influences of FG configurations on the fundamental natural frequencies are presented. Results from full-scale FE modeling and nonlinear analysis have shown the significant effects of structural curvature radii. The influences of beam lengths, strut radii, thicknesses of the core layer and facesheets, and charge parameters of the blast loadings are followed.

Modal Analysis of Delaminated Flax Fibre Reinforced Epoxy Composite Plate

This paper describes the influence of fibre orientation, delamination size and location on the natural frequencies of the single mid-plane delaminated unidirectional flax fibre reinforced epoxy (FFRE) composite plates under different boundary conditions numerically by using ANSYS MAPDL. The delaminated composite plate was modelled as two separate volumes divided at the midplane of the plate, with the nodes on the intact surfaces merged. In contrast, the nodes on the delaminated region remained separate. The results show that the CCCC delaminated composite plate has the highest fundamental natural frequency (219.996 Hz). Furthermore, for increasing fibre orientation from 0° to 45°, the fundamental natural frequencies decreased by 10.12% for the CCCC condition and increased by 6.01% for the SSSS condition. The fundamental natural frequency for the cantilever condition decreased 60.91% when fibre orientation increased to 90°. Moreover, the CCCC condition significantly reduces the fundamental natural frequency (up to 38.95%) with increasing delamination size. For CCCC and SSSS conditions, the centre delamination possesses the highest fundamental natural frequency (219.996 Hz and 116.525 Hz, respectively). The highest fundamental natural frequency for cantilever conditions is 33.081 Hz, with delamination located at the middle of the width and near the free end.

An Integrated Approach for the Determination of Young’s Modulus of a Cantilever Beam Using Finite Element Analysis and the Digital Image Correlation (DIC) Technique

This paper is an extended paper from the 24th International Conference on Mechatronics Technology, ICMT 2021. The basic mechanical characteristic that gauges the stiffness of a solid material is known as the Young’s modulus. To evaluate the Young’s modulus, destructive material testing is frequently used. This paper describes how to determine a material’s dynamic Young’s modulus using Digital Image Correlation (DIC) in conjunction with numerical back-analysis. Three different materials (brass, aluminum, and steel) were examined for their static and dynamic reactions. A static transverse displacement was first applied at the free end of the beam before it was released and the beam was allowed to vibrate freely. The resulting vibrations at the free end were monitored using the DIC method, following which the natural frequencies of the beam were derived by applying the Fast Fourier Transform (FFT) to the DIC measured time history. The Young’s modulus corresponding to the fundamental natural frequency of the beam was then obtained via modal back-analysis using the finite element program Ansys 2022 R1. In this way, the Young’s modulus of the material may be calculated using a combination of numerical and DIC techniques, thus allowing for the non-contact evaluation of the structural integrity without subjecting the material to destructive testing. Potential applications of this method include bridge and building assessments, and structural health monitoring (SHM).

Non-linear Isolator for Vibration and Force Transmission Control of Unbalanced Rotating Machines

PurposeThe objective of this paper is to investigate with simulations how non-linear spring and non-linear damper components of isolators can be employed to effectively reduce both the oscillations and the force transmitted to ground in the whole spinning range of unbalanced rotating machines.MethodsThe principal goal of this paper is twofold. First, to present a concise and consistent formulation based on the harmonic balance approach for the vibration response of spinning machines mounted on linear/non-linear, softening/hardening, un-tensioned/pre-tensioned springs and linear/non-linear dampers. Second, to provide a comprehensive overview of the vibration and force transmission control with non-linear isolators specifically tailored to unbalanced machines.ResultsThe study has shown that, the best vibration isolation is provided by a pre-tensioned linear and cubic softening spring combined with a linear and negative quadratic damper. The pre-tensioned spring should be designed in such a way as it holds the weight of the machine and thus produces on the vibrating machine a symmetric elastic restoring force proportional to the linear and cubic powers of the displacement. The cubic softening stiffness should then be tuned to minimise the frequency, and thus the amplitude, of the resonant response of the fundamental mode of the machine and elastic suspension system, while preserving stability and a desired static deflection. In parallel, to reduce the force transmission to ground above the fundamental resonance frequency, the negative quadratic damping effect should be tailored to maximize the energy absorption at higher frequencies.ConclusionThe study has shown that non-linear spring and non-linear damper components can be effectively employed to control the vibration and force transmission in the whole spinning range of the machine. In particular, a pre-tensioned softening cubic non-linear spring can be used to mitigate the vibration and force transmission at low frequencies, close to the fundamental natural frequencies of the elastically suspended machine. Also, a negative quadratic non-linear damper can be used to tailor the energy dissipation of the isolator in such a way as to have high damping at low frequencies and low damping at higher frequencies, which enhances the vibration and force transmission control at low frequencies and, rather importantly, mitigates the force transmission at higher frequencies.

A nondestructive approach to predict buckling load of composite lattice-core sandwich conical shells based on vibration correlation technique

In this paper the vibration correlation technique (VCT) has been used as a nondestructive method for predicting the buckling load of the composite lattice-core sandwich conical shells. This technique is capable of predicting the buckling load of different structures without reaching the failure point through modal testing. The composite lattice-core sandwich conical shell has been fabricated using a filament winding process. To perform the expriment, the fundamental natural frequency of the specimen is measured under stepped axial compression loading. The procedure is followed up without actually reaching the instability point when the structure collapses and is no longer usable. A finite element model has also been built in ABAQUS in order to determine the correlation between natural frequency and applied compressive load. A comparison of the results indicated that the VCT has provided a reliable estimate of the buckling load of composite lattice-core sandwich conical shells, especially when the structure is loaded up to at least 66% of the experimental buckling load and accuracy of the VCT decreases when the maximum load is lower than 43% of the buckling load. Results also revealed that the linear fitted curve is unsuitable for the correlation between frequency of vibration and applied load in order to predict buckling load.

An experimental investigation on enhancing the strength and stiffness of GFRP co-cured composite joint: effect of glass powder addition

Co-cure adhesive joints are preferred by various industries, namely, automobile, marine and aerospace, to join two surfaces in structural applications, as a useful replacement for mechanical fastenings. The present work focusses on the mechanical properties and free vibration behaviour of co-cured glass fiber compositesreinforced with glass powder. In the course of the experimentation, the adhesive is being reinforced concurrently with glass powder in four different weight percentages, such as 0%, 0.5%, 1%, 1.5% and 2%. The mechanical testing results reveal that the addition of 1.5% of glass powder to the epoxy could relatively help in increasing the tensile strength and flexural strength of the co-cured glass fiber composites respectively to the degree of 11.68% (364.29 Mpa) and 24.75% (256.16 Mpa). The Single lap shear results show that the 0.5% glass powder reinforcement significantly increases the shear strength of the cocured glass fiber composites by 20.91% (19.31 Mpa). Furthermore, the free vibrational study of 1.5% co-cured composites shows that they have a higher fundamental natural frequency than the glass powder reinforced co-cured composites that have a lower weight percentage. Furthermore, the addition of glass powder to the co-cured composites helps in increasing the damping factor of the composites due to the glass powder agglomeration. Neat and glass powder reinforced co-cured samples are further analysed afterwards, using the mechanical and shear test by scanning electron microscopy.

A comparative study on the effect of SMAs and CNTs on the vibration of composite plates exposed to thermal environments

The main purpose of this study is to compare the effects of two advanced materials, namely shape memory alloys (SMAs) and carbon nanotubes (CNTs) on the fundamental natural frequencies of rectangular graphite fiber/epoxy (GF/EP) composite plates. The performance of each of these materials is evaluated for different geometric conditions and boundary conditions as well as operating temperatures. Moreover, the glass transition temperature is considered as a limiting factor in the study. The governing equations are derived based on first-order shear deformation theory (FSDT) and then solved by generalized differential quadrature (GDQ) technique. The effective thickness-to-width ratio and temperature ranges are determined for both SMA wires and CNTs. The results of this study show that in some conditions, the use of CNTs is preferable over SMA wires and vice versa. Moreover, unlike SMA wires, the positive effect of the CNTs is limited to a certain extent. Furthermore, the numerical results indicate that depending on the different parameters, the use of SMAs may have constructive or destructive effects on the structural vibrations. Interestingly, it is shown that in some circumstances, the co-incorporation of SMAs and CNTs leads to a significant enhancement in the natural frequencies of the structure.

Resonance measurement and vibration reduction analysis of an office building induced by nearby crane workshop vibration

Tests were conducted on a 6-storey office building and factory building near where abnormal horizontal vibrations often occurred. The floor acceleration responses of the building were measured under the condition of crane operation, which was believed to be one of the sources of the vibration. A one-third octave spectrum and weighted acceleration levels were calculated from the measured floor acceleration time histories to assess human comfort levels. The modal parameters of the building were identified using the frequency domain decomposition method. The field test results indicated that the small crane's excitation frequency during the start and stop operations in the nearby factory was 3.6 Hz, which was the same as the fundamental natural frequency of the building. The resonance phenomenon between the building structure and the crane excitation caused the abnormal horizontal vibration. Finally, the influence of adjusting the excitation frequency, the excitation intensity, and the connection form of the foundation slab on the vibration responses was analyzed. Results showed that when the excitation frequency was adjusted to stagger the natural frequency of the structure by 20%, the acceleration level resulting from the same excitation could be reduced by half. The excitation intensity, the difference between the frequencies of excitation and structure was found to be the key factor influencing the structural resonance response.

Free Vibration Analysis of Isotropic Plates Using Regressive Ensemble Learning

The Finite Element Method (FEM) is a popular technique that is employed to analyze and understand the behavior of a structure. Although it has various advantages, there are some drawbacks such as developing accurate mathematical models, the computational cost for complex systems, and expertise. Thanks to recent advancements in computational science, those drawbacks can be eliminated by integrating artificial intelligence. This study presents an ensemble learning regressor-based technique to evaluate the fundamental natural frequencies of isotropic plate structures. For this purpose, Random Forest Regressor (RFR) has been considered. The isotropic plates have been taken into account as square and rectangular thin and thick plates whose materials have been selected as Structural Steel, Aernet 100, Al 7108, and Al 2024 since they are frequently used in various engineering fields. It has been evaluated that the proposed technique has a 0.9936 correlation score (R2) and 0.0019 mean square error (MSE). The average prediction accuracy has been obtained by 99.12% for the test set. Those indicated that the proposed approach is not only an appropriate model for such a problem but also predicts the fundamental natural frequency accurately. Considering its success (99.12%) and the execution speed (0.127 seconds), it is concluded that the proposed approach is an advantageous alternative technique to the other mathematical models.

Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance

The impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made from a hyperelastic material, providing large deformation under small excitation amplitude. A nonlinear strain energy function is proposed to capture the elastic energy stored in the flexible component of the device. The tip–sample interaction is modeled based on the van der Waals non-contact force. The nonlinear equation governing the AFM’s dynamics is established using the extended Hamilton’s principle, obeying the Euler–Bernoulli beam theory. As a result, the vibration behavior of the system is introduced by a nonlinear equation having a time-dependent boundary condition. To capture the steady-state numerical response of the system, a developed Galerkin method is utilized to discretize the partial differential equation to a set of nonlinear ordinary differential equations (ODE) that are solved by the combination of shooting and arc-length continuation method. The output reveals that while the resonator is set to be operating near twice the fundamental natural frequency, the response amplitude undergoes a significant drop to the trivial stable branch as the sample’s profile experiences depression in the order of the picometer. According to the performed sensitivity analysis, the proposed working principle based on principal parametric resonance is recommended to design AFMs with ultra-high detection resolution for surface profile scanning.

Analytical solution for vibration and buckling of cylindrical sandwich panels with improved FG metal foam core

In this research paper, a novel higher-order porosity distribution is proposed, and free vibration and buckling behavior of cylindrical sandwich panels with functionally graded metal foam core are investigated. It is assumed that the sandwich panel is made of two thin face metal sheets and a moderately thick functionally graded metal foam core. The dynamic governing equations are obtained based on the third-order shear deformation theory and utilizing the Hamilton principle. It is assumed that the voids are distributed non-uniformly along the thickness of the functionally graded metal foam core. The elastic modulus of the core depends on the square of the relative density, thus is changing nonlinearly through the thickness of the core. The Navier technique is implemented to derive closed form solutions for the natural frequencies and the buckling load of the simply supported cylindrical sandwich panels. The accuracy and effectiveness of the proposed model are verified by comparison with previous researches. Results revealed that the presented higher-order porosity distribution can increase the buckling load and fundamental natural frequency by 10% and 5% in comparison to the conventional porosity distributions, respectively. In addition, it is shown that if the flexural vibration is of interest, ignoring the in-plane and rotary inertias, which can significantly reduce the computational complexity, does not have any considerable effect on the natural frequencies.

Multiscale modelling of functionally graded porous beams: Buckling and vibration analyses

This paper combines the finite element (FE) homogenisation and structural assessments to conduct the multiscale modelling of laminated functionally graded (FG) porous beams made of closed-cell foams, with a focus on the beam buckling and vibration performances. In the FE homogenisation, representative volume elements (RVEs) are built up according to the relative densities, average cell sizes, and base material properties from foam samples. They are used to predict the foam Young’s modulus and verified against existing studies. A detailed investigation is then carried out to disclose the effects of RVE and porosity features, where the relative density is confirmed as the dominating factor in the calculation of foam modulus. Quantitative relations between pore structure and Young’s modulus are obtained via data fitting.In the subsequent structural assessment, the predicted Young’s modulus is employed in the buckling and vibration analyses of FG porous beams, which are constructed by a six-layer laminated beam model and consist of high-, medium-, and low-density layers with varying designated relative densities. The Timoshenko beam theory and the Ritz method are applied to derive and solve the governing equations. Convergence and validation studies are performed accordingly to ensure the validity of presented results, followed by a parametric study to examine various FG beams concerning different porosity distributions, boundary conditions, and slenderness ratios. The prominence of graded porosities is evidenced by apparently promoted beam stiffness with over 30% and 10% increments in the critical buckling load and fundamental natural frequency, respectively. The graded porosities can be linked to realistic closed-cell Aluminium foams with developed quantitative relations, shedding important and practical guidance into the porous structural design.