Fundamental Frequency Of Structure Research Articles

Flow field characteristics and vibration responses of saddle-shaped membrane structures

Elastically mounted flexible membrane roofs exposed to flows are prone to vortex-induced vibrations and even aero-instability due to the strong fluid–structure interaction (FSI). This study is to investigate the FSI mechanism in the saddle-shaped membrane structure over a range of Reynolds numbers and wind directions in laminar flows, by bridging structural vibration responses and flow dynamics. The aeroelastic characteristics of membrane structures, including statistics of displacement responses, oscillation frequency, and oscillation damping ratios, were identified from the perspective of time and frequency domains. Simultaneously, the particle image velocimetry system was employed to visualize the flow features, including velocity vector, turbulence intensity, and vortex evolution in both space and time. The flow modes were further decomposed by proper orthogonal decomposition (POD) to capture the salient aspects of the flow. Three patterns of POD modes are identified, and the first mode plays the dominant role in POD modes. It showed that as the wind Reynolds number increases, the space between the shear layer and membrane surface would be narrowed, and resultantly the vortices turn out smaller in scale and closer in space. This trend leads to an increase in the frequency of vortex shedding and a stronger FSI effect. When the frequency of vortex shedding approaches the fundamental frequency of structures, the vibration of the membrane would be shifted from turbulent buffeting to vortex-induced resonance, featured with lock-in frequency, significant amplified displacement, and negative aerodynamic damping ratio.

Fundamental frequency formulation and modeling of masonry slender structures: A comparative study of machine learning and regression techniques

This paper presents a novel method for determining the fundamental frequency and modeling slender masonry structures, which is particularly relevant in the context of structural dynamics. This research evaluates the effectiveness of machine learning techniques, specifically artificial neural networks (ANN), and regression methods, including multiple linear regression (MLR) and multiple nonlinear regression (MNLR), in predicting the fundamental frequency of structures, considering both their geometrical and mechanical properties. The objective is to provide a comprehensive comparison of these methods, emphasizing their benefits, limitations, and potential applications in structural health monitoring. The ANN model demonstrated superior performance to linear and non linear regression methods. The findings could significantly impact both theoretical understanding and practical applications in this field. Moreover, this work paves the way for future research, potentially leading to the creation of more accurate and efficient predictive models for slender masonry structures. This methodology ensures a thorough understanding of the model’s behavior and its responsiveness to variations in input parameters.

Effect of cushion types on the seismic response of structure with disconnected pile raft foundation

In recent years, the benefits of reducing the impacts of the earthquake on the seismic response of disconnected pile raft foundation (DPRF) have simulated increasing research on this type of foundation to provide references for foundation design. One effective way to study the seismic response of soil-structures is to investigate the scaled models in 1-g shaking table tests. In this paper, a series of scaled 1-g shaking table tests were carried out to study the seismic response of scaled nuclear power stations with DPRF under earthquake excitations founded in clay. Three different cushion types were adopted to study their different effects on the seismic response of the structure and the foundation. The fundamental structural frequency, horizontal displacement, and acceleration results showed that cushion A with well-graded gravel and cushion B with a mixture of two gravel sizes were better than cushion C with a single gravel size. Although the cushion type had an insignificant influence on the bending moments of the disconnected piles, the maximum bending moments in all cases were found to be proportional to the near-pile acceleration. Furthermore, design engineers should pay more attention to the rocking of a structure with DPRF under earthquake loads.

The Impact of the Cut-Out Shape on the Dynamic Behavior of Composite Thin Circular Plates

This study measures the impact of the cut-out shape on the fundamental frequency and the harmonic response of thin composite circular plates under fixed boundary conditions. For this purpose, the Finite Element Method has been employed using the SHELL181 element of ANSYS Workbench 18.2 software. Nine different circular plates having central equilateral triangle, square, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon, regular decagon, and circular cut-outs have been designed to understand the changes in the vibrational behavior of a structure as the cut-out geometry approximates to circular. Additionally, a solid circular plate has been modelled for comparison purposes. To investigate the effect of the cut-out shape more deeply, all structures have been designed as cross-ply and angle-ply composites. The free vibration analysis has been performed to obtain the fundamental frequency of each structure. The harmonic response analysis problem has been solved by employing the Mode Superposition Method and considering a constant damping ratio. The results of the study have been interpreted by considering the displacement response, stress, and phase shifts at a certain frequency range. The results indicate that the shape of the cut-out considerably affects the fundamental frequency and harmonic response of the circular structure regardless of its fiber orientation.

Seismic damage potential described by intensity parameters based on Hilbert-Huang Transform analysis and fundamental frequency of structures

This study aims to present new frequency-related seismic intensity parameters (SIPs) based on the Hilbert-Huang Transform (HHT) analysis. The proposed procedure is utilized for the processing of several seismic accelerograms. Thus, the entire evaluated Hilbert Spectrum (HS) of each considered seismic velocity time-history is investigated first, and then, a delimited area of the same HS around a specific frequency is explored, for the proposition of new SIPs. A first application of the suggested new parameters is to reveal the interrelation between them and the structural damage of a reinforced concrete frame structure. The index of Park and Ang describes the structural damage. The fundamental frequency of the structure is considered as the mentioned specific frequency. Two statistical methods, namely correlation analysis and multiple linear regression analysis, are used to identify the relationship between the considered SIPs and the corresponding structural damage. The results confirm that the new proposed HHT-based parameters are effective descriptors of the seismic damage potential and helpful tools for forecasting the seismic damages on buildings.

Size-dependent microstructure design for maximal fundamental frequencies of structures

Topology optimization on a unit cell is a common technique to improve the fundamental frequencies of periodic cellular solid structures. During this procedure, the effective properties of cellular solids are primarily computed by the homogenization method. This homogenization method is based on the classic continuum theory under the assumption that the unit cell is infinitely small. Hence, this classic strategy is inadequate to interpret the size dependence of the optimal results. The aim of this study was to describe and examine size dependence in relation to the topology design of the unit cell to achieve maximization of the structural fundamental frequencies. For this purpose, we determined the effective properties of the cellular solids and constructed the optimization formulation based on the couple-stress theory rather than the classic theory. A modified bound formulation of the objective and constraint functions was used to avoid the non-differentiability of repeated frequencies. Although the existing theory does not reflect size dependence, our optimization formulation was able to identify the size dependence of both the microstructural topologies and the fundamental frequencies. The size-dependent results are achieved by varying of the mechanisms to achieve the maximal fundamental frequencies in response to cell size variation. The present formulation is suitable for the unit cell design of cellular solid structures that possess local dimensions comparable to the cell size, and this novel formulation has expanded the application scope of the classic microstructural design problem for periodic materials.

Effects of site\u2013city interaction and polarization of the incident S-wave on the transfer function and fundamental frequency of structures

The variation of 2D fundamental frequency of stand-alone structure on rock ({F}_{{02{text{D}}}}^{text{S}} ) and in a basin ({F}_{{02{text{D}}}}^{text{BS}} ) with the polarization of the incident S-wave is presented. This paper also presents the role of city density and polarization of the exciting S-wave in the site–city interaction effects on the response of structures in a city as well as free-field motion. The seismic responses of the various considered basin and site–city models are computed using SH-wave and P-SV-wave finite-difference programs. A considerable decrease in the value of {F}_{{02{text{D}}}}^{text{S}} of stand-alone structure on rock is obtained with the increase in shape ratio for the SV-wave but not for the SH-wave, as compared to the 1D fundamental frequency of structure ( {F}_{{01{text{D}}}}^{text{S}} ). However, a considerable decrease in the value of {F}_{{02{text{D}}}}^{text{BS}} of a stand-alone structure in basin under double resonance condition is obtained for the SH-wave and not for the SV-wave. The spectral amplification factor at the top of a structure at {F}_{{02{text{D}}}}^{text{BS}} of structure is larger for the SV-wave as compared to the SH-wave. A splitting of the bandwidth of the fundamental mode of vibration of structure and very large reduction in spectral amplification factor at {F}_{{02{text{D}}}}^{text{BS}} of structure is obtained due to the site–city interaction effects under double resonance condition for both the S-wave polarizations. Further, an increase in these inferred effects with an increase in city density and number of structures in a city with a constant city density is obtained. This finding raises the question concerning the validity of ground-motion prediction using soil–structure interaction for the design of structures in an urban environment. Further, the decrease in spectral amplification factor at {F}_{{02{text{D}}}}^{text{BS}} of structure due to the site–city interaction effects is larger in the case of SV-wave as compared to SH-wave. Furthermore, a considerable site–city interaction effects on free-field motion is obtained.

Quantification of Fundamental Frequencies of 3D Basins and Structures and Site–City Interaction Effects on Responses of Structures

Large-scale commercialization in Indian metrocities has made realtors develop new construction sites by filling land depressions with loose soil, which may behave as small three-dimensional (3D) basins. This study presents the development of empirical relations to predict the fundamental frequency of basins ( $$F_{{03{\text{D}}}}^{\text{B}}$$ ) and structures ( $$F_{{03{\text{D}}}}^{\text{S}}$$ ) on rock for different shape ratios to study the effects of site–city interactions (SCIs) on the response of structures under a double resonance condition. The S-wave responses of the various considered basins, structures, and site–city models are simulated using the finite-difference method. Analysis of the simulation results reveals that the $$F_{{03{\text{D}}}}^{\text{B}}$$ of the basin and the $$F_{{03{\text{D}}}}^{\text{S}}$$ of the structure depend strongly on the shape ratio, on average matching with those obtained using the SV-wave response of the section of the respective basin/structure. However, the spectral amplification factor (SAF) obtained at $$F_{{03{\text{D}}}}^{\text{B}}$$ / $$F_{{03{\text{D}}}}^{\text{S}}$$ for the basin/structure is much larger than that obtained using the SV-wave response of a section of the respective basin/structure. Empirical relations are developed to predict the $$F_{{03{\text{D}}}}^{\text{B}}$$ of basins and $$F_{{03{\text{D}}}}^{\text{S}}$$ of structures in terms of the shape ratio and one-dimensional (1D) fundamental frequency of the respective model. Analysis of 3D SCI effects reveals a reduction of the SAF at the fundamental frequency of the structure in the basin ( $$F_{{03{\text{D}}}}^{\text{SB}}$$ ) with an increase of the number of structures as compared with that at the fundamental frequency ( $$F_{{03{\text{D}}}}^{\text{SB}}$$ ) of a standalone structure in the basin, being on the order of about 60 % in the case of a city with 25 structures. This finding indicates the need for 3D SCI studies in urban environments for cost-effective earthquake engineering.

Parameter optimization to avoid propeller-induced structural resonance of quadrotor type Unmanned Aerial Vehicle

Structural resonance in Unmanned Aerial Vehicle (UAV) is one of the major challenges that impose malfunctioning of the UAV sensor thereby degrading maneuverability. Vibration in quadrotor UAV is induced, mainly, due to the rotation of its motor-driven propellers. The constructive interference between the excitation frequencies of the propellers and fundamental frequencies of the UAV structure causes structural resonance. To avoid this structural resonance, the lowest fundamental frequency of the whole UAV structure has to be higher than the maximum working excitation frequencies of the propellers. The fundamental frequency of the quadrotor UAV structure depends on the parameters such as dimensions and stiffness of motor-supporting arms and landing gears as well as the mount location of the landing gears on the arms. The surrogate model that approximates functional dependency of the first fundamental frequency of the quadrotor UAV structure on the mentioned parameters is developed. Using the developed model and a non-linear sequential quadratic programming algorithm, the optimal values of the parameters at which the first fundamental frequency of the structure can be maximized are obtained. The adequacy of the developed surrogate model to approximate the functional form of the first fundamental frequency is verified through various statistical and experimental methods.

A novel method for the vibration optimisation of structures subjected to dynamic loading

The optimum design of structures with frequency constraints is of great importance in the aeronautical industry. In order to avoid severe vibration, it is necessary to shift the fundamental frequency of the structure away from the frequency range of the dynamic loading. This paper develops a novel topology optimisation method for optimising the fundamental frequencies of structures. The finite element dynamic eigenvalue problem is solved to derive the sensitivity function used for the optimisation criteria. An alternative material interpolation scheme is developed and applied to the optimisation problem. A novel level-set criteria and updating routine for the weighting factors is presented to determine the optimal topology. The optimisation algorithm is applied to a simple two-dimensional plane stress plate to verify the method. Optimisation for maximising a chosen frequency and maximising the gap between two frequencies are presented. This has the application of stiffness maximisation and flutter suppression. The results of the optimisation algorithm are compared with the state of the art in frequency topology optimisation. Test cases have shown that the algorithm produces similar topologies to the state of the art, verifying that the novel technique is suitable for frequency optimisation.

Empirical Formulation for Estimating the Fundamental Frequency of Slender Masonry Structures

ABSTRACTThe fundamental frequency of a structure enables better assessment of its seismic demand for an efficient design and planning of its maintenance and retrofit strategy. The frequency is independent of the type of external loads, however, depends on structural stiffness, mass, damping and boundary conditions. In the case of slender masonry structures such as towers, minarets chimneys, and pagoda temples, it is influenced by mass and stiffness distribution, connection to adjacent structures, material properties, aspect ratio and slenderness ratio. In this present article, the data collected from various literature reviews on the slender masonry structures regarding dynamic, geometrical, and mechanical characteristics have been correlated to identify the major parameters influencing the fundamental frequency of such structures. The database has been used for developing an empirical formulation for predicting the fundamental frequency of such structures. The comparison between the experimental fundamental frequencies and the estimated fundamental frequencies are carried out in order to define reliability and accuracy of these empirical formulae.

A novel horizontal to vertical spectral ratio approach in a wired structural health monitoring system

Abstract. This work studies the effect ambient seismic noise can have on building constructions, in comparison with the traditional study of strong seismic motion in buildings, for the purpose of structural health monitoring. Traditionally, engineers have observed the effect of earthquakes on buildings by usage of seismometers at various levels. A new approach is proposed in which acceleration recordings of ambient seismic noise are used and horizontal to vertical spectra ratio (HVSR) process is applied, in order to determine the resonance frequency of movement due to excitation of the building from a strong seismic event. The HVSR technique is widely used by geophysicists to study the resonance frequency of sediments over bedrock, while its usage inside buildings is limited. This study applies the recordings inside two university buildings attached to each other, but with different construction materials and different years of construction. Also there is HVSR application in another much older building, with visible cracks in its structure. Sensors have been installed on every floor of the two university buildings, and recordings have been acquired both of ambient seismic noise and earthquakes. Resonance frequencies for every floor of every building are calculated, from both noise and earthquake records, using the HVSR technique for the ambient noise data and the receiver function (RF) for the earthquake data. Differential acceleration drift for every building is also calculated, and there is correlation with the vulnerability of the buildings. Results indicate that HVSR process on acceleration data proves to be an easy, fast, economical method for estimation of fundamental frequency of structures as well as an assessment method for building vulnerability estimation. Comparison between HVSR and RF technique shows an agreement at the change of resonance frequency as we move to higher floors.

Robust structural topology optimization considering boundary uncertainties

In classical deterministic topology optimization, the effect of the possible boundary variations on the performance of the structure is not taken into account, which may lead to designs that are very sensitive to manufacturing errors. As a consequence, the performance of the real structure may be far from optimal and even not meet the design requirements. In the present paper, structural topology optimization considering the uncertainty of boundary variations is considered via level set approach. In order to make the optimal designs less sensitive to the possible boundary variations, we choose the compliance and fundamental frequency of structure enduring the worst case perturbation as the objective function for ensuring the robustness of the optimal solution. With use of the Schwarz inequality, the original Bi-level optimization problem is transformed to a single-level optimization problem, which can be solved efficiently. Numerical examples demonstrate the effectiveness of the proposed approach.

Topology Optimization of Plane Structures using Modal Strain Energy for Fundamental Frequency Maximization

This paper describes a topology optimization technique which can maximize the fundamental frequency of the structures. The fundamental frequency maximization is achieved by means of the minimization of modal strain energy as an inverse problem so that the strain energy based resizing algorithm is directly used in this study. The strain energy to be minimized is therefore employed as the objective function and the initial volume of structures is used as the constraint function. Multi-frequency problem is considered by the introduction of the weight which is used to combine several target modal strain energy terms into one scalar objective function. Several numerical examples are presented to investigate the performance of the proposed topology optimization technique. From numerical tests, it is found to be that the proposed optimization technique is extremely effective to maximize the fundamental frequency of structure and can successfully consider the multi-frequency problems in the topology optimization process.

The maximization of fundamental frequency of structures under arbitrary initial stress states

AbstractA general technique is proposed to maximize the lowest natural frequency of structures subjected to an arbitrary state of initial stresses. The arbitrary states of initial stresses are represented by nondimensional loading parameters that describe an admissible loading space, i.e. every possible initial stress state lies within the admissible loading space. The key to the proposed optimization strategy is shown to be the concavity of the first natural frequency with respect to variations of the loading parameters within the admissible loading space. A rigorous demonstration is presented to show that, provided buckling has not occurred, all the possible initial stress states must not be considered. Instead, assessment of only a small number of initial stress states must be done in order to guarantee that the first natural frequency does not decrease for all the other initial stress states within the admissible loading space. A minimax optimization technique is used to maximize the lowest natural frequency of a simply supported rectangular plate where the thickness distribution is the design variable and normal and shear initial stress states are considered. Copyright © 2005 John Wiley & Sons, Ltd.

Optimization of support positions to maximize the fundamental frequency of structures

AbstractIn this paper, the position optimization of simple supports is implemented to maximize the fundamental frequency of a beam or plate structure. Both elastic and rigid supports are taken into account. First, the frequency sensitivity with respect to the movement of a simple support is derived using the discrete method. By means of the shape functions of the finite element method, closed‐form sensitivity formulations are developed straightforwardly. Then, a heuristic approach, called evolutionary shift method, is presented for optimizing support positions with a fixed grid mesh scheme. Based on the design sensitivity analysis, the support with the highest efficiency is shifted in priority along the elementary edges with the interval (step) of the elementary size. To facilitate the convergence of the process, the interpolation technique is employed to evaluate the solution more accurately. Finally, three numerical examples are presented to demonstrate the validity of the sensitivity analysis and the effectiveness of the optimization method. Copyright © 2004 John Wiley & Sons, Ltd.

Structural modal excitation using travelling impulses—force frequency shifting

A review of existing hardware and methods for vibration testing of large structures is given by Koss and has shown that the size of inertial vibration shakers, to achieve a specific displacement, has to increase, as a structure becomes larger. In previous papers the concept of “force frequency shifting (ffs) for structural excitation”, was introduced to develop a more compact structural vibration exciter than is presently available for low frequencies. An ffs shaker operates at a frequency much greater than the natural frequency of the structure under test but generates a modal force at the lower frequency of the structure. This effect is accomplished by moving a vibrating force back and forth across the structure while the force is applied normally to its surface. For example, the generalized force generated by an ffs shaker at the fundamental structural frequency for a simply supported beam is given by 1.65 P r/l where P is the high frequency out of balance force, r is the throw amplitude and l is the beam length. The term that reduces the efficiency of force transfer from high to low frequencies is “ r/ l” as, usually, the length of a structure is much greater than the throw of the force. This paper introduces another force frequency shifting approach that allows r/ l to be large. This is accomplished by placing force exciters along a structure–spatial array, spaced a distance Δ X apart, and each force exciter is activated for a short period of time to simulate a travelling force traversing the structure forwards and backwards. The “force throw r “can thus be made large. Results of simulations and experiments verify that force frequency shifting can be accomplished using travelling impulses and modal identification can be achieved.

A nonlinear numerical model for sloped‐bottom tuned liquid dampers

AbstractShaking‐table data for a tuned liquid damper with a sloped bottom of 30° with the horizontal are investigated using a non‐linear numerical model previously developed by Yu, Jin‐kyu, Nonlinear characteristics of tuned liquid dampers. Ph.D. Thesis, Department of Civil Engineering, University of Washington, Seattle, WA, 98195 (1997). Stiffness and damping parameters for this model are obtained and compared with those previously derived for box‐shaped tanks. The values for these parameters reflect the softening spring behaviour of the sloped‐bottom system in contrast to the hardening system evident for the box‐shaped TLD. Consequently, the sloped‐bottom tank should be tuned slightly higher than the fundamental structural frequency in order to obtain the most effective damping. Copyright © 2001 John Wiley & Sons, Ltd.

Structral–control optimization withH2- andH∞-norm bounds

An integrated approach to minimum weight structural design and robust control system design is presented. The controller is designed to tolerate both the structured real parameter uncertainty in the structural natural frequencies and the unstructured unmodelled dynamics due to model truncation. The control approach utilizes a mixed H2–H∞ LQG compensator with an H∞-norm bound on the disturbance to the output transfer matrix in the closed-loop system and an upper bound on the H2-norm signifying the maximum value of the quadratic control performance index for the uncertain system. In structural–control optimization problems, constraints are imposed on the fundamental structural frequency and on the dB gain separation between the open-loop and closed-loop singular values at prescribed frequencies. The method is demonstrated on a 48-state structural truth model of a three-dimensional tapered box truss with collocated actuators and sensors in which the control design model is eighth-order including the compensator dynamics. © 1997 John Wiley & Sons, Ltd.

Dither-motor design with concurrent sensing and actuating piezoelectric materials (Ring laser gyroscope)

The authors present an analytical model to predict the model parameters of a dither-motor structure in a ring laser gyroscope in which the piezoelectric sensor and actuator are employed as driving mechanisms to avoid the problem of so-called lock-in effects. It is shown that the natural frequency of a dither motor is strongly influenced by: (1) the inertia and stiffness of piezoelectric elements and bonding layers, (2) the location of piezoelectric elements, and (3) the interaction between structural vibration and piezoelectric actuation. Conventionally. piezoelectric elements are used for sensor and actuator independently. A technique for utilizing each of the piezoelectric elements concurrently for dither rate sensing and dither motion actuation is also developed. Experimental results show that the system performance and reliability can be significantly increased by accurately predicting the fundamental structural frequency and by implementing the concurrent sensing/actuating technique.