Abstract
This paper reviewed the research on the nonlinear free vibration of pre‐stressed orthotropic membrane, which is commonly applied in building membrane structures. We applied the L‐P perturbation method to solve the governing equations of large amplitude nonlinear free vibration of rectangular orthotropic membranes and obtained a simple approximate analytical solution of the frequency and displacement function of large amplitude nonlinear free vibration of rectangular membrane with four edges simply supported. By giving computational examples, we compared and analyzed the frequency results. In addition, vibration mode of the membrane and displacement and time curve of each feature point on the membrane surface were analyzed in the computational example. Results obtained from this paper provide a simple and convenient method to calculate the frequency and lateral displacement of nonlinear free vibration of rectangular orthotropic membranes in large amplitude. Meanwhile, the results provide some theoretical basis for solving the response of membrane structures under dynamic loads and provide some computational basis for the vibration control and dynamic design of building membrane structures.
Highlights
The orthotropic membrane materials are mainly applied in building membrane structures
It is quite necessary to study the vibration characteristic of membrane structure to provide some computational basis for the design of membrane structure to ensure the safety of membrane structure
The amplitude of the membrane is much larger than its thickness in vibration process, so the geometric nonlinearity caused by large amplitude must be considered
Summary
The orthotropic membrane materials are mainly applied in building membrane structures. Zheng Zhou-lian et al 8 studied the geometric nonlinear vibration of orthotropic membranes They established the governing equations by applying Von Karman’s large deflection theory and D’Alembert’s principle of membrane, and applied Galerkin’s method and power series expansion method to solve the governing equations. We apply the L-P perturbation method to solve the nonlinear free vibration problem of orthotropic membranes in large amplitude. Through using the L-P perturbation method to solve the governing equations of large amplitude nonlinear free vibration of rectangular orthotropic membranes in this paper, we obtained an approximate analytical frequency solution and displacement function of the. Results obtained from this paper provide a simple and convenient new method to calculate the frequency and lateral displacement of large amplitude nonlinear free vibration of rectangular orthotropic membranes. The results provide some theoretical basis for solving the response of membrane structures under dynamic loads, and provide some computational basis for the vibration control and dynamic design of building membrane structures
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