In this paper, the static and dynamic analyses of mixed local/peridynamic (MLP) circular membranes are investigated, by both analytical and numerical approaches. The 2D kernel of both radial and angular peridynamic influence function is built from an equivalent partial differential equation, as a series of Bessel functions. As a special case, the kernel of the pure radial peridynamic influence function for symmetrical condition is obtained, as a piecewise modified Bessel functions of the first and the second kinds. The integro-differential equation of the mixed local/ peridynamic membrane problem is derived through variational arguments starting, from Hamilton’s principle. It is shown, for the considered kernel, that the integro-differential formulation can be straightforwardly converted in a higher-order differential format with bi-Laplacian operator. The transversal displacement of the mixed local/peridynamic membrane loaded by uniform distributed load is analytically derived using Bessel and confluent hypergeometric functions. For both unsymmetrical and symmetrical modes, the eigenfrequencies of the mixed local/peridynamic circular membrane can be obtained from a transcendental equation with Bessel’s functions, which generalizes Poisson’s and Bourget’s solutions, valid for local circular membranes. These exact peridynamic solutions (for the static or the vibration problems) are compared to numerical solutions based on a FDM discretization of the integro-differential problem, or the FDM discretization of the equivalent bi-Laplacian equation. The paper ends with the application of Rayleigh quotient to approximate the natural frequencies of the mixed local/peridynamic membrane, both in its continuous or its discretized form.

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