This study proposes an analytical model for vibrations in a cracked rectangular plate as one of the results from a program of research on vibration based damage detection in aircraft panel structures. This particular work considers an isotropic plate, typically made of aluminum, and containing a crack in the form of a continuous line with its center located at the center of the plate and parallel to one edge of the plate. The plate is subjected to a point load on its surface for three different possible boundary conditions, and one examined in detail. Galerkin’s method is applied to reformulate the governing equation of the cracked plate into time dependent modal coordinates. Nonlinearity is introduced by appropriate formulations introduced by applying Berger’s method. An approximate solution technique—the method of multiple scales—is applied to solve the nonlinear equation of the cracked plate. The results are presented in terms of natural frequency versus crack length and plate thickness, and the nonlinear amplitude response of the plate is calculated for one set of boundary conditions and three different load locations, over a practical range of external excitation frequencies.

Piezoelectric materials are widely used as smart structures in cubic reconnaissance satellites because of their sensing, actuating, and energy-harvesting abilities. In this study, an analytical model is developed in specific mechanical thermal shocking conditions. A special circuit and apparatus is designed for experimentation on the basis of the inverse piezoelectric effect. An equivalent circuit method is used to establish the relationship between the resistance and peak-to-peak voltage of lead zirconate titanate used as smart materials for cubic reconnaissance satellites. Various frequencies and resistance were applied in different mechanical thermal shocking conditions. Moreover, numerical simulations are conducted in various mechanical loading conditions to determine the accumulative effect. The model provides a novel mechanism to characterize the smart structures in cubic reconnaissance satellites. A rise in temperature increases peak-to-peak voltage; a rise in frequency decreases peak-to-peak voltage; and intensified resistance decreases peak-to-peak voltage. Based on experimentation and simulation, the optimum resistance is predicted for the various frequencies and temperatures. The various conditions may correspond to the different applications of smart structures for cubic reconnaissance satellites. The analytical calculations are in good agreement with experimental and numerical calculations.

This paper presents design, modeling, and analysis of satellite model used for remote sensing. A detailed study is carried out for the design and modeling of the satellite structure focusing on the factors such as the selection of material, optimization of shape and geometry, and accommodation of different subsystems and payload. The center of mass is required to be kept within the range of (1-2) cm from its geometric center. Once the model is finalized it is required to be analyzed by the use ofAnsys, a tool for finite element analysis (FEA) under given loading and boundary conditions. Static, modal, and harmonic analyses inAnsysare performed at the time of ground testing and launching phase. The finite element analysis results are also validated and compared with the theoretical predictions. These analyses are quite helpful and suggest that the satellite structure does not fail and retains its structural integrity during launch environment.

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Recent NATO funded research on methods for detection and interpretation methodologies for damage detection in aircraft panel structures has motivated work on low-order nonlinear analytical modelling of vibrations in cracked isotropic plates, typically in the form of aluminium aircraft panels. The work applies fundamental aspects of fracture mechanics to define an elliptical crack, and the local stress field and loading conditions, arbitrarily located at some point in the plate, and then derives an analytical expression for this that can be incorporated into the PDE for an edge loaded plate with various possible boundary conditions. The plate PDE is converted into a nonlinear Duffing-type ODE in the time domain by means of a Galerkin procedure and then an arbitrarily small perturbation parameter is introduced into the equation in order to apply an appropriate solution method, in this case the method of multiple scales. This is used to solve the equation for the vibration in the cracked plate for the chosen boundary conditions, which, in turn, leads to an approximate analytical solution. The solution is discussed in terms of the perturbation approximations that have been applied and highlights the phenomenology inherent within the problem via the specific structures of the analytical solution.