【摘要】：工程結(jié)構(gòu)物中常常含有分布形式復雜的非均勻結(jié)構(gòu)應(yīng)力,該應(yīng)力會影響結(jié)構(gòu)的振動特性。有限元法雖然可以求解,但不利于從本質(zhì)上分析結(jié)構(gòu)應(yīng)力與振動的內(nèi)在物理聯(lián)系、不方便研究結(jié)構(gòu)應(yīng)力對振動的影響規(guī)律,而且還有施加特定非均布應(yīng)力操作復雜、計算量較大等限制。在解析方法研究方面,以往的方法主要用來求解含整體均勻分布應(yīng)力的結(jié)構(gòu),不適用于實際工程結(jié)構(gòu)中的非均布應(yīng)力的情況。提出了一種求解含非均布應(yīng)力結(jié)構(gòu)振動的解析方法,以平板結(jié)構(gòu)為對象,用特殊級數(shù)形式表示非均布的結(jié)構(gòu)應(yīng)力,將應(yīng)力影響加到原平板振動方程,并實現(xiàn)結(jié)構(gòu)模態(tài)的部分解耦,然后對解耦后的方程進行求解得到解析解。推導出的解析方法適用于任意應(yīng)力狀態(tài)下的平板振動求解,并且相對于有限元法有計算量小、物理解釋明晰等優(yōu)點,方便定性地研究結(jié)構(gòu)應(yīng)力與振動之間的物理聯(lián)系,進行考慮結(jié)構(gòu)應(yīng)力的振動精確預報與控制。
[Abstract]:Engineering structures often contain inhomogeneous structural stresses with complex distribution forms, which will affect the vibration characteristics of structures. Although the finite element method can be solved, it is not conducive to the analysis of the internal physical relationship between structural stress and vibration in essence, and it is not convenient to study the influence of structural stress on vibration, and there are some limitations, such as the operation of specific heterogeneous stress is complex and the amount of calculation is large. In the aspect of analytical method, the previous methods are mainly used to solve the structure with uniform stress distribution as a whole, and are not suitable for the case of uneven stress in practical engineering structures. In this paper, an analytical method for solving the vibration of structures with non-uniform stress is proposed. Taking the plate structure as the object, the non-uniform structural stress is expressed in the form of special series, the stress influence is added to the original plate vibration equation, and the partial decoupling of the structural mode is realized, and then the analytical solution is obtained by solving the decoupling equation. The derived analytical method is suitable for solving plate vibration under arbitrary stress state. compared with the finite element method, it has the advantages of less computation and clear physical interpretation. It is convenient to qualitatively study the physical relationship between structural stress and vibration, and to accurately predict and control the vibration considering structural stress.
【作者單位】： 上海交通大學船建學院海洋工程重點實驗室;中船重工第七0二研究所上海分部;
【基金】：海洋工程國家重點實驗室基金資助(1507)
【分類號】：TB123

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