Analytical Modeling on Vibration Analysis of Cracked Functionally Graded Plate Submerged in Fluid

Background: It is established that the vibration response of submerged structures is quite different than that calculated in vacuum. Therefore, the study of vibration characteristics of submerged plate structures is important for safety and its designing purpose. Objective: To investigate the fundamental frequency of partially cracked Functionally Graded (FG) submerged plate based on analytical approach. Methods: The governing differential equation of the cracked-submerged plate is derived based on Kirchhoff’s thin classical plate theory in conjunction with the potential flow theory. The line spring model is used to incorporate the effect of crack in the form of additional bending whereas the effect of fluid medium is incorporated in form fluids forces associated with inertial effects of its surrounding fluids. The Bernoulli’s equation and velocity potential function are used to define the fluid forces acting on plate surface. Results: An approximate solution for governing equation of coupled fluid-plate system is obtained by using the Galerkin’s method. For validation of the present results, they are compared with the existing results of the previous published work, which are in good agreements. New results for natural frequencies as affected by gradient index, crack length, level of submergence and immersed depth of plate are presented for Simply Supported (SSSS) boundary condition. Conclusion: It has been concluded that the presence of crack and fluidic medium significantly affect the natural frequencies of the plate. It is observed that the increase in the length of crack and level of submergence decreases the fundamental frequency. In this paper, few patents have been discussed.

Crack identification based on the nonlinear response of plates with variably oriented surface crack.

In order to secure structural and operational safety of structures, it is important to implement a structural health monitoring (SHM) strategy to issue early warnings on damage or deterioration prior to costly repair or even catastrophic collapse. Developing a SHM strategy for structures enables evaluating structural integrity, durability and reliability of the monitored structure. Hence, the main objective of this work is to develop a damage detection procedure based on a plate’s dynamic response and the Hilbert transform. Rectangular plates are considered and assumed to contain a surface crack which is centrally located, with a depth of h0, a length of 2C and inclined with an angle β. Von Karman plate theory is adopted herein, and the crack is modeled through the line spring model given by fracture mechanics. The plate is assumed to behave nonlinearly due to large deformation. The differential quadrature method is used to investigate the linear and nonlinear dynamic behaviors of cracked plates. The influence of crack’s parameters on modal properties is discussed. The eigenfrequencies of cracked plates with respect to crack half length C and orientation β are performed. For crack characterization, Hilbert transform is applied to the obtained linear and nonlinear time responses. It is shown throughout this paper that identified backbones describe changes in crack orientation.

Nonlinear Large Deflection of Thin Film Overhung on Compliant Substrate Using Shaft-Loaded Blister Test

This paper presents the nonlinear large deflection of the thin film and the effect of substrate deformation on the thin film deflection through the shaft-loaded blister test. The blister of thin film can be divided into two parts, namely, the annular contact brim and the central noncontact bulge. A two-coupled line spring model is developed to describe the deformation of the contact part, and Föppl–Hencky equations are employed to study the constitutive relation between the applied load and the central deflection. The analytical and numerical solutions for the constitutive relation between the applied load and the deflection of thin film with considering the deformation of substrate are derived.

The Research about the Vibroacoustic Characteristics of the Surface Cracked Plate

Vibration characteristics of surface cracked plate are studied from the view of structural intensity .Line-spring model of the surface crack is put forward based on fracture mechanics. The relationship of the additional angle and displacement with the crack parameters is derived. The concept of additional structural intensity is presented and the additional structural intensity’s expression of shell finite element is deduced. The change regulars between structural intensity and vibration parameters with crack’s parameters are concluded by using ANSYS and MATLAB software, the simulation results are matched with the trend of theoretical formula.

Crack Identification in Vibrating Beams Using Haar Wavelets and Neural Networks

This study investigates the depth and location of cracks in homogeneous Euler-Bernoulli beams with free vibrations. The problem is frequently encountered in industrial design and modeling, where an exact model requires the frequency output to be calibrated with a physical measure. The crack is simulated by a line spring model. The boundary value problem is solved using the Haar wavelets. The characteristic parameters are predicted with the aid of neural networks. The proposed method is compared to an alternative approach based on neural networks and several frequencies only. The significance of the complex approach of Haar wavelets and neural networks lies in its ability to make fast accurate model-independent predictions calculating only one natural frequency and training the network only once.

Analysis of the Non-Linear Dynamic Responses of an Elastic Rotor With a Slant Crack

Considering a rotor system with a slant crack, and using an equivalent line-spring model to simulate the slant crack of the rotor, the flexibility model of the slant-cracked rotor is derived. Then considered the geometric non-linearity and based on the Lagrange equations, the non-linear dimensionless differential equations of motion for the slant-cracked rotor are obtained. Further the non-linear dynamic responses of the single rotor system with a slant crack are discussed by the Galerkin method and the harmonic balance method. It’s detailedly studied that the angle, the depth and the position of the slant crack on the rotor all affect on the non-linear dynamic responses of the rotor system, and the conclusion is very significant to the design of the rotor system in the practical reference aspect.