The present paper reports an extensive study on dynamic instability characteristics of curved panels under linearly varying in-plane periodic loading employing finite element formulation with a quadratic isoparametric eight nodded element. At first, the influences of three types of linearly varying in-plane periodic edge loads (triangular, trapezoidal and uniform loads), three types of curved panels (cylindrical, spherical and hyperbolic) and six boundary conditions on excitation frequency and instability region are investigated. Further, the effects of varied parameters, such as shallowness parameter, span to thickness ratio, aspect ratio, and Poisson’s ratio, on the dynamic instability characteristics of curved panels with clamped–clamped–clamped–clamped (CCCC) and simply supported-free-simply supported-free (SFSF) boundary conditions under triangular load are studied. It is found that the above parameters influence significantly on the excitation frequency, at which the dynamic instability initiates, and the width of dynamic instability region (DIR). In addition, a comparative study is also made to find the influences of the various in-plane periodic loads, such as uniform, triangular, parabolic, patch and concentrated load, on the dynamic instability behavior of cylindrical, spherical and hyperbolic panels. Finally, typical design charts showing DIRs in non-dimensional forms are also developed to obtain the excitation frequency and instability region of various frequently used isotropic clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from these charts without the use of any commercially available finite element software or any developed complex model.

中文翻译：

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平面内线性变化周期载荷曲线板动态不稳定性分析及设计图

本文报道了使用具有二次等参八点单元的有限元公式对线性变化的平面内周期性载荷下弯曲面板的动态不稳定性特性进行的广泛研究。首先，研究了三种线性变化的平面内周期性边缘载荷（三角形、梯形和均匀载荷）、三种曲面面板（圆柱、球面和双曲线）和六种边界条件对激励频率和不稳定区域的影响。 . 此外，不同参数的影响，例如浅度参数、跨度与厚度比、纵横比和泊松比，研究了三角载荷下夹-夹-夹-夹(CCCC)和简支-自由-简支-自由(SFSF)边界条件下曲面面板的动态不稳定性特性。发现上述参数对动态不稳定性开始的激励频率和动态不稳定性区域（DIR）的宽度有显着影响。此外，还对比研究了均匀、三角形、抛物线、贴片和集中载荷等各种面内周期性载荷对圆柱、球面和双曲线板动态失稳行为的影响。最后，