直交異方性有孔板の自由振動問題の一解析法

FREE VIBRATION OF ORTHOTROPIC SQUARE PLATES WITH A SQUARE HOLE

FREE-VIBRATION ANALYSIS OF RIGHT TRIANGULAR PLATES WITH VARIABLE THICKNESS

FREE VIBRATION ANALYSIS OF RECTANGULAR PLATES WITH VARIABLE THICKNESS

Coupled thermoelastic nonlocal forced vibration of an axially moving micro/nano-beam

Forced vibration analysis of isogrid-stiffened composite plates using VAM-based equivalent plate model

Orthotropic thin plates are essential in aerospace applications due to their high strength-to-weight ratio, which is critical for efficient structural performance. The mechanical properties of these structures are influenced by numerous factors, with free vibration characteristics being particularly significant. However, analytical solutions for free vibration are often limited to plates with simple boundary conditions (BCs). Few exact analytical solutions exist for plates with complex non-Lévy-type or rotationally restrained BCs. This study aims to analyze the free vibration behavior of orthotropic thin plates featuring three rotationally restrained edges and one free edge, employing the finite integral transform (FIT) method. A key advantage of this method is its simplicity and versatility, as it does not require the predefinition of a deflection function. By setting different values of the rotating fixed coefficient, the study offers analytical free vibration solutions for plates with various combinations of rotationally restrained, simply supported, clamped, and free BCs without additional derivations. The solutions derived using the FIT method are validated by comparison with numerical results obtained from ABAQUS software and available analytical solutions, confirming the method’s accuracy and reliability. Parameter analyses are conducted to examine the effects of aspect ratio, BCs, material properties, and rotating fixed coefficient on non-dimensional frequency parameters and corresponding vibration modes. The results reveal that these parameters significantly influence the frequency characteristics of orthotropic thin plates. The results can be used as a benchmark for validating other analytical and numerical methods.

This research paper focuses on analyzing the vibrational frequency characteristics of a square plate that is orthotropic and non-homogeneous. The plate has a circular variation in thickness in two dimensions and circular variation in density in one dimension at the clamped boundary. The temperature distribution across the plate is assumed to follow a two-dimensional parabolic pattern. The Rayleigh-Ritz technique is used to solve the governing equation and determine the vibrational modes. Convergence analysis is performed to ensure the accuracy and reliability of the obtained frequency modes for orthotropic square plates. The objective of this study is to provide numerical data that illustrate how the manipulation of plate parameters and design can control the vibrational frequencies, thereby enhancing the performance of orthotropic square plates for specific applications.

Breakout noise from HVAC ducts is important at low frequencies, and the coupling between the acoustic waves and the structural waves plays a critical role in the prediction of the transverse transmission loss. This paper describes the analytical calculation of breakout noise by incorporating three-dimensional effects along with the acoustical and structural wave coupling phenomena. The first step in the breakout noise prediction is to calculate the inside duct pressure field and the normal duct wall vibration by using the solution of the governing differential equations in terms of Green's function. The resultant equations are rearranged in terms of impedance and mobility, which results in a compact matrix formulation. The Green's function selected for the current problem is the cavity Green's function with modification of wave number in the longitudinal direction in order to incorporate the terminal impedance. The second step is to calculate the radiated sound power from the compliant duct walls by means of an ``equivalent unfolded plate'' model. The transverse transmission loss from the duct walls is calculated using the ratio of the incident power due to surface source inside the duct to the acoustic power radiated from the compliant duct walls. Analytical results are validated with the FE-BE numerical models.

Nonlinear deformation of axisymmetrically loaded polar orthotropic annular plates

In this paper, the free vibration of an annular membrane consisting of three con- centric segments is considered. The frequency equation and mode shapes are obtained by the use of the Green's function method. A numerical example to vibration problem of non- homogeneous annular membrane is presented. solution of the problem and vibration analysis of membranes with discontinuously varying thickness is presented. In reference (2) the finite element method in the analysis was also used. The free vibration problem of annular membrane with many discontinuous variation of the density is the subject of paper (3). Although the formulation of the problem deals with the vibration of membrane which consist of m segments (each of constant density), the numerical examples concern the antisymmetric modes of composite membrane consisting of two segments. In this case the frequency equation is obtained by setting the determinant of a 4x4 matrix of coefficients to a derived system of equation, which equals zero. In many papers various methods are applied to solution of the eigenvalue problems. The authors of paper (4) in solving the eigenproblem for annular membrane propose the method of fundamental solution. In this method the free space Green's function are ap- plied. In this paper the free vibration problem of a composite annular membrane con- sisting of three segments of constant densities is presented. The solution of the problem (frequency equation, mode shapes) is derived by using the properties of Green's functions corresponding to the Helmholtz operator in an annular domain. An example of numerical frequency analysis is given.

A VAM-based equivalent model for random vibration of composite sandwich plate with arrowhead-on cores

As an alternative to traditional wood framing in residential building construction, cold-formed steel (CFS) framing inherits many advantages of steel construction. However, if not appropriately designed, CFS floors with longer spans and lighter weight are likely to be susceptible to annoying vibrations induced by human activity such as walking. The fundamental frequency is a critical parameter for floor vibration serviceability. In current practice, the floor frequency is evaluated based on the simplification of a floor system to a simply-supported beam, which results in a considerable disparity in frequencies obtained from field tests and evaluation. In this research, based on current construction practice, the CFS floor system is modelled as an orthotropic plate with edges of joist-ends being partially restrained and edges that are parallel to floor joists being either freely or simply supported. The deflection of the partially restrained CFS floor joist is adopted as the admissible function of the plate in the derivation of equations to evaluate the fundamental frequency of the equivalent orthotropic plate. Simplified equations and equivalent rigidity properties are proposed for CFS floor systems.

Experimental tests for simultaneous explosive forming–welding for two inhomogeneous plates have been carried out. Sheets of copper, aluminium, and steel were used for simultaneous forming and welding. Also, analytical and numerical analyses were conducted. Given analytic model, is based on energy method, and considering support conditions, deformation, and critical amount of impacts. Two metal plates are converted to their equivalent homogeneous plate by a method similar to the analysis of combined beams. On the other hand, finite-element analysis has been done wherein the work plates have been modelled by Johnson–Cook material model. The maximum deformation of plates and the possibility of rupture have been predicted with respect to mechanical properties of the plates. Also, to measure the velocity of flyer plate, which is necessary to compute impact, an innovative method is presented. Then, the amounts of experimental deformation, stresses, and strains were compared with analytical and numerical results and rather good similarities have been observed.

To solve a problem on bending, vibration, and stability of plates, a hybrid finite element has been constructed on the basis of Zienkiewicz’s triangle. A mixed approximation is used for the plate deflection and turning angles. It is shown that with a decrease in the triangle dimensions the mixed approach ensures convergence both for the plate deflection and the bending moments, which is practically independent of the way the plate is split into triangular elements. In the problems on free vibrations and stability of plates, the mixed approach yields more exact values of the eigenfrequencies and critical loads as compared to a classical Zienkiewicz’s triangle. The results of the numerical analysis of the convergence and accuracy of the solutions to a number of test problems on bending, free vibration, and stability of a square plate are presented.

Lightweight lattice sandwich panels combine high stiffness-to-weight ratios with tailored vibration performance, making them ideal for aerospace structures. However, exact dynamic analysis of these structures remains computationally intensive and is frequently constrained by simplified boundary condition assumptions. This study proposes a novel solution framework that combines the asymptotic homogenization method (AHM) with the finite integral transform (FIT) method. The framework (1) uses the AHM to model a periodic lattice sandwich panel as an equivalent orthotropic thin plate, and (2) derives analytical natural frequency and mode shape solutions under non-Lévy-type boundary conditions via the FIT method. Comprehensive experimental and numerical validation demonstrates the accuracy and reliability of the AHM when applied to equivalent property prediction of lattice sandwich structures. All FIT-based analytical results achieve convergence to 5 significant digits within 15 terms, and demonstrate a maximum error of less than 1% when compared with the results from the finite element method-based equivalent model.