Vibration Behavior Of Structure Research Articles

Active vibration control of a large space telescope based on H∞ control with unilateral and constrained input

The development of the telescope with large aperture is driven by the increasing demand for higher imaging resolution and imaging area. The large membrane diffraction space telescope is particularly attractive due to their lightweight nature, ease of folding and unfolding, and high precision imaging capabilities. However, the flexible and large structure of these telescope makes them prone to long-time, low-frequency vibrations in space. These vibrations can degrade the imaging quality and potentially cause damage to the instrument in the space telescope. Therefore, it is crucial to develop effective active vibration control methods to suppress these structural vibrations. This paper proposes a control method that utilizes cables as actuators. Since cables can only withstand tension and have limited output tension, this constraint is taken into account during the control design process. Firstly, a dynamics model of the membrane diffraction space telescope with hinge flexibility is developed by the beam theory and finite element method. Next, an active controller is designed by combining H∞ control theory and Linear Matrix Inequalities (LMI). Additionally, the optimal positions of cable actuators are determined using the Gram controllability criterion and a particle swarm algorithm. Finally, the effectiveness of the control method is verified through numerical simulations. The simulation results demonstrate that the hinge flexibility significantly influences the structural vibration behavior of the telescope. Furthermore, the proposed control method demonstrates the ability to effectively suppress the vibrations of the telescope while also exhibiting robustness to changes in natural frequencies of the structure.

Nonlinear free vibrational behavior of temperature-dependent two-directional functionally graded truncated cone-like shells in thermal environment

This article investigates nonlinear free vibrations of temperature-dependent two-directional functionally graded (TDTDFG) cone-like shells in thermal environment. The structure material is a combination of ceramic and metal with temperature-dependent mechanical characteristics varying continuously in the thickness and longitudinal directions. Initially, the thermomechanical dynamic equations of the system are modeled based on the first-order shear deformation theory (FSDT) and the strain-displacement relations of von Kármán. Afterward, the final governing equation for the structure’s transverse motion is obtained using the Galerkin discretization method. Finally, the governing equation is solved using improved Lindstedt-Poincaré method as an analytical technique, resulting in an equation for calculating the nonlinear frequencies of the shell. To validate the research’s results, the system frequencies are calculated under different conditions and compared with the results of previous studies. After ensuring the accuracy of the results, a parametric study is performed to evaluate the effects of various parameters on the linear and nonlinear frequencies of the TDTDFG cone-like shell in thermal environment. The results of this study have demonstrated that gradient indices, geometric ratios, and thermal environment have a significant influence on the nonlinear vibration behavior of structures.

Linear vs nonlinear structural vibration behavior of steel-timber composite building elements

Composite structures including wood are increasingly coming into focus due to rising demand for sustainability and, at the same time, high-rise buildings, and long-span components. In this context, steel-timber hybrid building elements are gaining more attention since they offer sufficient load-carrying properties. However, such lightweight structures increase vibration levels and sound transmission. Accurate understanding of the structures is therefore indispensable. Consequently, herein, a novel steel-timber composite building element is studied concerning its vibrational behavior numerically and experimentally. Especially the influence of the joints between steel and timber components is investigated by considering nonlinear behavior due to frictional effects. Therefore, amplitude-dependency regarding eigenfrequencies and damping properties as well as multi-harmonic responses are studied. Hence, nonlinearities are revealed by slight amplitude-dependency and the occurrence of higher harmonics.

Free vibration characteristics of integrated fluted-core composite sandwich cylinders

Due to their excellent mechanical properties and inherent design versatility, fluted-core composite sandwich structures have gained substantial attention in aerospace and rail transit applications. This study investigated the free-vibration characteristics of composite fluted-core sandwich cylinders. Theoretical models were established following the Rayleigh-Ritz method to predict the natural frequencies of sandwich cylinders under free vibration. The representative cylindrical specimens were prepared using carbon fiber-reinforced plastics (CFRP) and integrated forming co-cured method. To analyze the additional effects of cutouts on vibration performance, specimens with circular cutouts were also fabricated. The vibration tests were performed to determine the natural frequencies and modal shapes under free-free boundary conditions. Validated finite element simulations were employed to assess the accuracy of theoretical results and investigate the influences of geometric parameters on the structural vibration behavior. The results indicated that circumferential lobar modes characterized the first five mode shapes. Significant enhancements were attained by increasing the structural stiffness through adjustments in the circumferential cell number, core-ribs thickness, or size of cutouts. However, when the structural stiffness increases beyond a certain threshold, it has limited effect on the vibration frequencies. The findings provided a comprehensive understanding of the vibration characteristics and optimized design of fluted-core sandwich cylinders.

Geometrically nonlinear free vibration of FG-GPLRC circular plate on the nonlinear elastic foundation

The current article deals with the nonlinear free vibration of nanocomposite circular plates reinforced with graphene platelets (GPL). The functionally graded (FG) plate is considered over a three parameter non-linear elastic foundation. In this research, three types of gradings are assumed for reinforcing the plate by GPLs. The Halpin-Tsai micromechanical rule is exploited to obtain the elastic modulus of the plate. The first order shear deformation plate theory associated with the nonlinear strain-displacement relations are applied to extract the governing motion equations. The generalized differential quadrature (GDQ) method is implemented to solve the equations of motion in the plate domain. Furthermore, an iterative displacement control technique associated with the weighted residual technique are used to linearize the present problem and obtain the linear and nonlinear frequencies. After examining the validation study, some parametric studies are tabulated and plotted to recognize the effects of the boundary condition, distribution types of GPL, GPL weight fraction, geometrical parameters, and elastic foundation parameters on the linear and non-linear free vibration behaviour of structure. It is shown that maximum frequencies of the plate belong to the FG-X case and the minimum ones are obtained in FG-O type.

Structural response recovery based on improved multi-scale principal component analysis considering sensor performance degradation

This article proposes an improved multi-scale principal component analysis approach to recover the structural dynamic response in the time domain from data measured by performance-deteriorated sensors. The proposed approach builds on discrete wavelet transform, principal component analysis, and inverse discrete wavelet transform. The main approach is based on a cross-correlation calculation to better preserve the true structural vibration behavior as well as to recover the structural response from data measured by deteriorated sensors. Three sensor performance degradation models are considered in this study. Numerical studies are conducted first to demonstrate the effectiveness and accuracy of the proposed approach to recover the structural vibration response of an example spatial truss model considering sensor performance degradation under different loading scenarios. Experimental data on an in-field benchmark bridge are also analyzed to further validate and demonstrate the performance of the proposed approach.

Analytical and experimental investigation of partially covered piezoelectric cantilever energy harvester

Electrical energy is normally generated through different sources such as hydroelectric, wind, heat, nuclear transformation, chemical reactions or vibrations. Nowadays, harvesting power from mechanical vibration is one of the novel technologies that usually can be done by systems based on electromagnetic, electrostatic, piezoelectric and combination of them. Piezoelectric systems can convert motion from the vibrating structures into electrical power. Cellulose Electro-active paper (EAPap) has been recognized as a novel smart piezoelectric material that can be used for energy harvesting purposes. One of the most prevalent method for vibration energy harvesting is using unimorph piezoelectric cantilever beams. In this paper, an analytical solution based on distributed parameter model is presented to calculate the generated energy from vibration of cantilever substrate that is partially covered by EAPap material. In the studied structure, piezoelectric layer thickness in comparison to the length of the beam and thickness of substrate material can be considered very thin. Thus its effect on the vibration behavior of structure is negligible. The results are validated by experimental values. The analytical data was found to be very close to experimental results and finite element simulation values. Findings from this study provide guidelines on system parameters that can be manipulated for more efficient performance in different ambient source conditions.

Dynamic Properties Evaluation of a Platform Structure

Regardless to the service lifetime of a structure, unwanted vibration can occur due to unknown sources. Excessive vibration may lead to uncomfortable feeling of the occupant, or deterioration of sensitive instruments in an industrial building. To determine the nature of the mentioned vibration problems, an evaluation of dynamic properties of the structure is required. Recently, researchers and engineers have spent a lot of effort to control the vibration behavior of structures. Several methods have been developed in the field of system identification. Alternative methods to estimate the structural modal parameters are SSI and ARMA. This paper discusses the evaluation of dynamic properties of existing platform structures. Unwanted vibration appears when the material is pumped into the pipe which tends to cause fatigue unwillingly. Dynamic evaluation is performed to obtain the natural frequency of structures by using the SSI and ARMA model. The response measurement is taken while the structure is under operational condition. In this contribution, the mentioned models give satisfactory result compared to FEM model.

Two Dimensional Functionally Graded Material Finite Thick Hollow Cylinder Axisymmetric Vibration Mode Shapes Analysis Based on Exact Elasticity Theory

Abstract A thick hollow cylinder with finite length made of two- dimensional functionally graded material (2D-FGM) is considered and its natural modes are determined, based on great importance of mode shapes information in order to understand vibration behaviour of structures. Three dimensional theory of elasticity implemented for problem formulation, since mode shapes of a thick cylinder are three dimensional even with axisymmetric conditions. The axisymmetric conditions are assumed for the 2D-FGM cylinder. The material properties of the cylinder are varied in the radial and axial directions, with power law functions. Effects of volume fraction distribution on the different types of symmetric mode shapes configuration and vibration behaviour of a simply supported cylinder are analyzed. Three dimensional equations of motion are used and the eigen value problem is developed, based on direct variation method.

A note on mathematical treatment of the Dirac-delta function in the differential quadrature bending and forced vibration analysis of beams and rectangular plates subjected to concentrated loads

There are many physical and mechanical phenomena that can be well described by means of the Dirac-delta function. For instance, the bending and vibration behavior of structures under concentrated loads, impulsive loading, moving loads, and impact loading; and thermoelastic vibration behavior of structures under heat source points can be mathematically modeled by means of the Dirac-delta function. It is well known that such phenomena or problems can be easily handled by weak form based methods such as the Ritz and finite element methods. However, the strong form based methods such as the finite difference and differential quadrature methods may encounter some difficulties in mathematical modeling and treatment of the Dirac-delta function. This is mainly caused by the fact that the properties of the Dirac-delta function are in the form of integrals and not in the form of derivatives. To overcome this difficulty, this paper presents a combined differential quadrature–integral quadrature method in which such type of problems can be easily and accurately modeled. Its accuracy and reliability are demonstrated through the static and dynamic analysis of beams and rectangular plates under concentrated loads. This paper also presents a simple differential quadrature formulation for the analysis of rectangular plates. The proposed formulation first reduces the original plate problem to two simple beam problems. Each beam problem in then discretized using the differential quadrature method (DQM) in a simple manner. Compared with the conventional DQM, the proposed DQM is superior since its implementation and programming are easier and simpler.

Transfer function modeling of structural vibration of complex aerospace structures based on finite element analysis

An approach to establish the transfer function of complex aerospace structures to express their structural vibration behavior through finite element modeling is proposed. The fundamental idea of the approach is to characterize the vibrations of complicated structures through the transfer function model for an advanced control system design, while the parameters of the model are identified from the response data obtained through finite element analysis. The proposed method comprises four steps, namely, finite element modeling and validation, data preparation based on the finite element analysis, parameter identification of the transfer function, and model validation, and is presented from both frequency and time domains. The developed approach is applied to a cantilever beam, a strap-on launch vehicle, and a local part of the aerospace structure to demonstrate the method’s effectiveness and satisfactory performance.

A Spectral-Tchebychev Solution for Three-Dimensional Vibrations of Parallelepipeds Under Mixed Boundary Conditions

Vibration behavior of structures with parallelepiped shape—including beams, plates, and solids—are critical for a broad range of practical applications. In this paper we describe a new approach, referred to here as the three-dimensional spectral-Tchebychev (3D-ST) technique, for solution of three-dimensional vibrations of parallelepipeds with different boundary conditions. An integral form of the boundary-value problem is derived using the extended Hamilton’s principle. The unknown displacements are then expressed using a triple expansion of scaled Tchebychev polynomials, and analytical integration and differentiation operators are replaced by matrix operators. The boundary conditions are incorporated into the solution through basis recombination, allowing the use of the same set of Tchebychev functions as the basis functions for problems with different boundary conditions. As a result, the discretized equations of motion are obtained in terms of mass and stiffness matrices. To analyze the numerical convergence and precision of the 3D-ST solution, a number of case studies on beams, plates, and solids with different boundary conditions have been conducted. Overall, the calculated natural frequencies were shown to converge exponentially with the number of polynomials used in the Tchebychev expansion. Furthermore, the natural frequencies and mode shapes were in excellent agreement with those from a finite-element solution. It is concluded that the 3D-ST technique can be used for accurate and numerically efficient solution of three-dimensional parallelepiped vibrations under mixed boundary conditions.

Structural Acoustic Reduction via Piezoelectric Actuation and Adaptive Eigenvector Optimization Algorithm

The purpose of this research is to investigate the feasibility of utilizing the adaptive eigenvector optimization algorithm to find the optimal combination of left and right eigenvectors for active structural acoustic reduction. As depicted in the previous studies, the structural acoustic radiation depends on the structural vibration behavior, which is strongly related to the mode shape distributions (represented by the right eigenvectors of system) as well as the ability of disturbance rejection (represented by the left eigenvectors of system). In this research, a novel adaptive optimization algorithm is developed to determine the optimal combination of left and right eigenvectors of the structural system for active structural acoustic control. The sound suppression performance index (SSPI) is defined by combining the orthogonality index of left eigenvectors and the modal radiation index of right eigenvectors. Through the proposed adaptive eigenvector optimization algorithm, both the left and right eigenvectors of the structural system are adjusted such that the SSPI quantity decreases, hence the optimal combination of the corresponding left and right eigenvectors of the closed-loop system can be found for reducing the structural acoustic radiation. The optimal combination of left-right eigenvectors is then synthesized to determine the feedback gain matrix of the closed-loop system. The result of the active acoustic control shows that the proposed method can significantly suppress the sound pressure radiated from the vibrating structure.

An adaptive left–right eigenvector evolution algorithm for vibration isolationcontrol

The purpose of this research is to investigate the feasibility of utilizing an adaptive left andright eigenvector evolution (ALREE) algorithm for active vibration isolation. As depictedin the previous paper presented by Wu and Wang (2008 Smart Mater. Struct. 17015048), the structural vibration behavior depends on both the disturbance rejectioncapability and mode shape distributions, which correspond to the left and righteigenvector distributions of the system, respectively. In this paper, a novel adaptiveevolution algorithm is developed for finding the optimal combination of left–righteigenvectors of the vibration isolator, which is an improvement over the simultaneousleft–right eigenvector assignment (SLREA) method proposed by Wu and Wang(2008 Smart Mater. Struct. 17 015048). The isolation performance index used inthe proposed algorithm is defined by combining the orthogonality index of lefteigenvectors and the modal energy ratio index of right eigenvectors. Through theproposed ALREE algorithm, both the left and right eigenvectors evolve such that theisolation performance index decreases, and therefore one can find the optimalcombination of left–right eigenvectors of the closed-loop system for vibration isolationpurposes. The optimal combination of left–right eigenvectors is then synthesizedto determine the feedback gain matrix of the closed-loop system. The result ofthe active isolation control shows that the proposed method can be utilized toimprove the vibration isolation performance compared with the previous approaches.

Vibration Analysis for Detecting Internal Corrosion

The vibration behavior of structures can be characterized in terms of resonance frequencies and mode shapes, which describe properties of the tested object in a global way but do not, in general, provide information about structural details. Following an asymptotic formalism, in much the same spirit as the work in [3] and recent text [1], we develop an efficient method to address the inverse problem of identifying an internal corrosive part of small Hausdorff measure in a two‐dimensional structure by vibration analysis. The viability of our reconstruction method is documented by a variety of numerical results from synthetic, noiseless and noisy data.

The Effect of Prestress on Vibration Behavior of Structures in Impedance Method Damage Detection

Structural health monitoring or damage detection has long been a research interest for its great potential for life safety and economic benefits to the industrialized world. Structural vibration behavior is an essential signature of the integrity of structures and hence has been used for damage detection. Structural vibration impedance by way of piezoceramic patch excitation offers a local damage detection technique. It has been known that temperature change has adverse effects on the measured impedance result and can complicate the damage analysis. It is believed that one way of temperature influence on vibration is through adding thermal prestress to the structure. Prestress affects vibration in different ways on different structures and application problems. For the impedance method, prestress comes not only from temperature change but also from other sources such as wind, gravity and working load. This paper deals with prestress effects in the context of local vibration behavior of structures. A theoretical analysis is given on how prestress affects the vibration. Experimental impedance measurement results for piezoceramic patch excited vibration of simple structures such as plates under prestress are presented.

A variable mass model for describing load impulses due to periodic jumping

This paper reviews the current philosophy for describing the effects of jumping humans on the vibration behaviour of structures. Focusing on the Semi-sinusoidal pulse force model, which is included in the BS 6399-96 code of practice for the description of jumping human loads, it was found that this model is unable to predict the correct shape of the load impulse or its dominant harmonic for jumping frequencies that are significantly less than 2 Hz. This paper presents a new general model, which incorporates impulse shape factors and is based on the treatment of the structure–jumper system as a pseudo-variable mass system. By considering recent findings in the technical literature, it is shown that the proposed model can be used to describe load impulses for all attainable jumping frequencies, by choosing appropriate impulse shape factors. In the experimental verification, the acceleration response of a structure with a fundamental frequency of 7.1 was found to be dominated by the second harmonic of the jumping frequency (ignoring the resonant frequencies) when a human subject jumped at 1 Hz, confirming that the load impulse is dominated by the second harmonic for this jumping frequency, as reported in the literature. The simulation of the jumping load impulse using the proposed model also predicted the same pattern in the acceleration response, verifying that the model is accurate.

Some Aeroelastic and Nonlinear Vibration Problems Encountered on the Journey to Ithaca

The present paper describes three basic aeroelastic and nonlinear vibration problems investigated by the author and his students: namely, 1) stall flutter and nonlinear divergence of a two-dimensional flat-plate wing, 2) nonlinear vibrations of a clamped and a buckled beam, and 3) dynamic stability of a pendulum under parametric excitation. All of these problems seemed simple and were easily modeled experimentally and analytically. Yet they revealed some fundamental and interesting characteristics of nonlinear aeroelastic and vibration behavior of structures. Some experimental data are presented here that still remain to be resolved.

Sensitivity analysis and modification of structural dynamic characteristics using second order approximation

This paper presents a formulation in the form of an inverse eigen value problem for modification of vibration behavior of structures. The proposed method which is based on the second order approximation in Taylor expansion is expressed in terms of variables relating to stiffness or mass matrix parameters in a finite element formulation. An initial sensitivity analysis identifies the regions within the structure where the modifications would yield the required changes in the structures dynamic characteristics. An algorithm is developed which allows efficient modification of structural dynamics characteristics without iterations. These modifications are conducted locally so that only elemental stiffness and matrices are affected. The algorithm is applied to four case studies and it is found that large modification of natural frequencies of up to 10% can be realized with an induced error of less than 5% for truss structures, and less than 3% for plane problems.

Damage identification based on ridges and maxima lines of the wavelet transform

The paper analyses the transient vibration behaviour of structures using the continuous wavelet transform (CWT), which provides effective tools for detecting changes in the structure of the material. The advantage of the CWT over commonly used time-frequency methods like the Wigner–Ville and the Gabor transform is its ability to decompose signals simultaneously both in time (or space) and frequency (or scale) with adaptive windows. The essential information is contained in the maxima of the wavelet transform. From the ridges, the modal parameters of the decoupled modes can be extracted and the signal can be reconstructed. From the maxima lines, defects can be localized. This paper presents a new approach for the calculation of wavelet transform ridges and maxima lines, which is based on a direct integration of differential equations. The potential of the method is demonstrated by the analysis of the impact vibration response of different bars.