DYNAMIC RESPONSE OF PLATES ON ELASTIC FOUNDATIONS DUE TO THE MOVING LOADS

Abstract

Abstract: This paper discusses the dynamic response of thin plates on the elastic foundations due to the moving loads by means of the varialional calculus. In the text we take the mass of moving loads into account, treat a series of questions such as the forced oscillations, the influence surfaces of the flexions and tke influence surfaces of the inner forces, resonance conditions and critical speed and so forth.

Key words: piezoelectric material, steady-state response, spherical coordinate system, actuator layer, sensor layer

Cheng Xiang-sheng. DYNAMIC RESPONSE OF PLATES ON ELASTIC FOUNDATIONS DUE TO THE MOVING LOADS. Applied Mathematics and Mechanics (English Edition), 1987, 8(4): 355-365.

TrendMD

References

[1] Willis,R.,Appendix to the Report of the Commissioners Appointed to Inquire into Application of Iron to Railway Structures,H.M. Stationery Office,London(1849).
[2] Jeffcott,H.H.,Phil.Mag.,Ser.,7,8(1929),66.
[3] Steuding,H.,Ing.-Arch.,5(1934),275.
[4] Schallenkamp,A.,Ing.-Arch.,8(1937),182.
[5] Odman,T.A.,Rull.Swedish Cement and Concrete Research Inst.,14(1948).
[6] Yeh Kai-yuan, Dynamic theory when trains pass through the bridge which takes the effect of mass and inertia forces of moving loads into account(Summary),Science Bulletin,.Feb.(1963),50-52. (in Chinese).
[7] Yeh Kai-yuan and Ma Guo-lin,Scientia Sinica,A,8(1984),831-846.
[8] Yeh Kai-yuan and Ma Guo-lin,Vibration theory of continuous beam under the action of moving load,Appl.math.and Mech.,6,10(1985),934-948.
[9] Dimentberg,M.F.,Engine.Jour.,1,2(1961),97-105. (in Russian).
[10] Kiserev,V.A.,theory of Plates and Shells,Ed.by Academy of Science of the WSSR,Kiev (1962),274-279. (in Russian).
[11] Cheng Chin-tung and Chong Shao-jan,Vibrations of shallow shell due to the moving loads,Tranactions of Architecture,2(1961),27-30. (in Chinese).
[12] Cheng Xiang-sheng,Forced vibrations of orthotropic shallow shell on elastic foundation due to the moving loads,Articles of Society of Mechanics in Jiangsu Province(1964).(in Chinese).
[13] Cheng Xiang-sheng,Forced vibrations of elastic shallow shell due to the moving mase,Appl.Math.and Mech.,6,3(1985),233-240.
[14] Vlasov,V.Z.and N.N.Leontchiev,Beams,Plates and Shells on the Elastic Foundation(1960).(in Russian).
[15] Vlasov,V.Z.,The General Thery of the Shelle,Gostechizdat(1949).(in Russian).
[16] Oniashivili,O.D.,Some Dynamic Problems of the Theory of the Shells,Ed.by Academy of Science of the USSR(1957).(in Russian).
[17] Barlow,P.,Treatise on the Strength of timber,cast iron and malleable iron,London(1851).
[18] timoshenko,S.,Vibration Problems in Engineering,second edition(1937).
[19] Bolotkin,V.V.,Works of MIIT 74 (1950);76(1952).(in Russian).
[20] Bolotkin,V.V.,Dynamic Stability of Elastic Systems(1956).(in Russian).
[21] Volmir,A.S.,Nonlinear Dynamics of Plates and Shells,Ed.by Science(1972).(in Russian).
[22] Lechnitsky,S.G.,Anisotropic Plates,Gostechizdat.,M.(1957).(in Russian).