중첩법을 이용한 네변고정 직사각평판의 횡진동해석

Abstract

평판의 횡진동해석에 가장 널리 사용되는 Rayleigh-Ritz방법을 사용한 근사해석에서는 어느 한 맞변 이상이 단순지지인 경우를 제외한 기타 경계조건의 경우, 지배미분방정식을 정확히 만족하는 함수를 찾아 고유진동수 및 진동모드를 구하는 일이 일반적으로 용이하지 않다. 반면, 중첩법을 사용한 진동해석에서는 지배미분방정식을 정확히 만족하는 급수해를 선택하여 정밀고유진동수를 얻을 수 있다. 선박의 국부진동해석에는 다양한 경계조건과 세장비를 가진 직사각평판의 고유치를 ?맨求? 것이 대단히 중요하며 이에 대한 정확한 설계자료가 초기설계시 필요하다. 따라서 네변고정 직사각평판의 진동해석에 중첩법을 적용하여 겅밀해를 계산할 필요성이 있다.

본 논문에서는 네변고정 직사각평판의 진동해석에 중첩법을 사용하여 국내, 국외에서 일반적으로 제공된 다섯 가지 세장비 외에, 1.0에서 3.25까지를 0.25 간격으로 10차까지의 무차원화된 고유치를 계산하였고, 이 결과를 테이블로 정리하여 직접 계산에 활용할 수 있게 하였다. 해석 방법의 타당성 여부를 확인하기 위하여 이론치를 문헌자료 및 상용프로그램인 ANSYS에 의한 계산값과 비교 검토해 본 결과, 잘 일치하고 있음을 확인하였고, 또한 충격가진을 이용한 실험결과치와 이론치를 비교, 검토해 본 결과 비교적 잘 일치함을 확인하였다.

It is well known that some difficulties have been encountered when attempting to analyze the free vibration of plates that do not have at least one pair of opposite edges simply supported. It is not an easy task to select appropriate series of functions to represent plate lateral displacement when using the Rayleigh-Ritz method. In fact, in the case of plates with free edges, it has been demonstrated that fully appropriate functions do not exist.

In this paper, the superposition method which satisfy the governing differential equation exactly throughout the entire domain of the plate is utilized to analyze the natural frequencies and mode shapes of fully clamped rectangular plates. The method is found to work extremely well and excellent agreement is obtained when comparison is made between computed results and earlier reliable published data. And it needs to be noted that agreement between theory and experiment is good. Accurate eigenvalues are tabulated for a wide range of plate geometries(values of aspect ratio vary from 1.0 to 3.25 in intervals of 0.25) and vibration mode families.

It is well known that some difficulties have been encountered when attempting to analyze the free vibration of plates that do not have at least one pair of opposite edges simply supported. It is not an easy task to select appropriate series of functions to represent plate lateral displacement when using the Rayleigh-Ritz method. In fact, in the case of plates with free edges, it has been demonstrated that fully appropriate functions do not exist.

In this paper, the superposition method which satisfy the governing differential equation exactly throughout the entire domain of the plate is utilized to analyze the natural frequencies and mode shapes of fully clamped rectangular plates. The method is found to work extremely well and excellent agreement is obtained when comparison is made between computed results and earlier reliable published data. And it needs to be noted that agreement between theory and experiment is good. Accurate eigenvalues are tabulated for a wide range of plate geometries(values of aspect ratio vary from 1.0 to 3.25 in intervals of 0.25) and vibration mode families.