a b s t r a c tIn this paper, He's Frequency-Amplitude Formulation (HFAF) and He's Energy Balance Method (HEBM) are employed to solve the generalized Duffing equation in the form ofFor any arbitrary power of n, a frequency analysis is carried out and the relationship between the natural frequency and the initial amplitude is obtained in analytical form. Accuracy and validity of the proposed techniques are then verified by comparing the numerical results obtained based on the HFAF, HEBM and exact integration method. Numerical simulations are extended for even very strong nonlinearities and very good correlations are achieved between the numerical results.

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The ride comfort of high-speed trains passing over railway bridges is studied in this paper. A parametric study is carried out using a time domain model. The effects of some design parameters are investigated such as damping and stiffness of the suspension system and also ballast stiffness. The influence of the track irregularity and train speed on two comfort indicators, namely Sperling's comfort index and the maximum acceleration level are also studied. Two types of railway bridges, a simple girder and an elastically supported bridge are considered.Timoshenko beam theory is used for modelling the rail and bridge and two layers of parallel damped springs in conjunction with a layer of mass are used to model the rail-pads, sleepers and ballast. A randomly irregular vertical track profile is modelled, characterized by its power spectral density (PSD). The 'roughness' is generated for three classes of tracks. Nonlinear Hertz theory is used for modelling the wheel-rail contact. The influences of some nonlinear parameters in a carriage-track-bridge system, such as the load-stiffening characteristics of the rail-pad and the ballast and that of rubber elements in the primary and secondary suspension systems, on the comfort indicators are also studied. Based on Galerkin's method of solution, a new analytical approach is developed for the combination between the rigid and flexural mode shapes, which could be used not only for elastically supported bridges but also other beam-type structures.

Vibration suppression in beams subjected to random excitations with peaked Power Spectral Densities (PSDs) is studied in this paper. An optimal Tuned Mass Damper (TMD) system is used to suppress the undesirable vibration. The Timoshenko beam theory is applied to the beam model and the governing equations of motion are solved using the Galerkin method. Using the Sequential Quadratic Programming (SQP) method, the problem is solved to obtain the optimum values of the design variables (i.e. frequency ratio and the damping ratio) of the TMD system. Subsequently, a parametric study is carried out and the effects of the input parameters, such as the mass ratio, structural damping ratio, and the peak frequency of the random excitation on the design variables were investigated. The robustness of the optimal control system is also studied. Based on the PSD of the random excitation and using a Monte Carlo simulation algorithm, a set of numerical data for the excitation force is generated in the time domain and the effectiveness of the designed TMD system is investigated.

Piezoelectric (PZT) components are one of the most popular elements in vibration sensing and also energy harvesting. They are very well established, cost effective and available in different geometries however there are still several challenges in their application particularly in vibration energy harvesting. They are normally narrow-band elements and work in high-frequency range. Their efficiency and power extraction density are also generally low compared with different electromagnetic techniques. Auxetic structures are proposed here to enhance efficiency of the piezoelectric circular patches in vibration energy harvesting. These kinds of patches namely PZT buzzers are inexpensive (less than 10 USD) elements and easily available. Two novel circular auxetic substrates are proposed to improve power extraction capacity of the conventional piezoelectric buzzers. Negative Poison’s ratio of the proposed meta-structure helps in efficiency enhancement. The concept is introduced, analyzed and verified through the finite element modeling and experimental testing. The idea is proved to work by comparing the harvested electrical power in the auxetic design against the conventional plain system. A parametric study is then carried out and effects of important electrical and geometrical parameters as well as the material property on the power extraction efficiency are assessed to arrive at optimum parameters. It is shown that by employing the auxetic design, a remarkable improvement in the harvested power is achievable. It is shown that for the two proposed auxetic designs, at the resonance frequency, we could reach to 10.2 and 13.3 magnification factor with respect to the plain energy harvester. Another important feature is that the resonant frequency in these new designs is very much lower than the conventional resonators. Results of this study can open a new path to application of inexpensive PZT buzzers in large-scale vibration energy harvesting.