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Listing 3-18. Audio Data Callback void audioDataCallback (void *inClientData, UInt32 inNumberBytes, UInt32 inNumberPackets, const void *inInputData, AudioStreamPacketDescription *inPacketDescriptions) { SimpleStreamer *self = (SimpleStreamer *)inClientData; // Run through the incoming packets. for (int i=0; i<inNumberPackets; i++) { @synchronized(self) {

where U = strain energy stored in structure yi = displacement of point of application of force Fi in the direction of Fi

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

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i = angular displacement at Ti i = slope or angular displacement at moment Mi If a displacement is desired at a point on the structure where no force or moment exists, then a fictitious force or moment is placed there. When the expression for the corresponding displacement is developed, the fictitious force or moment is equated to zero, and the remaining terms give the deflection at the point where the fictitious load had been placed. Castigliano s method can also be used to find the reactions in indeterminate structures. The procedure is simply to substitute the unknown reaction in Eq. (38.2) and use zero for the corresponding deflection. The resulting expression then yields the value of the unknown reaction. It is important to remember that the displacement-force relation must be linear. Otherwise, the theorem is not valid. Table 38.2 summarizes strain-energy relations.

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Figure 38.1 shows a cantilevered ring segment fixed at C. The force F causes bending, torsion, and direct shear. The moments and torques at the fixed end C and at any section B are shown in Table 38.3. The shear at C is RC = F. Stresses in the ring can be computed using the formulas of Chap. 36. To obtain the deflection at end A, we use Castigliano s theorem. Neglecting direct shear and noting from Fig. 38.1b that l = r d , we determine the strain energy from Table 38.2 to be U=

if (self.queueStarted && (!self.queueRunning)) { // Stop if the queue is not running. return; } } // Get size and offset of the current packet's data SInt64 packetOffset = inPacketDescriptions[i].mStartOffset; SInt64 packetSize = inPacketDescriptions[i].mDataByteSize; // See if there's enough byte space left in the current buffer. size_t bufSpaceRemaining = kAQBufSize - self.playQueueDataRecs[self.currentBufferIndex].bytesFilled; if (bufSpaceRemaining < packetSize) { // Not enough space in the current buffer, so enqueue it and // go to the next buffer. enqueueCurrentBuffer(self); } // Copy data to the audio queue buffer AudioQueueBufferRef fillBuf = elf.playQueueDataRecs [self.currentBufferIndex].buffer; memcpy((char*)fillBuf->mAudioData + self.playQueueDataRecs[self.currentBufferIndex].bytesFilled, (const char *)inInputData + packetOffset, packetSize); // Fill out packet description self.playQueueDataRecs[self.currentBufferIndex].packetDescriptors[self.playQueueDataRecs [self.currentBufferIndex].packetCount] = inPacketDescriptions[i]; self.playQueueDataRecs[self.currentBufferIndex].packetDescriptors[self.playQueueDataRecs [self.currentBufferIndex].packetCount].mStartOffset = self.playQueueDataRecs[self.currentBufferIndex].bytesFilled; // Keep track of bytes and packets filled in the current buffer self.playQueueDataRecs[self.currentBufferIndex].bytesFilled += packetSize; self.playQueueDataRecs[self.currentBufferIndex].packetCount += 1; // See if we've run out of packet space size_t packetDescriptorsRemaining = kAQMaxPacketDescs - self.playQueueDataRecs[self.currentBufferIndex].packetCount; if (packetDescriptorsRemaining == 0) { // No more packet descriptors in the current buffer, // so add it to the queue. enqueueCurrentBuffer(self); } } }

(38.3)

(38.4)

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The terms for this relation are shown in Table 38.3. It is convenient to arrange the solution in the form y= Fr 3 A B + 2 EI GK (38.5)

where the coefficients A and B are related only to the span angle. These are listed in Table 38.3. Figure 38.2a shows another cantilevered ring segment, loaded now by a distributed load. The resultant load is W = wr ; a shear reaction R = W acts upward at the fixed end C, in addition to the moment and torque reactions shown in Table 38.3. A force W = wr acts at the centroid of segment AB in Fig. 38.2b. The centroidal radius is r= 2r sin ( /2) (38.6)

The audio data callback s purpose is to receive parsed audio packets and accumulate them in the current buffer. When the buffer fills, it adds it to the audio queue via a utility function called enqueueCurrentBuffer(). Incoming data in this callback can consist of an arbitrary number of audio packets, with the actual number depending on how much data has been received from the network. The body of the function loops through the packets one at a time. It starts by checking to see whether the current buffer has enough space to hold the packet s data. If not, it

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