A Note on Free Vibration of a Double-beam System with Nonlinear Elastic Inner Layer

In this note, small amplitude free vibration of a double-beam system in presence of inner layer nonlinearity is investigated. The nonlinearity is due to inner layer material and is not related to large amplitude vibration. At first, frequencies of a double-beam system with linear inner layer are studied and categorized as synchronous and asynchronous frequencies. It is revealed that the inner layer does not affect higher modes significantly and mainly affects the first frequency. Then, equation of motion in the presence of cubic nonlinearity in the inner layer is derived and transformed to the form of Duffing equation. Using an analytical solution, the effect of nonlinearity on the frequency for simply-supported and clamped boundary conditions is analyzed. Results show that the nonlinearity effect is not significant and, in small amplitude free vibration analysis of a double-beam system, the material nonlinearity of the inner layer could be neglected

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In the present study, large amplitude free vibration of beams resting on variable elastic foundation is investigated. The Euler–Bernoulli hypothesis and the Winkler model have been applied for beam and elastic foundation, respectively. The beam is axially loaded and is restrained by immovable boundary conditions, which yields stretching during vibrations. The energy method and Hamilton’s principle are used to derive equation of motion, where after decomposition an ordinary differential equation with cubic nonlinear term is obtained. The second order homotopy perturbation method is applied to solve nonlinear equation of motion. An explicit amplitude-frequency relation is achieved from solution with relative error less than 0.07% for all amplitudes. This solution is applied to study effects of variable elastic foundation, amplitude of vibration and axial load on nonlinear frequency of beams with simply supported and fully clamped boundary conditions. Proposed formulation is capable to dealing with any arbitrary distribution of elastic foundation

Large amplitude free vibration of axially loaded beams resting on variable elastic foundation

In the present study, large amplitude free vibration of beams resting on variable elastic foundation is investigated. The Euler–Bernoulli hypothesis and the Winkler model have been applied for beam and elastic foundation, respectively. The beam is axially loaded and is restrained by immovable boundary conditions, which yields stretching during vibrations. The energy method and Hamilton’s principle are used to derive equation of motion, where after decomposition an ordinary differential equation with cubic nonlinear term is obtained. The second order homotopy perturbation method is applied to solve nonlinear equation of motion. An explicit amplitude-frequency relation is achieved from solution with relative error less than 0.07% for all amplitudes. This solution is applied to study effects of variable elastic foundation, amplitude of vibration and axial load on nonlinear frequency of beams with simply supported and fully clamped boundary conditions. Proposed formulation is capable to dealing with any arbitrary distribution of elastic foundation

Developing general acoustic model for noise sources and parameters estimation

Noise measured at various points around the environment can be evaluated by a series of acoustic sources. Acoustic sources with wide surface can be broken down in fluid environment using some smaller acoustic sources. The aim of this study is to make a model to indicate the type, number, direction, position and strength of these sources in a way that the main sound and the sound of equivalent sources match together in an acceptable way. When position and direction of the source is given, the strength of the source can be found using inverse method. On the other hand, considering the non-uniqueness of solution in inverse method, a different acoustic strength is obtained for the sources if different positions are selected. Selecting an arrangement of general source and using the optimization algorithm, the least possible mismatch between the main sound and the sound of equivalent sources can be achieved

Position parameters optimization of surface piercing propeller by artificial neural network

Abstract Improving the performance of surface-piercing propellers is achieved by investigating the influential factors. In this study, Artificial Neural Network is used to identify nonlinear models for estimating various phenomena. Non-Dominated Sorting Genetic Algorithm II is considered as an optimization tool. In this study, in order to optimize the position parameters, including the immersion ratio, angle of attack, and yaw angle, data from experimental tests at the HYDROTECH center of IUST were collected as the initial data field for the generation of training data by the artificial neural network, then experimental tests were implemented in the position of the Non-Dominated Sorting Genetic Algorithm II proposed as the output, and the results were compared. The Artificial Neural Network results showed that the mean error of the trained verified and test data is 7.5e−5, 1e−4, and 1e−4, respectively. Comparing the experimental and optimization results, the thrust coefficient showed a relative error of 9.7%, while the torque coefficient showed a relative error of 7.5%, this algorithm can be used as a cost-effective, time-saving method for a similar problem

Numerical and experimental study of bursting prediction in tube hydroforming of Al 7020-T6

In this study, forming limit diagram (FLD) of tubular material (Al 7020-T6) was determined numerically and experimentally. A set of experimental bulge tests were carried out to determine FLD under combined internal pressure and axial feeding. Also, a numerical approach which is based on the acceleration of plastic strain (i.e., the second derivation) was applied to compute the hydroforming strain limit diagram. Based on this method, the localized necking would be started when the acceleration of the max plastic strain got its maximum value. Finally, the numerical FLD was verified by experimental test results on the aluminum tube 7020-T6 and a good agreement between the proposed method and the experimental works was observed