In this paper, a novel family of low-cost, magnet-free bistable piezoelectric energy harvesters with a simple structure is designed, fabricated, and tested to evaluate their nonlinear dynamics and performance for harvesting energy from broadband vibrations. A laser-machined bistable structure, consisting of a buckled beam and two supporting beams, is employed as the host structure for constructing this energy harvester with piezoelectric transducers. The integration of buckled beams and constraints provided by supporting beams allows for the configuration of this bi-stable buckled piezoelectric beam under cantilevered boundary conditions without requiring external operation. The proposed harvester's static mechanical properties and dynamic responses are predicted using a finite element model, while its basic dynamics are understood through a simple analytical model. The frequency-sweep results demonstrate that the proposed harvester exhibits a broadband characteristic compared to the linear piezoelectric beam with a similar configuration, and various vibration modes and their corresponding performance of energy harvesting are analyzed and characterized. The potential of this proposed harvester is explored by adjusting the geometry parameters, such as the width of the supporting beam and thickness, to optimize its dynamics and energy harvesting performance. Finally, an multistable energy-harvesting array consisting of four proposed harvesters with adjacent broadbands is fabricated to enhance overall performance, achieving a broadband width of 13.7 Hz at an acceleration of 0.75 g. The proposed method introduces a novel design philosophy for nonlinear vibrational energy harvesters.
In this paper, a simple method for topology optimization of linearly elastic continuum structures is presented. For prescribed loading and boundary conditions, and subject to a specified amount of structural materia l, the optimum structural topology is determined from the condition of maximum integral stiffness, which is equivalent to minimum elastic compliance. The SIMP (Simple Isotropic Material with Penalization) is improved in order to save the computation time. Instead of using isotropic material with SIMP method, the material is assumed to be pseudo orthotropic continuum by setting the principal axis of the material to principal stress directions and introducing a new penalty function to the young’s modulus at the minor principal stress direction. Numerical examples illustrate that the present method is more efficient than the SIMP method.
Variable-angle tow describes fibers in a composite lamina that have been steered curvilinearly. In doing so, substantially enlarged freedom for stiffness tailoring of composite laminates is enabled. Variable-angle tow composite structures have been shown to have improved buckling and postbuckling load-carrying capability when compared to straight fiber composites. However, their structural analysis and optimal design is more computationally expensive due to the exponential increase in number of variables associated with spatially varying planar fiber orientations in addition to stacking sequence considerations. In this work, an efficient two-level optimization framework using lamination parameters as design variables has been enhanced and generalized to the design of variable-angle tow plates. New explicit stiffness matrices are found in terms of component material invariants and lamination parameters. The convex hull property of B-splines is exploited to ensure pointwise feasibility of lamination parameters. In addition, a set of new explicit closed-form expressions defines the feasible region of two in-plane and two out-of-plane lamination parameters, which are used for the design of orthotropic laminates. Finally, numerical examples of plates under compression loading with different boundary conditions and aspect ratios are investigated. Reliable optimal solutions demonstrate the robustness and computational efficiency of the proposed optimization methodology.
A geometrical nonlinear analysis of a symmetric, variable angle tow (VAT), composite plate structure under inplane shear load is investigated in this work. The nonlinear vonKarman governing differential equations (GDEs) based on stress function and displacement function are derived for postbuckling analysis of symmetric VAT plate structures. A numerical methodology based on the differential quadrature method (DQM) is developed for solving the GDEs of VAT plates. The methodology is applied to solve the postbuckling problem of VAT plates with linear fibre angle orientations under simply supported plate boundary conditions. To show the accuracy and robustness of DQM, results are compared with commercial finite element analysis. The postbuckling behaviour of VAT plates under positive and negative shear is studied for different VAT fibre orientations, aspect ratios and their performance is compared with straight fibre composites. In addition, the influence of the direction of shear on the postbuckling behavior of VAT plates under axial compression is studied.
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