Free vibration analysis of rectangular plates with arbitrary elastic boundary conditions

boundary conditions are In this paper, an improved Fourier series method is presented for the free vibration analysis of rectangular plates with arbitrary elastic conditions. The stiffness value of the restraining springs is determined as required to simulate the arbitrary elastic boundary conditions. The exact solution of plates with arbitrary elastic boundary conditions is solved by the introduced supplementary func-tions. The matrix eigenvalue equation of plates is derived by using boundary conditions and the governing equations. Compared with exist methods, the presented method can be easily applied to most of plate vibration problems with different boundary conditions. To validate the accuracy of the presented method, numerical simulations with different boundary conditions are presented.presented.

A Unified Analysis for the Free Vibration of the Sandwich Piezoelectric Laminated Beam with General Boundary Conditions under the Thermal Environment

This article mainly analyzes the free vibration characteristic of the sandwich piezoelectric beam under elastic boundary conditions and thermal environment. According to the first-order shear deformation theory and Hamilton’s principle, the thermo-electro-elastic coupling equations of the sandwich piezoelectric beam are obtained. Meanwhile, elastic boundary conditions composed of an array of springs are introduced, and the displacement variables and external potential energy of the beam are expressed as wave functions. By using the method of reverberation-ray matrix to integrate and solve the governing equations, a search algorithm based on golden-section search is introduced to calculate the required frequency parameters. A series of numerical results are compared with those reported in literature studies and obtained by simulation software to verify the correctness and versatility of the search algorithm. In addition, three parametric research cases are proposed to investigate the frequency parameters of sandwich piezoelectric beams with elastic restraint conditions, material parameters, thickness ratio, different temperature rises, and external electric potential.

Normal Mode Analysis for Connected Plate Structure Using Efficient Mode Polynomials with Component Mode Synthesis

In the engine room and stern adjacent to the main excitation force of the ship, there are many fuel and fresh water tank structures required for ship operation which are always exposed to vibrations. Therefore, it is necessary to review the anti-vibration design to prevent such vibration problems at the design stage, and for this reason, although commercial finite element analysis (FEA) programs are widely used, approximate analysis methods are still developed and used because of the limited time until modeling and analysis results are obtained. Until now, only known elastic boundary conditions have been used in many studies using approximate analysis methods used to calculate natural vibrations for beams or plates. However, many local structures, such as tank edges and equipment foundations, consist of connected structures and it is very difficult to find suitable elastic boundary conditions. Vibration analysis of many local structures in ships, such as tanks and supports for equipment, can be simplified by breaking them up into smaller subsystems which are related through geometrical conditions and natural conditions at junctions. In this study, polynomials for simple support and fixed support were proposed to represent each subsystem and a polynomial to be applied to the plate constituting the tank was proposed by combining them. Until now, there have been many studies on single beams or single plates for approximate analysis. However, there was no research on this to the extent that no reference material could be found for the connected structure. The proposed method has been applied to tanks which are bounded by bulkhead and a deck. The results of this study shows good agreements with those obtained by the FEA Software (Patran/Nastran).