A vibration analysis method for an orthotropic opposite-side simply-supported rectangular thin plate

Abstract

The invention discloses a vibration analysis method for an orthotropic opposite-side simply-supported rectangular thin plate. The method is based on a free vibration equation of an orthotropic rectangular thin plate, and comprises the following steps: firstly, establishing a vibration mode differential equation to complete the construction of a Hamiltonian regular equation; Secondly, according toan octane geometry method, using a separation variable method to perform solving, deriving expressions of characteristic values corresponding to the characteristic equation, and analyzing the value taking conditions of the two groups of characteristic values; constructing a general solution form of a vibration mode function containing an undetermined constant, deducing an intrinsic value and an intrinsic vector expression of the intrinsic value in combination with an edge-to-edge simple support boundary condition, and proving the octyl orthogonality and completeness of an intrinsic vector system; Unfolding an octangular eigenvector to obtain an expression of a state vector, thereby obtaining a general solution of the vibration mode function; And finally, aiming at six common boundary conditions of the opposite edge simple support, corresponding frequency equations are derived respectively, so that accurate solution of the free vibration frequency is realized, and a foundation can be laid for carrying out dynamic analysis and related application of the free vibration frequency.

Description

technical field [0001] The invention belongs to the technical field of plate free vibration analysis and solution, and particularly relates to a vibration analysis method for an orthotropic simply supported rectangular thin plate on opposite sides. The rational derivation and accurate solution of the free vibration frequency of the rectangular thin plate provide a theoretical reference for further applications such as dynamic analysis and performance evaluation, fault diagnosis, and vibration and noise reduction of the rectangular thin plate. Background technique [0002] Vibration is a common physical phenomenon in engineering and widely exists in aerospace, civil engineering and other fields. Vibration problems have caused many aircraft and bridge accidents, and vibrations also exist during take-off, landing and the entire flight process of aircraft. Therefore, it is of great engineering significance to reasonably analyze and accurately solve vibration problems. [0003]...

AI Technical Summary

Problems solved by technology

Although the superposition method is helpful to solve this problem, because it is still based on the semi-inverse method, when dealing with some complex rectangular plate problems, the selection of superposition items is irregular and often makes people feel at a loss.

[0004] Over the years, many scholars have used numerical methods such as the Rayleigh-Leeds method, finite element method, and differential quadrature method to directly solve the problem. Although there is no need to assume in advance, there are calculation errors, and the high-precision requirements often require an astonishing amount of calculation.

There are also scholars who directly separate the variables of the mode shape function. Although they have obtained accurate results, they have not proved its rationality from a mathematical point of view. This method of separating variables will be limited by the spectrum of self-conjugate operators. and completeness are theoretically not guaranteed

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