The nonlinear forced vibrations of functionally graded material (FGM) sandwich cylindrical shells with porosities on an elastic substrate are studied. A step function and a porosity volume fraction ...are introduced to describe the porosities in FGM layers of sandwich shells. Using the Donnell’s nonlinear shallow shell theory and Hamilton’s principle, an energy approach is employed to gain the nonlinear equations of motion. Afterwards, the multi-degree-of-freedom nonlinear ordinary differential equations are carried out by using Galerkin scheme, and subsequently the pseudo-arclength continuation method is utilized to perform the bifurcation analysis. Finally, the effects of the core-to-thickness ratio, porosity volume fraction, power-law exponent, and external excitation on nonlinear forced vibration characteristics of FGM sandwich shells with porosities are investigated in detail.
The Parameter Continuation Theorem is the theoretical foundation for polynomial homotopy continuation, which is one of the main tools in computational algebraic geometry. In this note, we give a ...short proof using Gröbner bases. Our approach gives a method for computing discriminants.
We show global uniqueness in the fractional Calderón problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work 10 considered the case ...of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes.
Control-based continuation is a recently developed approach for testing nonlinear dynamic systems in a controlled manner and exploring their dynamic features as system parameters are varied. In this ...paper, control-based continuation is adapted to follow the locus where system response and excitation are in quadrature, extracting the backbone curve of the underlying conservative system. The method is applied to a single-degree-of-freedom oscillator under base excitation, and the results are compared with the standard resonant-decay method.
We present a coherent and effective theoretical framework to systematically construct numerically exact nonlinear solitary waves from their respective linear limits. First, all possible linear ...degenerate sets are classified for a harmonic potential using lattice planes. For a generic linear degenerate set, distinct wave patterns are identified in the near-linear regime using a random searching algorithm by suitably mixing the linear degenerate states, followed by a numerical continuation in the chemical potential extending the waves into the Thomas–Fermi regime. The method is applied to the two-dimensional, one-component Bose–Einstein condensates, yielding a spectacular set of waveforms. Our method opens a remarkably large program, and many more solitary waves are expected. Finally, the method can be readily generalized to three dimensions, and also multi-component condensates, providing a highly powerful technique for investigating solitary waves in future works.
•We systematically developed the linear limit continuation method.•The method is extensively applied to two-dimensional BECs, and numerous solitary waves are found.•The theoretical and computational framework can be readily extended to constructing three-dimensional and vector solitary waves.
This paper describes a generic Taylor series-based continuation method, the so-called asymptotic numerical method, to compute the bifurcation diagrams of nonlinear systems. The key point of this ...approach is the quadratic recast of the equations as it allows to treat in the same way a wide range of dynamical systems and their solutions. Implicit differential-algebraic equations, forced or autonomous, possibly with time-delay or fractional-order derivatives are handled in the same framework. The static, periodic and quasi-periodic solutions can be continued and also transient solutions.
This article reports on a study examining the factors influencing post-hackathon project continuation in a company with presence in several African countries. The research was conducted as a case ...study, and focused on hackathon events held by the company between 2018 and 2020. The study identified three core factors that influenced the potential for project continuation after the corporate hackathons: (1) availability of financing; (2) team skills fit and diversity; and (3) degree of project integration into company operations. Where one or more of these elements was insufficiently present,then project continuation became less likely-and the likelihood of project discontinuation increased. The findings are of potential utility to corporate hackathon organisers seeking to increase the levels of project continuation-and, by, extension, return on investment-from their companies' hackathon projects.
•A novel solution approach for nonlinear multi-dofs dynamic response is proposed, in which both stable and unstable solutions are considered.•A coupled modeling for composite structures with ...micro-voids in complex multi-physics fields is presented.•Nonlinear multiple internal resonances and bifurcations of FG piezoelectric shells are studied.•The influence of key parameters on nonlinear amplitude-frequency response curves is discussed.
This paper develops a new solution approach to solve nonlinear forced vibrations of functionally graded (FG) piezoelectric shells in multi-physics fields. The FG piezoelectric shells are subjected to electric-thermo-mechanical loads, and the effect of micro-voids is considered here. Motion equations are obtained by using Hamilton's principle, and combining with the Donnell nonlinear shallow shell theory. Afterwards, a new method combining multi-mode Galerkin scheme and Pseudo-arclength continuation method is used to solve the nonlinear multiple internal resonances and bifurcations of the multi-degree-of-freedom systems. The novel feature of this approach is that it can efficiently obtain the unstable solution and tackle the difficult problems in mathematics encountered during formulation. The results show that the external applied voltage, temperature change, external excitation, power-law exponent, and porosity volume fraction play important roles on nonlinear vibration response and bifurcation analysis of FG piezoelectric shells with micro-voids.
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