# Modal Synthesis Compilation of Mechanical Sub-structures and Acoustical Sub-systems

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Page 57 ï~~MODAL SYNT COMPILATION OF MECHANICAl ACOUSTICAL SUB CALVET Olivier, LAURENS Ronan, ADRIE? IRCAM Place St Merri Paris 75004, uucp net actress. je Tel (1) 42 77 12 33 ext 4814 Telex 212 034 F IRCAM ABSTRACT: We present in this paper modal the reduction of insignificant connections bet musical instrument model. This optimizati compatible with general modal synthesis algori modal specifications of complex structures eith the sub-structures, or directly from geometrical mechanical and acoustic elastic structures. Introduction

Page 58 ï~~(1)2.M r + K r ).1 i where 71 stands for the vector of modal coordinates. If having respectively n and m degrees of freedom, and c applied to each sub-structure will produce of n+m equati The complete structure has in fact (n+m-j) degrees of free order to find the (n+m-j) normal modes. These equatio each sub-structure: two kinds of junctions are consid sticking junctions, used for instance to model the links b elastic junctions, more appropriate for connecting sub-st or air columns linked by their extremities. Mass / mass the following scheme and can be associated with the follc sub-structure nÂ~1 -N - - se -. (qi)1 ' '4 (q j) Ior (qJ)1 -.1 a 46I,A.1 v Z -. Z %X -1 t N

Page 59 ï~~numbers. This classical equation has been the starting computation method developed Causse, Kergor characterizing the tube at its input. For the purposes ol the tube, we may write the propagation equation in the ft 1 a2 1--(S(x) (E) ax as(: ax F' LA' axL where F2 is the product ZvYt. The above form of the dynamic equation that can be associated with a mechanic would correspond to the displacement x and the flow q tc In fact the expression (E) describes the behavior of a admit any analytical solution. The problem is thus solv the tube is made up with a large number N of finite c stands for the total length of the tube. The discretized foi the mechanical corresponding equation. The generic ten Si.Ax f aaA. _f "A. " - -_. "a a