Relevant bibliographies by topics / Free vibration of plate

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Free vibration of plate'

Author: Grafiati
Published: 4 June 2025
Last updated: 23 June 2025

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Journal articles on the topic "Free vibration of plate"

1

Morozov, N. A., G. I. Grebenyuk, V. I. Maksak, and A. F. Gavrilov. "Free vibrations of rectangular plates." Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture 25, no. 3 (2023): 96–111. http://dx.doi.org/10.31675/1607-1859-2023-25-3-96-111.

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The paper investigates free vibrations of rectangular metal plates. The finite element method and analytical calculation are particularly used to determine the vibration frequency. The analytical calculation is based on the equation of motion of a thin rectangular plate. The asymptotic method is applied to determine the dynamic edge effect. As a result, the free vibration frequency is determined for the rectangular metal plate. The finite element analysis is performed in Lira and SolidWorks software packages. For this, a solid plate model with sensors is created to measure the free vibration frequency; the effective mass participation factor was determined.The plate vibration tests were conducted to confirm the results of analytical calculations. The method of smooth sinusoidal vibrations is used. Spectrum graphs of the plate vibrations are suggested based on the vibration acceleration of sensors. Errors are identified in the free vibration frequencies depending on the applied method. The paper does not consider frequencies with the low effective mass participation factor.
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2

Afshari, Payman, and G. E. O. Widera. "Free Vibration Analysis of Composite Plates." Journal of Pressure Vessel Technology 122, no. 3 (2000): 390–98. http://dx.doi.org/10.1115/1.556198.

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A series of plate elements, based on the modified complementary energy principal, are developed to study the free undamped vibration response of laminated composite plates. The Mindlin thin plate theory is selected to govern the general characteristics and behavior of these plate elements. A series of in-plane strain functions are assumed from which the corresponding in-plane strains and corresponding stresses for each lamina are determined. The transverse stresses are then computed by satisfying the equations of the equilibrium. Eight-noded isoparametric elements are utilized to describe the displacement field. These hybrid plate elements are used to form the stiffness and the consistent mass matrices. The fundamental natural frequencies are then computed by solving the generalized eigenvalue problem and their application demonstrated via a number of examples. [S0094-9930(00)02603-7]
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Khetib, Mounia, Hichem Abbad, Nourredine Elmeiche, and Ismail Mechab. "Effect of the Viscoelastic Foundations on the Free Vibration of Functionally Graded Plates." International Journal of Structural Stability and Dynamics 19, no. 11 (2019): 1950136. http://dx.doi.org/10.1142/s0219455419501360.

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This paper presents a two-variable refined plate theory for free vibration of functionally graded material (FGM) plates lying on viscoelastic Winkler–Pasternak foundations. The present work aims to examine the vibrations by a higher-order shear deformation theory including a new function of warping. The governing equations are derived from the principle of virtual displacements. Some illustrative examples are given in an attempt to solve the free vibration problem of a rectangular plate with various boundary conditions. The effects of damping on free vibrations, considering various parameters, are examined in detail. In the end, it is concluded that the present results with the new shear shape function of viscoelastic foundation are found to be in good agreement with other available results and the proposed method can easily be used to solve free vibration problems of the FGM plates.
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Haciyev, Vaqif C., Gulnar R. Mirzoeva, and Matlab G. Agayarov. "Free vibrations of anisotropic rectangular plate laying on a heterogeneous viscouselastic basis." Structural Mechanics of Engineering Constructions and Buildings 15, no. 6 (2019): 470–76. http://dx.doi.org/10.22363/1815-5235-2019-15-6-470-476.

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The aim of the work. Free, transverse vibrations are considered heterogeneous along the three spatial coordinates of rectangular plates lying on an inhomogeneous viscoelastic base. It is assumed that the boundary conditions are homogeneous. A closed solution for the problem of free vibration of an inhomogeneous rectangular orthotropic plate based on an inhomogeneous viscoelastic foundation is developed in the article. Young's moduli and the density of the orthotropic plate continuously change with respect to three spatial coordinates, while the characteristics of a viscoelastic base change depending on the coordinates in the plane. Methods. The corresponding equation of motion is obtained using the classical theory of plates. The solution to the problem was constructed using the method of separation of variables and the Bubnov - Galerkin method. Results. Explicit formulas of the fundamental tone of the frequency of the transverse vibration of an anisotropic plate lying on an inhomogeneous viscoelastic base are determined. The influence of heterogeneity of orthotropic materials, viscosity inhomogeneities, inelastic and elastic substrates at dimensionless plate frequencies have been studied in detail.
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Le, Vinh An, and Xuan Tung Nguyen. "The Effect of Cracks on the Free Vibration of a Plate with Parabolic Thickness." Engineering, Technology & Applied Science Research 13, no. 4 (2023): 11100–11105. http://dx.doi.org/10.48084/etasr.5923.

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This paper uses first-order shear deformation theory and the finite element method to analyze the vibrations of rectangular plates with one or more cracks. The study investigated the influence of cracks (length, angle of inclination), the number of cracks, and the ratio of plate thickness to the natural vibration frequency of the plate, using phase field simulation. Plate thickness varies nonlinearly with the parabolic function. The results of the proposed method were compared with reputable studies to verify its reliability. In addition, some pictures of the characteristic vibration patterns of the plate with varying thickness are presented when cracks appear.
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Johansson, Prof Clara, and Prof Ingrid Dahlberg. "A COMPARATIVE ANALYSIS OF FREE VIBRATION IN STIFFENED VERSUS UNSTIFFENED PLATES." International Journal of Research in Engineering 3, no. 4 (2023): 7–11. https://doi.org/10.55640/ijre-03-04-02.

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This study presents a comprehensive investigation into the free vibration characteristics of stiffened plate structures, which are commonly used in aerospace, marine, and civil engineering applications. By employing analytical and finite element methods, the influence of various stiffener configurations, boundary conditions, and material properties on the natural frequencies and mode shapes of the plate structures was evaluated. The results demonstrate that both the orientation and geometry of stiffeners significantly affect the dynamic behavior, offering potential for tailored vibration performance in engineering design. The findings also highlight the accuracy of numerical simulations in capturing complex vibrational responses when validated against analytical models.
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7

Altekin, Murat. "Free In-Plane Vibration of Super-Elliptical Plates." Shock and Vibration 18, no. 3 (2011): 471–84. http://dx.doi.org/10.1155/2011/613521.

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Free in-plane vibration of super-elliptical plates of uniform thickness was investigated by the Ritz method. A large variety of plate shapes ranging from an ellipse to a rectangle were examined. Two cases were considered: (1) a completely free, and (2) a point-supported plate. The geometrical boundary conditions were satisfied by the Lagrange multipliers. The results were compared with those of rectangular plates. Basically good agreement was obtained. Matching results were reported, and the discrepancies were highlighted.
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8

Shiau, Le-Chung, and Teng-Yuan Wu. "Free Vibration of Buckled Laminated Plates by Finite Element Method." Journal of Vibration and Acoustics 119, no. 4 (1997): 635–40. http://dx.doi.org/10.1115/1.2889774.

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Free vibration behavior of buckled composite plates are studied by using a high precision triangular plate element. This element is developed based on a simplified high order plate theory and von Ka´rma´n large deformation assumptions. The nonlinear governing equations of motion for the plates is linearized into two sets of equations by assuming small amplitude vibration of the laminates about its buckled static equilibrium profile. Results show that, in the postbuckling regime, the fundamental mode may be shifted from the first mode to the second due to squeezing effect of the in-plane force on the plate. For plate with certain boundary conditions, the natural frequency may have a sudden jump due to buckle pattern change of the plate in the postbuckling regime.
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9

Slawinska-Budzich, Justyna, Wojciech Sulisz, and Jaroslaw Przewlocki. "Modeling of free vibrations and resonant frequencies of simply-supported submerged horizontal plate." PLOS ONE 19, no. 3 (2024): e0298290. http://dx.doi.org/10.1371/journal.pone.0298290.

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A theoretical approach was applied to study the vibration of simple-supported submerged horizontal plate. The derived analytical solution was used to determine natural frequencies for a horizontal plate vibrating in fluid. The investigations were conducted for a very wide range of material density and elasticity modulus covering all materials used in engineering practice. Analysis shows that plate vibration frequency decreases with increasing plate width and draft, and decreases with decreasing plate thickness. Moreover, the results show that a substantial effect on vibration of submerged plate has mass of water above plate. The results also show that plate vibration frequency decreases with increasing plate material density and decreases with decreasing elasticity modulus. The dominant factors affecting the vibration of the submerged plate are the plate width, the plate thickness, and elasticity modulus. For moderate and low values of elasticity modulus, vibration frequency is becoming lower than frequency of water waves. This is very important because wave frequencies overlap with the natural plate vibration frequencies, which may lead to resonance and failure of a structure. The problem is that the overlap of plate vibration frequencies and wave frequencies occurs for very wide range of wave and plate parameters. Laboratory experiments confirm theoretical results.
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Verenkar, Saeesh, I. Sridhar, and P. S. Shivakumar Gouda. "Numerical Investigations on Free Vibration Analysis of Delaminated Composite Plate." Indian Journal Of Science And Technology 16, no. 42 (2023): 3714–20. http://dx.doi.org/10.17485/ijst/v16i42.1866.

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Dissertations / Theses on the topic "Free vibration of plate"

1

Chattopadhyay, Arka Prabha. "Free and Forced Vibration of Linearly Elastic and St. Venant-Kirchhoff Plates using the Third Order Shear and Normal Deformable Theory." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/102661.

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Employing the Finite Element Method (FEM), we numerically study three problems involving free and forced vibrations of linearly and nonlinearly elastic plates with a third order shear and normal deformable theory (TSNDT) and the three dimensional (3D) elasticity theory. We used the commercial software ABAQUS for analyzing 3D deformations, and an in-house developed and verified software for solving the plate theory equations. In the first problem, we consider trapezoidal load-time pulses with linearly increasing and affinely decreasing loads of total durations equal to integer multiples of the time period of the first bending mode of vibration of a plate. For arbitrary spatial distributions of loads applied to monolithic and laminated orthotropic plates, we show that plates' vibrations become miniscule after the load is removed. We call this phenomenon as vibration attenuation. It is independent of the dwell time during which the load is a constant. We hypothesize that plates exhibit this phenomenon because nearly all of plate's strain energy is due to deformations corresponding to the fundamental bending mode of vibration. Thus taking the 1st bending mode shape of the plate vibration as the basis function, we reduce the problem to that of solving a single second-order ordinary differential equation. We show that this reduced-order model gives excellent results for monolithic and composite plates subjected to different loads. Rectangular plates studied in the 2nd problem have points on either one or two normals to their midsurface constrained from translating in all three directions. We find that deformations corresponding to several modes of vibration are annulled in a region of the plate divided by a plane through the constraining points; this phenomenon is termed mode localization. New results include: (i) the localization of both in-plane and out-of-plane modes of vibration, (ii) increase in the mode localization intensity with an increase in the length/width ratio of a rectangular plate, (iii) change in the mode localization characteristics with the fiber orientation angle in unidirectional fiber- reinforced laminae, (iv) mode localization due to points on two normals constrained, and (iv) the exchange of energy during forced harmonic vibrations between two regions separated by the line of nearly stationary points that results in a beating-like phenomenon in a sub-region of the plate. This technique can help design a structure with vibrations limited to its small sub-region, and harvesting energy of vibrations of the sub-region. In the third problem, we study finite transient deformations of rectangular plates using the TSNDT. The mathematical model includes all geometric and material nonlinearities. We compare the results of linear and nonlinear TSNDT FEM with the corresponding 3D FEM results from ABAQUS and note that the TSNDT is capable of predicting reasonably accurate results of displacements and in-plane stresses. However, the errors in computing transverse stresses are larger and the use of a two point stress recovery scheme improves their accuracy. We delineate the effects of nonlinearities by comparing results from the linear and the nonlinear theories. We observe that the linear theory over-predicts the deformations of a plate as compared to those obtained with the inclusion of geometric and material nonlinearities. We hypothesize that this is an effect of stiffening of the material due to the nonlinearity, analogous to the strain hardening phenomenon in plasticity. Based on this observation, we propose that the consideration of nonlinearities is essential in modeling plates undergoing large deformations as linear model over-predicts the deformation resulting in conservative design criteria. We also notice that unlike linear elastic plate bending, the neutral surface of a nonlinearly elastic bending plate, defined as the plane unstretched after the deformation, does not coincide with the mid-surface of the plate. Due to this effect, use of nonlinear models may be of useful in design of sandwich structures where a soft core near the mid-surface will be subjected to large in-plane stresses.<br>Doctor of Philosophy
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Asdal, Bent. "Static and free vibration analysis of advanced composites using shear-deformable rectangular plate finite elements." Thesis, Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/80092.

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A comparison of rectangular finite elements based on a first order shear deformation plate theory and a refined higher order plate theory is presented. Special attention is given to the representation of transverse shear strain, the phenomenon of "shear locking", and the selection of the interpolating polynomial. Both C⁰ and C¹ continuity elements are represented; the elements range from: 3 or 5 DOF per node, and 12 - 27 DOF per element. Static and free vibration analysis of isotropic and laminated plates with thicknesses ranging from extremely thin to very thick are presented, along with a convergence study. The finite element results are compared with the exact plate theory solutions. Of the elements investigated, the modified refined higher order theory element exhibits the best overall behavior.<br>Master of Science
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Saliba, H. T. "Free vibration analysis of non-rectangular quadrilateral plates." Thesis, University of Ottawa (Canada), 1986. http://hdl.handle.net/10393/5264.

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Alizadeh, Y. "Free vibration of partially supported plates and shells." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/10751.

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First-order transverse shear-deformation Mindlin theory has been used to predict the free vibration frequencies and modal shapes for isotropic, laminated and composite plates or shells. A finite element model based on the small deflection linear theory has been developed to obtain numerical solutions for this class of problems. The results for some of the degenerate cases are compared with other results available in the literature. These analyses involve a wide number of variables, namely; material properties, aspect ratios, support conditions and also radius to base ratio. The cracked base plates, shells and blades are idealized as partially supported models with varying support lengths. The effects of the detached base length on natural frequencies, modal shapes and nodal lines of these types of structures are investigated. Although the expected decrease in frequency with increase in the detached base length is observed almost for all modes it is seen that this behavior is very pronounced for higher modes in both plates and shells. Analysis also showed that the variation of the detached base length has a small effect on the natural frequencies of plates and shells with large aspect ratios ( b/a > 2, r/a > 2).
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Mochida, Yusuke. "Bounded Eigenvalues of Fully Clamped and Completely Free Rectangular Plates." The University of Waikato, 2007. http://hdl.handle.net/10289/2508.

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Exact solution to the vibration of rectangular plates is available only for plates with two opposite edges subject to simply supported conditions. Otherwise, they are analysed by using approximate methods. There are several approximate methods to conduct a vibration analysis, such as the Rayleigh-Ritz method, the Finite Element Method, the Finite Difference Method, and the Superposition Method. The Rayleigh-Ritz method and the finite element method give upper bound results for the natural frequencies of plates. However, there is a disadvantage in using this method in that the error due to discretisation cannot be calculated easily. Therefore, it would be good to find a suitable method that gives lower bound results for the natural frequencies to complement the results from the Rayleigh-Ritz method. The superposition method is also a convenient and efficient method but it gives lower bound solution only in some cases. Whether it gives upper bound or lower bound results for the natural frequencies depends on the boundary conditions. It is also known that the finite difference method always gives lower bound results. This thesis presents bounded eigenvalues, which are dimensionless form of natural frequencies, calculated using the superposition method and the finite difference method. All computations were done using the MATLAB software package. The convergence tests show that the superposition method gives a lower bound for the eigenvalues of fully clamped plates, and an upper bound for the completely free plates. It is also shown that the finite difference method gives a lower bound for the eigenvalues of completely free plates. Finally, the upper bounds and lower bounds for the eigenvalues of fully clamped and completely free plates are given.
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Kaul, Vibhu. "Free vibration analysis of continuous orthotropic plates and bridge decks." Thesis, University of Ottawa (Canada), 1986. http://hdl.handle.net/10393/4821.

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Ohman, Hans J. L. "Free vibration analysis of rectangular plates with internal point supports." Thesis, University of Ottawa (Canada), 1991. http://hdl.handle.net/10393/7492.

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Interest in the free vibration frequencies and associated mode shapes of rectangular plates resting on internal point supports has arisen in connection with the design of electronic circuit boards, solar panels and other industrial problems. An analytical solution is presented for the free vibration analysis of rectangular plates with multiple internal point supports. The solution is also shown to be easily modified to account for the effects of attached masses. The basic solution for each case consists of the Levy type solution for a plate with one discrete point support. N similar solutions for N discrete point supports are then superimposed to create an eigenvalue matrix from which the plate's natural frequencies and associated mode shapes can be determined. Due to the nature of the Levy type solution, only plates with two opposite edges simply supported are considered. The remaining edges are either simply supported, clamped or free. There are therefore six possible combinations of plate boundary conditions. The objective of this thesis is to give a concise and clear description of the mathematical procedure employed and to present the results of some representative frequency and mode shape studies.
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8

Fulford, Sarah Xochitl. "Analytical analysis of the free vibration of partially clamped cantilever plates." Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/6536.

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The method of superposition is used to analyze the free vibration of thin rectangular plates, partially clamped along one edge and free everywhere else. This study has been undertaken because of interest in the dynamic behaviour of electronic circuit boards which are sometimes given support of this nature. This problem is not known to have been studied before using an analytical type method. Eight building blocks are superimposed to obtain the final solution. Each building block is solved individually using the Levy-type solution. A detailed mathematical development of the solution is shown for each building block in dimensionless form. The natural frequencies and mode shapes for plates with varying aspect ratios and clamped lengths can be found using this method. Eigenvalues are shown to converge and tabulated values are given to at least three digit accuracy. Frequencies and mode shapes agree very well with experimentally found results and with results found using a commercially used finite element method software package.
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Nguyen, Khang V. "Free vibration analysis of rectangular orthotropic cantilever plates with point supports." Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/10365.

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The free vibration analysis of rectangular plates has been of interest to many scholars and practitioners over the years due to their wide range of applications. However, most of the studies involve the typical case of isotropy. A study has been done in the analysis of free vibration of orthotropic cantilever plates with internal point supports. The analysis makes use of the Superposition Method which, by superimposing appropriate building blocks, can provide "exact" analytical solution to this problem of orthotropy. In each case of symmetric and antisymmetric vibration modes under study, three different plate problems whose Levy-type solutions can be obtained, are superimposed. The constants in each solution, created during their boundary condition formulations, are adjusted in such a way so their combination would provide boundary conditions the same to those required for the cantilever plate. Upon superimposing, an eigenvalue matrix is created which allows the eigenvalues to be determined. Accuracy of the resultant eigenvalues is verified by recognising that the governing differential equation is satisfied exactly and that the required plate boundary conditions are satisfied to certain desired degree of exactitude. The objective of this thesis is to describe the necessary modifications to adapt the superposition method to orthotropic plate problems, and to show the mathematical procedures employed in the analysis. In addition, the results of some representative frequency and mode shape studies will be presented which include a wide range of plate geometries and various levels of orthotropy.
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Javanshir, Hasbestan Jaber. "Free Flexural (or Bending) Vibration Analysis Of Certain Of Stiffened Composite Plates Or Panels In Flight Vehicle Structures." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12611489/index.pdf.

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In this study, the &ldquo<br>Free Flexural (or Bending) Vibrations of Stiffened Plates or Panels&rdquo<br>are investigated in detail. Two different Groups of &ldquo<br>Stiffened Plates&rdquo<br>will be considered. In the first group, the &ldquo<br>Type 4&rdquo<br>and the &ldquo<br>Type 6&rdquo<br>of &ldquo<br>Group I&rdquo<br>of the &ldquo<br>Integrally-Stiffened and/or Stepped-Thickness Plate or Panel Systems&rdquo<br>are theoretically analyzed and numerically solved by making use of the &ldquo<br>Mindlin Plate Theory&rdquo<br>. Here, the natural frequencies and the corresponding mode shapes, up to the sixth mode, are obtained for each &ldquo<br>Dynamic System&rdquo<br>. Some important parametric studies are also presented for each case. In the second group, the &ldquo<br>Class 2&rdquo<br>and the &ldquo<br>Class 3&rdquo<br>of the &ldquo<br>Bonded and Stiffened Plate or Panel Systems&rdquo<br>are also analyzed and solved in terms of the natural frequencies with their corresponding mode shapes. In this case, the &ldquo<br>Plate Assembly&rdquo<br>is constructed by bonding &ldquo<br>Stiffening Plate Strips&rdquo<br>to a &ldquo<br>Base Plate or Panel&rdquo<br>by dissimilar relatively thin adhesive layers. This is done with the purpose of reinforcing the &ldquo<br>Base Plate or Panel&rdquo<br>by these &ldquo<br>Stiffening Strips&rdquo<br>in the appropriate locations, so that the &ldquo<br>Base Plate or Panel&rdquo<br>will exhibit satisfactory dynamic response. The forementioned &ldquo<br>Bonded and Stiffened Systems&rdquo<br>may also be used to repair a damaged (or rather cracked) &ldquo<br>Base Plate or Panel&rdquo<br>. Here in the analysis, the &ldquo<br>Base Plate or Panel&rdquo<br>, the &ldquo<br>Stiffening Plate Strips&rdquo<br>as well as the in- between &ldquo<br>adhesive layers&rdquo<br>are assumed to be linearly elastic continua. They are assumed to be dissimilar &ldquo<br>Orthotropic Mindlin Plates&rdquo<br>. Therefore, the effects of shear deformations and rotary moments of inertia are considered in the theoretical formulation. In each case of the &ldquo<br>Group I&rdquo<br>and &ldquo<br>Group II&rdquo<br>problems, the &ldquo<br>Governing System of Dynamic Equations&rdquo<br>for every problem is reduced to the &ldquo<br>First Order Ordinary Differential Equations&rdquo<br>. In other words the &ldquo<br>Free Vibrations Problem&rdquo<br>, in both cases, is an &ldquo<br>Initial and Boundary Value Problem&rdquo<br>is reduced to a &ldquo<br>Two- Point or Multi-Point Boundary Value Problem&rdquo<br>by using the present &ldquo<br>Solution Technique&rdquo<br>. For this purpose, these &ldquo<br>Governing Equations&rdquo<br>are expressed in &ldquo<br>compact forms&rdquo<br>or &ldquo<br>state vector&rdquo<br>forms. These equations are numerically integrated by the so-called &ldquo<br>Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)&rdquo<br>. In the numerical results, the mode shapes together with their corresponding non-dimensional natural frequencies are presented up to the sixth mode and for various sets of &ldquo<br>Boundary Conditions&rdquo<br>for each structural &ldquo<br>System&rdquo<br>. The effects of several important parameters on the natural frequencies of the aforementioned &ldquo<br>Systems&rdquo<br>are also investigated and are graphically presented for each &ldquo<br>Stiffened and Stiffened and Bonded Plate or Panel System&rdquo<br>. Additionally, in the case of the &ldquo<br>Bonded and Stiffened System&rdquo<br>, the significant effects of the &ldquo<br>adhesive material properties&rdquo<br>(i.e. the &ldquo<br>Hard&rdquo<br>adhesive and the &ldquo<br>Soft&rdquo<br>adhesive cases) on the dynamic response of the &ldquo<br>plate assembly&rdquo<br>are also presented.
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Books on the topic "Free vibration of plate"

1

Wu, K. Chauncey. Free vibration of hexagonal panels simply supported at discrete points. National Aeronautics and Space Administration, Langley Research Center, 1991.

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Ayowole, Oyediran Abraham, and George C. Marshall Space Flight Center., eds. Free vibration of rectangular plates with a small initial curvature: Final report. Marshall Space Flight Center, 1988.

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A, Kolkailah Faysal, Elghandour Eltahry I, and United States. National Aeronautics and Space Administration., eds. Modal analysis of embedded passive damping materials in composite plates with different orientations: Final report for NASA-Dryden Flight Research Center, joint research interchange, May 1, 1997-July 24, 1998. National Aeronautics and Space Administration, 1998.

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A, Kolkailah Faysal, Elghandour Eltahry I, and United States. National Aeronautics and Space Administration., eds. Modal analysis of embedded passive damping materials in composite plates with different orientations: Final report for NASA-Dryden Flight Research Center, joint research interchange, May 1, 1997-July 24, 1998. National Aeronautics and Space Administration, 1998.

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Abbassian, F. Free vibration benchmarks. NAFEMS, 1987.

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Hagedorn, Peter. Vibrations and Impedances of Rectangular Plates with Free Boundaries. Springer Berlin Heidelberg, 1986.

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Hagedorn, Peter, Klaus Kelkel, and Jörg Wallaschek. Vibrations and Impedances of Rectangular Plates with Free Boundaries. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-82906-2.

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Klaus, Kelkel, and Wallaschek J. 1960-, eds. Vibrations and impedances of rectangular plates with free boundaries. Springer-Verlag, 1986.

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Lucio, Maestrello, Bayliss Alvin, and Langley Research Center, eds. Coupling between plate vibration and acoustic radiation. National Aeronautics and Space Administration, Langley Research Center, 1992.

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P, Townsend Dennis, Coy John J, United States. Army Aviation Systems Command., and United States. National Aeronautics and Space Administration., eds. Minimization of the vibration energy of thin-plate structure. National Aeronautics and Space Administration, 1992.

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Book chapters on the topic "Free vibration of plate"

1

Grigorenko, Alexander Ya, Maksym Yu Borysenko, Olena V. Boychuk, and Natalia P. Boreiko. "Free Vibration Corrugated Open Cylindrical Shells." In Recent Approaches in the Theory of Plates and Plate-Like Structures. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87185-7_6.

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Rout, Mrutyunjay, and Amit Karmakar. "Free Vibration of Rotating Twisted Composite Stiffened Plate." In Lecture Notes on Multidisciplinary Industrial Engineering. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-96968-8_17.

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Sadangi, Rajendra Kumar, Mihir Kumar Sutar, and Sarojrani Pattnaik. "Parametric Study of Composite Plate Using Free Vibration Analysis." In Lecture Notes in Mechanical Engineering. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-4488-0_76.

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Mohanty, Abhijit, Sarada Prasad Parida, and Rati Ranjan Dash. "Numerical Study of Free Vibration of Sandwich FGM Plate." In Sustainable Materials, Structures and IoT. CRC Press, 2024. http://dx.doi.org/10.1201/9781003596776-31.

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Grigorenko, Alexander, Maksym Borysenko, Olena Boychuk, and Nataliia Boreiko. "Numerical Analysis of Free Vibration Frequencies of Hexagonal Plate." In Selected Problems of Solid Mechanics and Solving Methods. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-54063-9_15.

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Maji, A., P. K. Mahato, S. K. Sharma, G. Shankar, and D. Sarkar. "Free Vibration Analysis of Laminated Composite Plates Based on Refined Plate Theory." In Lecture Notes in Mechanical Engineering. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-3173-2_44.

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Chiboub, Khaoula, Majdi Yangui, Slim Bouaziz, Mounir Ben Amar, and Mohamed Haddar. "Free Vibration Analysis of Laminated Plates." In Lecture Notes in Mechanical Engineering. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57324-8_37.

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Kumar Bhardwaj, Harsh, and Vipin Kumar Sharma. "FEM-based design and free vibration analysis of composite plate." In Additive Manufacturing in Industry 4.0. CRC Press, 2022. http://dx.doi.org/10.1201/9781003360001-5.

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Zhou, Chen, Yingdan Zhu, Xiaosu Yi, and Jian Yang. "Free Vibration Analysis of Laminated Composite Plate with a Cut-Out." In Mechanisms and Machine Science. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-15758-5_96.

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Basu Dutta, D., and S. Das. "Free Vibration of Sandwich Cantilever-Folded Plate with a Homogeneous Core." In Lecture Notes in Mechanical Engineering. Springer Nature Singapore, 2024. https://doi.org/10.1007/978-981-97-6667-3_51.

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Conference papers on the topic "Free vibration of plate"

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MCFARLAND, D., and LAWRENCE BERGMAN. "Free vibration of constrained plates and plate-oscillator systems." In 30th Structures, Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics, 1989. http://dx.doi.org/10.2514/6.1989-1248.

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CHEN, HSIN-PIAO, and PATRICK GOGGIN. "Free vibration of a compressed delaminated plate." In 33rd Structures, Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics, 1992. http://dx.doi.org/10.2514/6.1992-2388.

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Abrate, Serge. "Vibration of Functionally Graded Plates." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95778.

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This article considers the free vibration of plates for which materials properties vary continuously though the thickness. First, an examination of results available in the literature led to the discovery that the natural frequencies of such functionally graded plates are proportional to those of isotropic plates. In the usual formulation of existing plate theories, the midplane is taken as the reference surface and the variation in material properties through the thickness leads to coupling between inplane and bending deformations. The second part of this paper shows that it is possible to select a different reference plane so that this coupling is eliminated and the motion of the graded plate is governed by the same equation as that of homogeneous isotropic plates. This explains the relationship between the natural frequencies that was observed in the results presented by previous investigators. The study of functionally graded plate is made much simpler and results available for isotropic plates can be used directly.
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Luo, Albert C. J., and Hamid R. Hamidzadeh. "The Nonlinear Vibration and Stability of Axially Traveling Thin Plates." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48439.

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Frequency and responses for the free vibration of traveling, nonlinear, elastic plates are obtained that are based on a nonlinear plate theory developed by Luo in 2000. The plate theory includes the in-plane inertial forces, the centrifugal forces, curvature effects and the in-plane Coriolis inertia. The critical speeds are obtained while the frequency of the prebuckled plate vanishes, and the critical speed for the mode (1,1) response is not always minimal.
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Shiau, L. C., and S. T. Hwang. "Free Vibration of Rectangular Composite Laminates With Delamination." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43036.

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In this paper, the effect of delamination on natural frequencies and natural modes of a simply supported rectangular symmetric composite plate with through-width delamination was investigated by the finite strip method. The delamination was assumed to be located at mid-plane of the laminate so that the contact/impact phenomenon between delaminated interfaces does not exist for the free vibration of the laminate. A finite strip with bending and in-plane stiffnesses was derived for the free vibration analysis. The effects of delamination length, delamination location, fiber angle, stacking sequence, and aspect ratio of the laminate on the natural frequencies of the laminate were studied and presented. Results show that the above mentioned factors have considerable effect on the natural frequencies of the laminate. The aspect ratio of the plate is also having significant effect on the frequency of the laminates, especially on the mode 2 frequency of the cross-ply laminate.
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Lee, Jinkyo, and Lawrence A. Bergman. "Free and Forced Vibration of Stepped Levy Plates." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0239.

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Abstract The study of the transverse vibration of thin rectangular plates has been mainly confined to plates of uniform thickness. There are few publications available on the vibration of plates with nonuniform thickness. These plates have application in various fields such as civil engineering and aerospace structures and are often found in high frequency acoustic transducers. Furthermore, it is sometimes possible to achieve minimum weight design of plates by having suitable variations in thickness. For the special case of a plate with two opposite edges simply supported and thickness discontinuities perpendicular to the simply supported edges, an analytical solution is possible using a dynamic flexibility method. Several examples are discussed.
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Wang, Gang, and Norman Wereley. "Free in-plane vibration of rectangular plates." In 19th AIAA Applied Aerodynamics Conference. American Institute of Aeronautics and Astronautics, 2001. http://dx.doi.org/10.2514/6.2001-1476.

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Budiman and Imam Jauhari Maknun. "Free vibration analysis of FGM plate using MITC3 element." In 2ND INTERNATIONAL CONFERENCE ON ADVANCED INFORMATION SCIENTIFIC DEVELOPMENT (ICAISD) 2021: Innovating Scientific Learning for Deep Communication. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0136459.

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de Almeida, Sérgio Frascino Müller, and Jorn S. Hansen. "Free Vibration Analysis of Composite Plates With Tailored Thermal Residual-Stresses." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0721.

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Abstract Thermal residual-stresses introduced during manufacture and their effect on the free vibration of stringer stiffened composite plates is investigated. The principal idea in the work is to include stiffeners on the perimeter of a composite plate in which the laminate for the stiffeners and the plate are different. Such an arrangement yields manufacturing induced thermal residual-stresses which result from the difference in manufacturing and operating temperatures as well as the difference in thermal expansion coefficients and elastic properties of the plate and the stiffeners. The analysis is based on an enhanced Reissner-Mindlin plate theory and involves two separate calculations. In the first, the thermal residual-stress state is determined for an unconstrained plate. In the second, the free vibration problem is solved; thermal effects from the first calculation are included by way of nonlinear membrane-bending coupling which in turn defines the free vibration reference state. The problem is solved using a finite element formulation to determine the natural frequencies and vibration modes of the plates. Two different plate-stiffener geometries are used to illustrate the effects of stringer size, stringer placement and temperature difference. Two principal results are obtained: first, it is shown that thermal residual-stresses can have a significant effect on the natural frequencies; secondly, thermal residual-stresses can be tailored to increase natural frequencies.
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Yao, Xiaohu, Qiang Han, and Liming Dai. "Free Vibration of Elliptical Plates in Uniform Temperature Field." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85775.

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The free vibration of clamped elliptical plate, when temperature and stress fields are coupled, is analyzed based on the fundamental equations of nonlinear thermo-elastic vibrations. A system of nonlinear differential equations of time is obtained with utilization of Galerkin’s method. The vibration states are compared with respect to different coefficients. The effects of thermo-elastic coupling on the amplitude and frequency are also presented.
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Reports on the topic "Free vibration of plate"

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Cook, R. D., and D. E. Thompson. Flat Plate Vibration Analysis Experimental and Numerical Fillet Study. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada218789.

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Tang, Yu, and Y. W. Chang. Free vibration analysis of a tank containing two liquids. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10162462.

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Tang, Yu, and Y. W. Chang. Free vibration analysis of partially filled liquid storage tanks. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10178843.

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Nukala, P. K. Implementation of rotary inertia effect on the free vibration response of beams. Office of Scientific and Technical Information (OSTI), 1999. http://dx.doi.org/10.2172/11000.

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Gharib, Mory, Sid Valluri, and Anatol Roshko. The Interaction of Shear Flows Generated by a Surface-Piercing Splitter Plate w/Free Surface. Defense Technical Information Center, 1997. http://dx.doi.org/10.21236/ada335279.

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Smalley, A. J., and P. J. Pantermuehl. TR-97-2 Foundation Guidelines. Pipeline Research Council International, Inc. (PRCI), 1997. http://dx.doi.org/10.55274/r0011730.

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These guidelines provide guidance to engineers responsible for installing or repamng the foundations of reciprocating compressors. If followed, the guidance should help assure an installation with a long life of trouble-free service. They address, in particular, mechanical integrity of the compressor/foundation installation, with emphasis on design of mounts, anchor bolts, and foundation block to carry the required dynamic loads. They defer to existing texts on vibration engineering for foundation blocks on their soil.
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Stevens, R. D., B. V. Chapnik, and B. Howe. L51960 Acoustical Pipe Lagging Systems Design and Performance. Pipeline Research Council International, Inc. (PRCI), 1998. http://dx.doi.org/10.55274/r0010392.

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Noise levels radiated from the exterior of a pipe wall can significantly contribute to the overall noise levels on the site of a gas plant and at neighboring properties. The noise inside the piping is generated both by the gas compressor itself, and by the flow of gas through valves, elbows and fittings. Sound inside the pipe couples to the pipe wall by exciting vibration modes, some of which are radiated from the exterior of the pipe into the air. Piping is geometrically circular, which provides it with considerable increased stiffness versus a flat plate, and thereby assists in its ability to contain low frequency sound inside the pipe. At high frequencies, where the wavelength of sound is short compared to the dimensions of the pipe, the response of the pipe approaches that of a flat plate, and considerably more sound is transmitted. Between the low and high frequency ranges lies the ring frequency, at which the wavelength of sound is equal to the circumference of the pipe; at this resonant frequency, a maximum amount of noise is transmitted out the pipe wall. For smaller pipe sizes, the ring frequency occurs above 5 kHz. For larger pipe sizes on the order of 24 inches to 36 inches, the ring frequency occurs in the range 1 kHz to 3 kHz. These frequencies fall in the most audible range of the sound spectrum. Low frequency sound is not usually of concern for pipe radiated noise, unless the source generates considerably low frequency energy. Acoustical lagging systems typically include one or more layers of porous insulation, to absorb sound and decouple vibration, and one or more layers of an impervious, heavy barrier material to contain the sound. The test configurations for this study were based on systems reported as commonly being used by PRCI member companies. Most of the member companies use fixed-in-place lagging configurations in which the various materials are applied in discrete layers to the pipe during installation. Self-contained, removable blanket systems are also in use by some member companies instead of fixed-in-place configurations, or around equipment such as valves where periodic removal of the lagging is necessary. This study provides a review of acoustic lagging systems for above ground gas piping to minimize noise.
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van de Sand, Ron, and Jörg Reiff-Stephan. FrostByte Dataset. Technische Hochschule Wildau, 2021. http://dx.doi.org/10.15771/1894.

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It is with great pleasure that we announce the release of the “Frost Byte” dataset. The dataset was collected during research on fault detection and diagnosis (FDD) approaches and their transferability to heterogeneous systems of industrial refrigeration systems at the Technical University of Applied Sciences Wildau. The data collection took place between 2018 and 2019 and is intended to supplement the ASHRAE 1043-RP dataset (Comstock &amp; Braun, 1999), which has been the only publicly available data source in this area to date. For comparison purposes, the method of data collection was chosen similarly, whereby this dataset collection was carried out using a ~ 100 kW refrigeration capacity ammonia system with plate heat exchangers. The dataset contains steady-data equally sampled from five classes: 1. Normal (fault-free operating condition) 2. Reduced Condenser Water Flow 3. Reduced Evaporator Water Flow 4. Non-Condensable Gases 5. Refrigeration Leak Each class was investigated under changing operational conditions and varying fault severity levels (SL).
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THE BENDING BEHAVIOR AND FREE VIBRATION OF THE CONCRETE-STEEL COMPOSITE FLOORS. The Hong Kong Institute of Steel Construction, 2023. http://dx.doi.org/10.18057/ijasc.2023.19.3.3.

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The paper aims to investigate the bending behavior and free vibration of the concrete-steel composite floors, including high temperatures. The inspected properties are analyzed for the maximum displacement, load capacity, energy absorption capacity, and acceleration by using bending tests for varying stud density and elevated temperatures. Withal, bolts are used as studs throughout this study. The result of bending tests implies that, decreasing the spacing of the studs and the addition of mesh reinforcement and steel fiber will increase the energy absorption and maximum load capacity of the steel composite floors. Besides, the increasing the stud density reduces the vibration response of the composite floors, and the mesh reinforcement eliminates the efficiency of the steel fiber on the vibration response of the steel composite floors. Meanwhile, increasing the steel-fiber content causes the reduction in the vibration response of the slabs exposed to high temperatures.
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POWER FLOW ANALYSIS OF BRIDGE U-RIB STIFFENED PLATES BASED ON THE CONCEPT OF STRUCTURAL INTENSITY. The Hong Kong Institute of Steel Construction, 2022. http://dx.doi.org/10.18057/icass2020.p.061.

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Due to its advantages of good mechanical properties, simple appearance and strong adaptability, the steel box girder is being widely utilized in urban bridges. The noise radiated by steel box girders subjected to vehicle impacts has the characteristics of wide-spectrum, high-magnitude and control difficulty. U-rib stiffened roof, as a part of the steel box girder, directly bears the input load, which is the basis of studying the vibration of the steel box girder. Currently, the investigation on the vibro-acoustic performance of U-rib plates is very limited. With this regard, this paper introduces the concept of Structural Intensity (SI). The SI vector is calculated by the Finite Element (FE) method. The power flow is visualized by the self-programming post-processing code. The global and local vibration energy transmission characters of a U-rib stiffened plate under a harmonic nodal force are analyzed. Further, the influence of plate thickness is investigated. The optimum design is carried out based on the engineering standard dimensions. The research results indicate that increasing the thickness ratio of the U-rib to the baseplate is beneficial to reducing the vibration.
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