CAJ | 학술논문

夹层板壳结构由于其优异的力学特性在工程中被广泛使用，但有关其非线性振动特性的研究还不够完善，其精确解答一般很难得到。本文对具有软夹心和极薄表层夹层矩形板的非线性自由振动方程进行简化，并将振型设成时间和空间函数的分离形式，时间函数取谐函数，空间函数未知。将假定的振型函数带入微分方程，得到对边简支梁式夹层板无量纲化的空间模态控制方程。采用修正迭代法和伽辽金法对其进行求解，得到了梁式夹层板振型的一个解析解，以及梁式夹层板非线性振动的振幅和振频的解析关系式，并进一步分析了夹层板剪切参数对非线性振动特性的影响。
협층판각결구유우기우이적역학특성재공정중피엄범사용，단유관기비선성진동특성적연구환불구완선，기정학해답일반흔난득도。본문대구유연협심화겁박표층협층구형판적비선성자유진동방정진행간화，병장진형설성시간화공간함수적분리형식，시간함수취해함수，공간함수미지。장가정적진형함수대입미분방정，득도대변간지량식협층판무량강화적공간모태공제방정。채용수정질대법화가료금법대기진행구해，득도료량식협층판진형적일개해석해，이급량식협층판비선성진동적진폭화진빈적해석관계식，병진일보분석료협층판전절삼수대비선성진동특성적영향。
The sandwich plates and shells are widely used in engineering because of their excellent mechanical characteristic. How-ever, researches about their nonlinear vibration characteristics, of which the accurate solution is difficult to achieve, are still not perfect.In this paper,the fundamental equations of the nonlinear free vibration for rectangular sandwich plates with the soft interlayer and the extremely thin surface are simplified firstly. And the vibration mode are assumed as the separate form of time and space function, the time function employs the simple harmonic, the space function is unknown. The assumed vibration mode function is substituted into the differential equation to get the dimensionless control equation of the space modality for the beam sandwich plate with two opposite edges simply supported. The equations are solved with the aid of the modified iteration method and the Gal-erkin method to achieve an analytical solution for the vibration mode of the beam sandwich plate and an analytical relation of the amplitude-frequency response for the nonlinear vibration of the beam sandwich plate. At last, how the shear parameter impacts the characteristic of the nonlinear vibration are discussed further.